1)
2)
3)
4)
Course: Finance 300, 320  Principle of Corporate Finance
Answer all questions. Total points: 150.
No late turnin or extension. No allowance and credit will be given to any
late assignment.
Provide clear statements and analyses. State your assumptions whenever
you need them.
Good Luck!
1. (10 points) Explain the ideas of Market Risk and Diversifiable Risk. What
is the main difference of these two concepts? Will adding more assets in
the portfolio help to reduce the diversifiable risk? Why or Why not?
Explain your reasons.
2. (40 points) You are given with the following information of two projects
planned by your company. Two projects are of the same initial costs
with $3 millions.
Project
A
B
Year 1
650
560
Table 1: (in thousands)
Year 2
Year 3
Year 4
720
 50
1000
1875
1600
Year 5
2800
Answer the following questions.
a) Suppose the cost of capital is 12%. What are the Net Present Values for
these two projects?
b) Suppose the financial manager discovered that if we postponed the
project B to two years later, the cost of capital could be 8% due to possible
low future interest rates. However, the deferment may cost the firm
additional $0.5 million to restart the facilities and the initial cost must be
spent now, instead of two years later. Will you recommend waiting for
additional 2 years to start?
c) Let the corporate income tax rate be 30%, the cost of debts be 6%, the
cost of equity be 25% and there is no preferred stock issued by the firm.
What is the debttoequity ratio for your company?
d) Find the IRR (Internal Rate of Return) for project A and project B.
e) Suppose there is a 40% chance that the market may be bad and the cash
flows for both projects will change to
Project
A
B
Year 1
650
560
Year 2
720
1875
Year 3
 50
1500
Year 4
100
Year 5
500
That is to say, the original cash flows in Table 1 only have 60% chance to
happen. What is your decision for each project? What is the present value
of the “marginal value of choice” for each project?
f) Suppose now these projects are about to invest in foreign countries. The
projects are to finance locally. Let the local capital market offer the interest
rate as 5% and the local tax rate is 15%, the “beta’s” for project A and B
are 1.2 and 1.5 respectively, where the riskfree rate is 5% and market
index rate of return is on average 16%, the debttoequity ratio is 1 to 4,
what are the riskadjusted Net Present Values for these two projects?
3. (20 points) You have the following information for the company
Exxon. The “beta” coefficient for Exxon is .85 based on the past
information. The 3year average of 30day Tbill rate is 2%, the
average market return of (say, S&P 500 index) in the same period is
16%. Answer the following questions:
a) What is the required return for Exxon? Why do we call it “required”
return?
b) Suppose that Exxon’s current dividend is $.60 per share with possible
expected growth rate as 4% per year from now on, what is your
assessment for the value of Exxon’s stock?
c) Suppose the current market price for the Exxon’s stock is $9 per share.
Let the capital market be efficient as ideally assumed. That is, the
current stock price is equal to the stock fair value. What is the required
return for this stock now if the information in (b) still applies? What is
the “beta” associated with this stock now?
d) Exxon has the following capital structure: the firm issued 6 million
shares of common stock with the stock price in c), the firm also issued
1.5 million shares of preferred stock with $4.5 preferred dividend per
share, currently, Exxon has $25 millions in debts with interest rate as
6.5%. Suppose the current preferred stock price is $6 per share and the
current common stock price is as in question (c), and the corporate tax
rate is 25%. What is the (aftertax) weighted average cost of capital for
Exxon?
e) Why is Exxon able to undertake so much in debts? Is this related with
the industry or business risk?
f) Will this firm undertake high operating leverage? Why or why not?
4. (20 points) Let the information on your portfolio be given as follows.
You have three assets in the basket. The "beta's" among them are
given as follows; 1 = 0.45, 2 = 0.89 3 = 1.2, Answer the following
questions;
a) Why do we need these "beta's" to construct the portfolio?
b) If the riskfree rate is given as 3%, what are the required returns for
asset 1 and asset 2 if the market rate of return is expected to have 10%?
c) Is it possible to construct a riskfree (or zerobeta) portfolio by
combining asset 1 and asset 2? If yes, what is the required return for
this portfolio? If the transaction cost for this portfolio requires 4.5% of
commission, will you do it?
d) If you'd like to form a portfolio with these three assets that mimic the
overall market, what are the weights of this portfolio? (Notice that there
may be more than one answer for this problem).
5. (20 points) You are given with the following information of two
proposal of financing programs for your home loan. Suppose the new
house costs you $650,000 (sales taxes and others are included). One
program is asking you to deposit a 20% down payment on the
$650,000 and it provides you with 5.5% interest rate for 15year
monthly payments of the remaining balance, the other program is a
100% financing program which gives you a 2.5% for the first 5 year
with the balloon payment as 600,000 plus the PMI (property mortgage
insurance) as $200 per month and the rate increases to 6.75%
afterward for a 30year mortgage if no balloon payment for the
remaining balance or refinancing is pursued. Let there be no
prepayment penalty. That is, you may pay off the loan should you have
some extra cash later on. The brokerage fees and commissions are
already considered in all the numbers given. Answer the following
questions.
a) What is the monthly payment for each program in the first 5 years?
Which one is more favorable to you if your monthly income is $6,000
before tax? (Notice that most lenders will require the borrower to have
ratio between mortgage payment and monthly income no greater than
33%).
b) Suppose 4 years later, the market price of your house is $800,000. The
tax rate on gains/losses on house sales is 8%. Will you consider selling this
house and buy a bigger one if your income has gained to $7000 per month?
What is the annualized rate of return in your investment on housing? (Hint:
you need to apply amortization of loan here first).
c) Which way of financing the house originally gives you more rate of
return if you in fact, sell the house?
6. (20 points) Company JJ gives you the following information for its
operation. The expected profit (before tax) is $60 millions next year.
Suppose there is a 35% corporate income tax imposed on the
company. Company JJ has no debt originally. There are 8 million
shares of common stocks outstanding. Let the current market price
for the stock be $25 per share. Suppose that there is no expansion plan
for the company to either spend on working capital vs. longterm
investment or to apply the accumulated retained earning. Answer the
following questions:
a) Suppose that Company JJ also has issued some 5year coupon bonds
recently. The bond carries 6% coupon with $1,000 par value. Let the
current bond price be $700 per bond, what is the yield to maturity for this
bond? What are the assumptions you make here? Is there any limitation for
this model?
b) Let Company JJ’s total debts on coupon bond be $70 millions. How
much will be the value of stockholders’ equities under Modigliani and
Miller’s proposition?
c) What is the cost of equity for Company JJ, if there’s no preferred stock
issued for this company?
d) What is the weighted average cost of capital after Company JJ has
debts?
e) Will the application of debts increase the “beta” of Company JJ’s
common stock? Why or why not? (Note: You don’t need to calculate it.
Just explain the reasons).
7. (20 points) You are given with the following information of a firm "JoJo Bear", assuming that the firm did not issue preferred stocks while the
firm may have some foreign subsidiaries overseas. The firm is making
perfumes and cosmetics for middleincome class of consumers. This
industry tends to have high gross profit margin such as 25% and the setup costs are also high due to the production and technology. The R&D
(Research and Development) costs are entirely reported as operating
expenses according to the GAAP.
Balance Sheet (in millions)
2017
2018
2019
1230
50
1420
260
210
200
1350
1578
1070
0
2200
1450
2873
0
5833
2205
430
5973
90
1329
6139
107
421
1685
75
147
20
1025
130
326
1792
198
120
15
1976
30
534
657
62
128
35
2450
2001
74
278
5833
1201
156
59
5973
1975
144
124
6139
Income Statement(in millions)
2017
2018
2019
Net Sales
Cost of Goods Sold
5418
3109
6883
3310
Assets
Cash
Marketable securities
Accounts Receivable
Inventory
Plant, Building,
and Equipments (net)
Investments in affiliates
Total Assets
Liabilities
Shortterm debts
Advances from customers
Accounts payable
Interest payable
Tax payable
Other Accrued Expenses
Bonds payable
Stockholders' Equity
Common stock
Additional paidin capital
Retained earning
Total liabilities and equities
4529
2215
Selling and General Expenses
Depreciation Expense
Interest Expense
Income Tax Expense
Net Income
771
213
97
175
1058
812
298
109
137
953
1059
284
621
154
1455
a) Perform the Ratio Analysis for the firm. (Need all the ratios that cover the
activity analysis, liquidity analysis, solvency analysis to the profitability
analysis)
b) Given your result in a), what is your opinion on the firm's performance so
far? What is the firm's strategy in raising capital? What are the firm's possible
business and financial strategies in your opinions?
Capital Structure and The Theory
Usually, the firm would keep their financing of capital as the industry will do.
Balance Sheet (in millions)
2013 2014 2015
Assets Cash
Marketable securities
Accounts Receivable
Inventory
Plant Building and Equipment
Investments in affiliates
Total Assets
230
50
1420
1260
2873
0
5833
210
100
1350
1578
1205
430
4873
970
0
1300
1450
990
1329
6039
Liabilities
Shortterm debts
Advances from customers
Accounts payable
Interest payable
Tax payable
Other Accrued Expenses
Bonds payable
Common stock
Additional paidin capital
Retained earning
Total liabilities and equities
107 130 1030
421 326 534
685 792 657
75 98
62
147 120 128
20 15 35
3025 1976 1450
1001 1201 1875
74 156 144
278 59 124
5833 4873 6039
One can easily calculate the solvency analysis:
• As the debttoequity ratio = 2.24 in 2013
•
= 1.395 in 2014
•
= 0.677 in 2015
• By which the firm is using the equity to replace the debts they had.
Yet, the situation is that we have to compare it with the industry’s
average or standard.
• Even so, the industry’s average is not quite the standard for the firm’s
finance of capital.
Capital Structure Theory
• M&M Proposition:
• Given that there is a “frictionless” capital market,
• The firm’s productivity or generation of future cash flows is
independent of the financing decision,
• No transaction cost,
• The firm has no difficulty in reporting its value through the accounting
procedures,
• There is no tax in the market,
• The investors can finance themselves equally efficient as the firm can
do,
• The capital market can be “efficient” in all the investors can get the
information as they want,
Assumptions (Cont’d)
• The payout ratio is 100%
• There’s no brokerage fee.
• There is no arbitrage opportunity. “Arbitrage” means to create a zerofee transaction and have a “sure” profit.
• There’s no classification for the shareholder’s equity.
• Suppose the firm only has to pay the principal until the maturity of the
debt,
• The market value of the debt is equal to its book value
M&M proposition 1:
• If there’s no tax, the value of the firm is the same when the firm has
debt or have no debt.
• Intuitively, if the firm’s generation of future cash flows are
independent of its financing, then the firm’s value was determined by
its productivity and not by how it may form its capital structure.
• See, if the firm’s productivity is unchanged, the firm can use any
methods to form its financing, yet its productivity remains the same.
• Example: Say we have firm Eddy which has the 100 million shares
outstanding. Currently the firm’ stock pays $2.50 dividend per share
with stock price currently as $20 per share. Suppose the firm wants to
raise $300 millions debt with 5% interest rate, what is the possible
expected rate of return of its stock after raising the debt?
Example (Cont’d)
• When looking at the firm’s productivity, we can get
• $2.5*(100 million shares) = $250 million for its possible future cash flow
• The rate of return before debt
• Ru= 2.5/20= 12.5%
• Now the firm is going to have $300 millions debt, according to M&M
proposition 1, the firm will have the leftover cash flows as it pays the
interest payment
• $250 million – (0.05)*300 million = 250 – 15 = $235 millions
• So according to the M&M proposition 1
•
𝑉𝐿 = 𝑉𝑈
• Where 𝑉𝑈 stands for the value of firm before debt, 𝑉𝐿 stands for the value
of the firm after the debts.
Example (cont’d)
• That is, the shareholder’s equity for the firm after debt will be
•
$2000 millions – $300 millions = $1700 millions
• Since there are 100 millions shares of common stock outstanding.
• Hence, the possible stock price after debts is equal to $17 per share.
Yet the dividend per share will become $2.35 per share. Hence, based
on the perpetuity model we can find that the rate of return now
becomes
• 2.35/17= 13.823% > 12.5% originally
• So raising debts will increase the rate of return for the stock since the
application of debt reduced the profitsharing of the shareholders.
M&M Proposition 2:
• Following the same set of assumptions, and allows there is corporate
income tax then,
• The M&M Proposition 2 says
•
𝑉𝐿 = 𝑉𝑈 + 𝑇𝑐 𝐷
• Where 𝑇𝑐 is the corporate income tax rate
• The main idea is that even though debts are not favorable, the tax
deductibility of interest payment is of use. Hence, the firm can undertake
some debts.
• Example: Let the “Eddy” has the same of information, except that we have
the corporate income tax as 25%
Example:
• The value of the unleveraged firm as
• $20*(100 millions shares) = $ 2000 millions
Yet according to the M&M proposition 2 we have the value of the firm after
debt becomes
• $2000 millions + (.25)*300 millions = $2075 millions after debts
• Given the accounting identity (total assets = total liabilities + total equity),
the shareholder’s equity = 2075 300 =1775 millions after having debts.
So the stock price becomes $17.75 per share.
Example (con’t)
• To find the income for dividends we need to find the EBIT, that is,
• $2.50*(100 millions shares) = (1  .25)EBIT
• Hence, EBIT = $250 millions/.75 = $ 333.33 millions
• This gives the operating income of the firm. Now it remains the same
after debt due to the independence of the firm’s productivity with its
financing decision.
Example (cont’d)
• Hence, the income for dividends becomes
• (1.25)(333.33 – (.05)*(300)) since the interest payment is tax
deductible.
• Hence, income available for dividends is 239 million.
• That is, the dividend per share is $2.39
• So the rate of return becomes 2.39/17.75 = 13.46%
• Because there is corporate income tax, even the debt is not in favor of
the shareholders, the tax deductibility of interest payment is preferred.
Hence, the rate of return is higher than when there is no debt and
lower than there is no tax.
The Capital Asset Pricing Model (CAPM)
• The model describes the “equilibrium” expected rate of return for
a risky asset as
•
•
𝐸 𝑅𝑖 = 𝑅𝑓 + 𝛽𝑖 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
• Where 𝐸(𝑅𝑚 ) is the expected rate of return for the market
portfolio which is approximated by the market index’s average rate
of return. That is, this is the bottomline expected rate of return the
asset deserts.
• The term as 𝐸(𝑅𝑚 ) − 𝑅𝑓 can be called the market premium
which shows how the capital market rewards the investor is taking
extra risk
Diversification with the systematic risk
Asset 1 has the 𝛽1 =1.5 , asset 2 has 𝛽2 = 0.5 and asset 3 has 𝛽3 =0.9. The
combinations of these assets will have the systematic risk as 1. We are
going to have the portfolio as
𝜔1 𝛽1 + 𝜔2 𝛽2 + 𝜔3 𝛽3 = 1
And
𝜔1 + 𝜔2 + 𝜔3 = 1
Where 𝜔1 , 𝜔2 and 𝜔3 are not always positive
By the capital asset pricing model with 𝑅𝑓 = 2%, 𝐸 𝑅𝑚 = 12%
• we have 𝐸 𝑅1 = 17%
• And 𝐸 𝑅2 = 7%, 𝐸 𝑅3 = 11%
• Hence, we trying to obtain the
• 𝑀𝑎𝑥 𝐸 𝑅𝑝 = 𝜔1 𝐸 𝑅1 + 𝜔2 𝐸 𝑅2 + 𝜔3 𝐸(𝑅3 )
• By the linearity and the “betas” are known, the
• 𝐸 𝑅𝑝 = 𝜔1 (𝑅𝑓 + 𝛽1 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )) + 𝜔2 ( 𝑅𝑓 + 𝛽2 (𝐸(𝑅𝑚 ) − 𝑅𝑓 ))
• +𝜔3 (𝑅𝑓 + 𝛽3 (𝐸(𝑅𝑚 ) − 𝑅𝑓 ))
= (𝑅𝑓 + 𝛽𝑝 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
Since 𝛽𝑝 = 1
• We can find that
•
• 𝐸 𝑅𝑝 = 𝑅𝑓 + 𝛽𝑝 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
•
= 𝑅𝑓 + (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
• This implies that the systematic risk of the portfolio will be the linear
combinations of the risky assets’ “beta’s” and so is the expected rate of return of
the portfolio should be the linear combinations of the risky assets. One can see
that the linearity guarantees that the combinations of asset has the systematic risk
of the portfolio is simply the linear combinations of the assets’ “beta’s” and the
expected rate of return for the portfolio is also the same liner combinations of the
assets’ expected rate of return. That it, the same CAPM should also work for the
portfolio.
Several Characteristics of CAPM
• 1. It determines the equilibrium rate of return when given the measure of
systematic risk of the risky asset. Hence, it can be used to determine the bottomline rate of return for the equity.
• 2. It’s a linear model with respect to systematic risk.
• 3. The systematic risk of the risky asset can be determined by the sensitivity of the
asset versus the entire capital market.
• 4. It shows if the combination of different assets is efficient, the expected rate of
return for the portfolio will be also on the same line. That is, the portfolio’s
expected rate of return versus its systematic risk (of the portfolio) must be on the
same line as CAPM
Example
• Now suppose we want to construct a portfolio with three assets together. Let the
systematic risk for asset 1 is 0.8, for asset 2 is 1.2 and asset 3 is 0.9. The
combinations for the assets are ( ½, , ¼ ,¼) to make the portfolio. Suppose the Tbill rate is 2%, and S&P 500 index return has the average rate as 12%.
• 1) what is the expected rate of the portfolio (in equilibrium)?
• Let the systematic risk of the portfolio be given as
• ½*(0.8)+ ¼ *(1.2) + ¼*(0.9) = (0.4)+(0.3) +(0.225) = 0.925
• Hence, by the CAPM we have
• E(R) = 2% + (0.925)(12%2%) = 11.25%
• 2) Suppose we want to create a zerobeta portfolio of asset one and asset two with
the transaction cost as $5 for the trade. Would you do it?
• Say, in this case, you can have the portfolio as (3, 2,0) and the portfolio will have
the zero beta in the systematic risk. A negative number shows that the short sell is
applicable in the portfolio. But would you do it?
Apparently, you will not do it.
• If you don’t do anything, simply buying the Tbill rate is 2%. Yet constructing the
portfolio will end up with a zero beta, the CAPM will give the 2% rate of return,
too. Doing the construction of the portfolio is simply the same as doing nothing.
• And the transaction cost is additional $5 fee that you have to pay. Would you do
it? Certainly not.
• Constructing the portfolio is a good idea. Yet, if the portfolio does not give you the
expected rate of return subject to the risk is taking, the portfolio is not good
enough to hold. Example: some mutual funds may boast of their rates of return
from the past history. Yet they never show you the risk they are taking. In fact, if
compare to the risk they’re taking, the portfolios may not be good enough.
So, in the earlier capital budgeting questions, we usually assume the given discount rate.
• We now can use this model to determine the underlying bottomline Weighted
Average Cost of Capital as the following. Say suppose there is no preferred stock
issued. And the debt ratio is given as ¼, the equity ratio is 3/4., the tax rate is 15%.
The current interest rate of the debt is 8%. And we use the above portfolio for
financing our equity, the WACC is found as
•
(1/4)*8%(115%)+(3/4)(12%) = 10.7%
• We can then use this rate for our capital budgeting decision using NPV or IRR
decision rules.
Now suppose the firm Apple Bees originally was in the restaurant industry the firm
originally has the WACC as 7.5%,
• The firm is considering the investment project in the computer game industry. Let
the typical firm in the computer game industry be given as Zebra who has the debt
ratio as ¼ for the debt requires 5% interest rate and the equity ratio as ¾ and the
“beta’ the systematic risk is as 1.5 with the S&P 500 index rate of return as 10%
and the Tbill rate as 2%. The tax rate in that industry is 15%.
• Now the WACC for the Apple Bees’ investment is not the same as the original as
it was before. Instead, we should choose the Zebra’s WACC as the investment’s
discount rate. That is, we need to get the expected rate of return for Zebra for the
cost of equity of the forthcoming investment
• That is, E(R) = 2% + 1.5(10%2%) = 14%
• WACC = ¼*5%(115%)+3/4(14%) = 11.56%
• Hence, this rate should be used for the capital budgeting question later on.
Now suppose the investment project involves the following expected cash flows.
Year 1
Year 2
Year 3 Year 4
Project 1
200
300
300
400
Project 2
300
200
500
Both projects will have the initial outlay as 150. The net present values of these
projects are shown as
• 𝑁𝑃𝑉1 = −150 +
200
1+11.56%
+
300
1+11.56% 2
+
200
1+11.56% 2
+
300
1+11.56% 3
+
500
1+11.56% 3
• and
• 𝑁𝑃𝑉2 = −150 +
300
1+11.56%
+
400
(11.56%)4
Compare to the NPV in using the original WACC of Apple Bees
• 𝑁𝑃𝑉1 = −150 +
200
1+7.5%
• 𝑁𝑃𝑉2 = −150 +
300
1+7.5%
+
300
1+7.5% 2
+
200
1+7.5% 2
+
300
1+7.5% 3
+
500
1+7.5% 3
+
400
(1+7.5%)4
• The assessment in using the original WACC has overstated the effectiveness of the
investment project. Hence, using the capital budgeting criterions should be
considering the nature of the investment. One can not simply use the original
WACC for the investment project in all cases.
How to estimate the systematic risk and its relationship with systematic
risk
• the Capital Asset Pricing Model (CAPM):
• the tradeoff between the (required) expected rate of return and the socalled systematic risk.
• 1) it is a simple linear model,
• 2) it is feasible to calculate the expected rate of return once one can
easily obtain the assessment that how sensitive the asset will be
associated with the market as a whole
The Capital Asset Pricing Model (CAPM)
• The model describes the “equilibrium” expected rate of return for a
risky asset as
•
•
𝐸 𝑅𝑖 = 𝑅𝑓 + 𝛽𝑖 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
• Where 𝐸(𝑅𝑚 ) is the expected rate of return for the market portfolio
which is approximated by the market index’s average rate of return.
• The term as 𝐸(𝑅𝑚 ) − 𝑅𝑓 can be called the market premium which
shows how the capital market rewards the investor is taking extra risk.
Example:
• Suppose there is a stock with beta risk around 1.2 and the market
index’s rate of return as 12% on the average. Let the basically Tbill
rate be 2%, the required rate of return for this stock is
•
E(R) = 2% + 1.2(12%  2%) = 14%,
• This is the “required” rate of return as the capital market equilibrium.
Hence, we can use the rate as the cost of equity for the stock. So, in
the capital budgeting problem, this becomes the discount rate for the
future cash flows if the firm is fullequity. If the firm is also financed
with debt, then the weighted average cost of capital will become
• W.A.C.C.= (debt ratio)*(cost of debt)(1tax)+(equity ratio)*(cost of
equity)
Diversification with the systematic risk and applications in capital budgeting
Asset 1 has the 𝛽1 =1.5 , asset 2 has 𝛽2 = 0.5 and asset 3 has 𝛽3 =0.9. The
combinations of these assets will have the systematic risk as 1. We are
going to have the portfolio as
𝜔1 𝛽1 + 𝜔2 𝛽2 + 𝜔3 𝛽3 = 1
And
𝜔1 + 𝜔2 + 𝜔3 = 1
Where 𝜔1 , 𝜔2 and 𝜔3 are not always positive
By the capital asset pricing model with 𝑅𝑓 = 2%, 𝐸 𝑅𝑚 = 12%
• we have 𝐸 𝑅1 = 17%
• And 𝐸 𝑅2 = 7%, 𝐸 𝑅3 = 11%
• Hence, we trying to obtain the
• 𝑀𝑎𝑥 𝐸 𝑅𝑝 = 𝜔1 𝐸 𝑅1 + 𝜔2 𝐸 𝑅2 + 𝜔3 𝐸(𝑅3 )
• By the linearity and the “betas” are known, the
• 𝐸 𝑅𝑝 = 𝜔1 (𝑅𝑓 + 𝛽1 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )) + 𝜔2 ( 𝑅𝑓 + 𝛽2 (𝐸(𝑅𝑚 ) − 𝑅𝑓 ))
• +𝜔3 (𝑅𝑓 + 𝛽3 (𝐸(𝑅𝑚 ) − 𝑅𝑓 ))
= (𝑅𝑓 + 𝛽𝑝 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
Since 𝛽𝑝 = 1
• We can find that
•
• 𝐸 𝑅𝑝 = 𝑅𝑓 + 𝛽𝑝 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
•
= 𝑅𝑓 + (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
• This implies that in equilibrium, the expected rate of return for the portfolio
simply follows the linear combination of the expected rates of return where
each expected rate of return simply follows the capital asset pricing model.
• Thus, if the firm’s stock follows with systematic risk as 1.2, we can get the
expected rate of return as capital asset pricing model indicates that
(assuming that the say, Tbill rate is 2% and the market index rate of return
is 12%, the expected for the firm’s stock is
• 𝑅𝑓 + (1.2)(𝐸(𝑅𝑚 ) − 𝑅𝑓 ) = 14%
1
3
Suppose the firm has the debt ratio as and there is no tax
• We have the weighted average cost of capital as
•
1
3
5% +
2
(14%)
3
= 11%
• We can base on this rate for the net present value in the capital budgeting
problem or the bottomline rate of return in the IRR function of the same
problem.
• Now instead of basing on the given rate of return in the capital budgeting
problem, the cost of capital now takes into account the way to determine the
cost of equity by using the capital asset pricing model.
Capital budgeting with Option
• Capital Budgeting: So far, there are three things we assume
• 1) The projects’ future cash flows are determined or assumed,
• 2) The discount rate for the cash flows is given,
• 3) The projects are continued until the projects are done.
• Yet, in the real time, the projects can be deferred, stop, selloff and
abandoned.
The example:
Suppose the project follows the forecasted cash flows based on whether
the years are good or bad.
Let the cost of capital be given as 10%, the initial outlay for the projects
for both cases are $150 (in thousands)
There are two cases for the projects’ cash flows and they depend on
whether the years are good or bad. The usual capital budgeting simply
consider the expected cash flow from taking both chances into account
and calculate the expected cash flows and determine the projects are
doable or not.
• The cash flows of the projects:
• Project
•
1
•
1
•
•
2
2
Chance
60%
40%
Year 1
250
100
Year 2
300
100
Year 3
350
200
60%
40%
300
120
350
200
450
200
• It is not reasonable to consider the projects when the bad year hits. The
firm may stop the projects when the expected cash flows turn negative.
The usual analysis:
• Obtain the expected cash flows in the projects together and consider
whether it pays off.
• The expected cash flows are
• Year 1: for project 1 (.6)*(250)+(.4)*(100) = 190
•
• Year 2: for project 1 (.6)*(300) + (.4)*(100) = 140
• Year 3: for project 1 (.6)*(350) + (.4)*(200) = 130
• Hence, the usual capital budgeting with net present value will give
The net present value:
•[
190
1+10%
+
140
1+10% 2
+
130
]−
1+10% 3
150 = 𝟐𝟑𝟔. 𝟏 > 0
• In the usual sense, this project is doable, and the firm would continue the
project until the end. And if the firm considers the option to discontinue the
project if the year is bad, the cash flows may look like the following:
• Project
• 1
• 1
Chance
60%
40%
Year 1
250
100
Year 2
300

• Hence, the net present value will become ቂ
.6 350
ቃ
3
1+10%
project.
Year 3
350

190
1+10%
+
.6 ∗ 300
1+10% 2
+
− 150 = 𝟑𝟐𝟗. 𝟑 > 0 which there’s a marginal gain for stopping the
Rate of Return and Risk
So far, we assume the discount rate is given. Yet in reality, this
is subject to estimation and assessment.
Risk: Systematic
Idiosyncratic
Systematic: when the risk may affect all the risky securities in
the capital market.
Idiosyncratic: when the risk is confined to a certain securities,
certain industries and certain sectors.
How to estimate the systematic risk and its relationship with systematic
risk
• the Capital Asset Pricing Model (CAPM):
• the tradeoff between the (required) expected rate of return and the socalled systematic risk.
• 1) it is a simple linear model,
• 2) it is feasible to calculate the expected rate of return once one can
easily obtain the assessment that how sensitive the asset will be
associated with the market as a whole
The Probability Space
State of the World Probability
Rate of Return
Recession
1/4
Recovery
1/2
20%
Boom
1/4
14%
10%
The Statistics
• The expected rate of return (according to the assessment from the
probability distribution assessed perhaps subjectively) is
• 1/4 ( 10% ) + 1/2 (20%)+ 1/4 ( 14% ) = 11%.
• standard deviation as
1
(14%
4
1
(−10%
4
− 11%)2
+
− 11%)2 as approximately as 12.37%
1
(20%
2
− 11%)2 +
Suppose there are two assets of portfolio
State of the world
Probability
R1
R2
Recession
1/4
10%
4%
Recovery
1/2
20%
12%
Boom
1/4
14%
8%
More statistics
• It is easy to see that the assettwo's expected rate of return is
• 1/ 4 ( 4% ) + 1/2 ( 12% ) + 1/4 ( 8% ) =9%.
• And the variance of asset two is 44% 2 .
• Namely, the covariance of these two assets,
• cov( R 1 , R 2 ) = 1/4 ( 10%11% ) (4%  9%)+ 1/2 ( 20%11% )
(12%  9%)+ 1/4 ( 14%11% ) ( 8%9% ) =156 %2 .
• Remember that the covariance is defined with “Two” arguments
only. That is, the covariance must explain the association between
two arguments only. If one has more than two assets, one can not
explain among all arguments in one covariance alone.
Mean Variance Analysis
• For any riskaverse investor, suppose there are only two assets, the
objective is to
• 𝑀𝑎𝑥𝑊 𝐸 𝑅𝑝 subject to
• 𝑊1 + 𝑊2 = 1,
• 𝑅𝑝 = 𝑊1 𝑅1 + 𝑊2 𝑅2 ,
• 𝑉𝑎𝑟 𝑅𝑝 = 𝑊12 𝑉𝑎𝑟 𝑅1 + 𝑊22 𝑉𝑎𝑟 𝑅2 + 2𝑊1 𝑊2 𝐶𝑜𝑣(𝑅1 , 𝑅2 ),
• Where 𝐸 𝑅𝑝 = 𝑊1 𝐸 𝑅1 + 𝑊2 𝐸(𝑅2 )
Mean Variance Analysis
• The problem is to maximize the expected rate of return and is subject
to the constraints for the choice variables are the “weights” for each
asset in the portfolio.
• The problem depends heavily the estimates for the means, variances,
and the covariance(s). Therefore, the problem centered on the statistics
for the assets we choose.
• Yet, the entire definition depends on the risk assessed as the “total
risk” the assets may behave.
• It shows the individual optimality only. No market equilibrium.
The Systematic Risk
• 𝛽𝑖 =
𝐶𝑜𝑣(𝑅𝑖 ,𝑅𝑚 )
,
2
𝜎𝑚
where 𝑅𝑚 represents the rate of return for the market
portfolio which can be approximated by the market index’s rate of
2 is the variance of the rate of return for the market portfolio.
return, 𝜎𝑚
It is easy to see that the numerator represents the corespondence with
the market altogether, while the denominator represents the volatility of
the entire market. In other words, it shows how sensitive the rate of
return for asset i with the market entirely.
The Capital Asset Pricing Model (CAPM)
• The model describes the “equilibrium” expected rate of return for a risky asset as
•
•
𝐸 𝑅𝑖 = 𝑅𝑓 + 𝛽𝑖 (𝐸(𝑅𝑚 ) − 𝑅𝑓 )
• Where 𝐸(𝑅𝑚 ) is the expected rate of return for the market portfolio which is
approximated by the market index’s average rate of return.
• The term as 𝐸(𝑅𝑚 ) − 𝑅𝑓 can be called the market premium which shows how the
capital market rewards the investor is taking extra risk.
Example:
• Suppose there is a stock with beta risk around 1.2 and the market
index’s rate of return as 12% on the average. Let the basically Tbill
rate be 2%, the required rate of return for this stock is
•
E(R) = 2% + 1.2(12%  2%) = 14%,
• This is the “required” rate of return as the capital market equilibrium.
Hence, we can use the rate as the cost of equity for the stock. So, in
the capital budgeting problem, this becomes the discount rate for the
future cash flows if the firm is fullequity. If the firm is also financed
with debt, then the weighted average cost of capital will become
• W.A.C.C.= (debt ratio)*(cost of debt)(1tax rate)+(equity ratio)(14%)
Another example:
• Suppose the firm’s stock has the required rate of return as 12% and the
Tbill rate as 2% and the market index’s rate of return as 10%, then we
can find the firm’s stock is subject to the
• 𝛽𝑖 = (12%  2%)/(10%2%) = 1.25
• That is, the firm’s stock is somewhat more responsive than the market
index in the impact from the systematic news.
Capital Budgeting 2
Internal Rate of Return (IRR):
The discount rate that sets the discounted cash flows of the
project equal to the initial outlay. Or in other words, the
discount rate that sets the Net Present Value of the project
equal to zero.
It’s a breakeven rate of the project. Hence, it’s not the genuine
rate of return of the project.
It’s the worstcase scenario indicates the highest discount rate
that the project can undertake.
Decision Rule:
• Choose the projects that the IRR exceed the actual financing cost.
• Start with the project of the highest IRR.
• Go to the secondbest project if capital leftover
• Go the rest if additional capital is available
Example:
• Suppose we have the projects to decide as follows
. Project Initial Outlay Year 1 Year 2 Year 3
• 1.
150
60
80
180
• 2.
300
80
120
100
• 3.
100
70
90
100
• The equations can be written as
•[
60
1+𝐼𝑅𝑅1
•
80
1+𝐼𝑅𝑅2
•
70
1+𝐼𝑅𝑅3
+
80
1+𝐼𝑅𝑅1 2
+
120
1+𝐼𝑅𝑅2 2
+
90
1+𝐼𝑅𝑅3 2
+
180
]
1+𝐼𝑅𝑅1 3
+
100
1+𝐼𝑅𝑅2 3
+
100
1+𝐼𝑅𝑅3 3
Year 4
250
− 150 = 0
+
250
1+𝐼𝑅𝑅2 4
− 100 = 0
− 300 = 0
Excel Applications
• Go to Excel spreadsheet
• Key in the associated cash flows for each project as
• A
B
C
• Project 1
Project 2
Project 3
• 150
300
100
• 60
80
70
• 80
120
90
• 180
100
100
•
250
Excel Example (continued)
• Go to the function wizard
• Ask for the “financial” function
• Go to IRR function
• The function will ask for the “Value”.
• Highlight the area for the project’s cash flows. Say for project 1. It’s
• For column A and the second cell and on. So that’s A2..A5. Then, it
will ask you for guess. (The reason is that the IRR may have multiple
solutions.) You may ignore the question.
• The IRR will give
• 𝐼𝑅𝑅1 = 39.68%
• 𝐼𝑅𝑅2 = 24.12%
• 𝐼𝑅𝑅3 = 62.92%
Excel Applications (continued)
• Suppose the actual cost for financing is 20% then, all the projects are
doable.
• The decision rule will be
• 1) Try with project 3 first.
• 2) Go to project 1 next if some capital is available
• 3) Try with project 2 last.
• The result is similar to the decision making with NPV.
Limitation:
• 1. The IRR is not the genuine rate of return for the project. Hence, it does
not necessarily indicate the profitability of the investment.
• 2. The IRR may have multiple solutions when the associated cash flows are
of alternating signs. That is, the project may have some positive cash flows
and some negative cash flows for a certain years.
• IRR does not consider the possible the firm may change their decisions once
the project begins.
• All the cash flows expected are predetermined.
• Once the project is chosen, it will be continued as to the end.
Limitation (continued)
• The decisions based on NPV and IRR may not be the same. Hence,
simply use one decision rule to determine the capital budgeting is
dangerous.
• For example, we have the following cash flows from the two projects.
• Project Initial Outlay Year 1
Year 2
Year 3
• 1
250
350
150
280
• 2
220
250
20
150
• If use the IRR decision rules, both will have the IRR as 50%. Yet if the
actual discount rate of the projects is 10%, the NPV for project 1 is
140.53, white the second one has 124.09.
Other decision rules
• Payback Period: The time span needed that the forecasted future cash
flows of the project may cover the initial outlay. That is, it’s a breakeven analysis.
• Example: Based on the earlier case with three projects, we have
• Payback Period for project 1 = 3
• Payback Period for project 2 = 3
• Payback Period for project 3 = 2
• Decision Rule:
• 1. Choose projects that the payback periods are shorter than the
preliminary cutoff time span.
• 2. Choose the project that its payback period is minimal.
Limitation:
• 1. The decision rule emphasizes the time span needed to cover the
resource spent and forget the profitability.
• 2. All the future cash flows are not considered their time values of
money.
• 3. No alternative decision is considered, That is, the project once
selected will continue until the end.
Discounted Payback Period
• The time span needed when the sum of discounted cash flows of the
project breakeven with its initial outlay.
• Similar to the earlier example, suppose the discount rate is 12%,
• Discounted Payback Period for project 1 = 3
• Discounted Payback Period for project 2 = 4
• Discounted Payback Period for project 3 = 3
• The decision:
• 1. it is indifferent to try project 1 or 3.
• 2. If there’s any capital leftover, then go to project 2.
Limitation:
• 1. It depends on the discount rate applied.
• 2. The emphasis of decision rule is the breakeven point for the
investment, not profitability.
• 3. It does not consider that the firm may have any alternatives when
the project is chosen to do. No deferment, no stop or abandonment
may be considered.
Weighted Average Cost of Capital
• So far, the analysis is to assume that the discount rate is given. In fact,
the discount rate should consider that the rate should suffice to cover
what the investor may want.
• Weighted Average Cost of Capital (WACC) is the rate of financing the
firm’s operation which represents the “minimum” requirement the
investor may with respect to the portions of their contribution.
• WACC is not the firm’s profitability index. It does not represent the
firm’s rate of return. It is the minimal of what they should obtain.
Calculation Format
•
•
•
•
•
WACC
= (Debt Ratio)*Cost of Debt *(1Tc) + (Equity Ratio)*Cost of Equity
If the firm is financed with debt and equity only.
Notice that in this case Debt Ratio + Equity Ratio = 1.
Tc is the corporate tax rate. (because the debt payments are taxdeductible)
• = (Debt Ratio)*Cost of Debt*(!Tc) + (Common Equity Ratio)*(Cost of
Common Equity) + (Preferred Equity Ratio)*(Cost of Preferred Equity)
• If the firm has issued preferred stock.
•
The Format
• The cost of debt and cost of equity are the required rates of return to
return to the investors. “required” means minimal requirement to
satisfy the said investors.
• Hence, if the firm issued bonds, the required rate of return for the firm
is the bond’s yield. (that is, the yield to maturity at least).
• And the cost of equity represents the rate that makes the investors in
equity would consider the rate is fair enough for them to investigate in
the stocks.
Example:
• Suppose the firm has the following information –
• The firm has issued 200,000 shares of common stock, no tax rate is
given.
• 50,000 shares of preferred stock,
• $400,000 in bonds,
• Common stock price = $25
• Preferred stock price = $15
• Cost of common stock = 25%
• Cost of preferred stock = 10%
• Cost of debt = 5%
• Total Capital = (200,000*25)+(50,000)*15)+400,000 = 6,150.000
Calculation of WACC
• WACC =
•
5,000,000
6,150,000
× 25%
750,000
+
6,150,000
× 10% +
400,000
6,150,000
× 5%
≈ 21.87%
• We can then, use this rate as the discount rate for the cash flows of
each project to choose.
• That is, this is the rate will on the average, cover the minimal
expectations for different sources for the capital may obtain.
• This is the rate that the firm may satisfy the requirement for the
different sources of capital it finances.
Perpetuity and Stock Valuation
Present Value of StockInfinite Stream of Cash Flows: (Why?)
𝐶
PV=
𝑖
If there’s a constant growth rate for the cash flows
𝐶(1 + 𝑔) 𝐶(1 + 𝑔)2
𝐶(1 + 𝑔)
𝑃𝑉 =
+
+⋯=
2
1+𝑖
(1 + 𝑖)
𝑖−𝑔
Assumptions and applications for the model
• 1. The cash flows are not necessarily the genuine payments. They are
the forecasted cash flows.
• 2. The discount rate is constant over time.
• 3. There are so many periods involved. Hence, the infinite number of
periods is a good approximation.
• 4. No default is considered.
• By the formula, it is feasible to say that
•𝑖=
𝐶(1+𝑔)
𝑃𝑉
+𝑔
• That is, we can use the current information and the possible growth
rate of the entity to forecast the rate of return in the investors.
Some examples
• Inferences from the market data
• Suppose the current stock price is $20.00 per share
• Expected growth rate of earning 5%
• Current dividend is $2.00 per share
• i = [2(1+5%))/20] +5% =15.5%
• By the same token, if the discount rate is 15%
• The expected stock price can be shown as
• PV=(2(1+5%))/(15%5%)=$21.00
Example 2
• Notice that this is for stock valuation, it is not for the stock price
prediction.
• Suppose the dividends will grow 5% annually for 5 years
• And go down to 2% perpetually,
• Suppose the current dividend is $ 2.00 per share
• The discount rate is 15%, the valuation is
•
2 1+5%
[
1+15%
+
2(1+5%)2
1+15% 2
+
2 1+5% 5
⋯+
]
5
1+15%
+
1
2 1+5% 5 (1+2%)
(1+15%)5
(15%−2%)
• The first part in the bracket is for the discount value of cash flows in
the first 5 years, the second part is the present value of the discounted
cash flow of the dividends that grow with 2% perpetually.
Cautions:
• 1. One should be careful about the time frame.
• 2. The idea of “present value’ means the valuation on the time spot
you’re standing.
• 3. The formula for present value is for the time frame that was set as in
the assumptions for cash flows shown. One can not simply apply the
formula without checking the patterns of the cash flows.
Bond Valuation
• Assumptions:
• 1. The predetermined cash flows are given (that’s why the bond
securities are usually called fixedincome securities)
• 2. No default or prepayment penalties.
• 3. The discount rates (usually called as yield) are constant.
• 4.The interest rate for the face value (the denomination) is usually
fixed and called coupon rate.
Example
• Suppose you are given the corporate bond as 5%coupon with face value as $1000
for 10 years, paid semiannually and discount rate is as 5%=10%/2,
•
25
(1
(5%)
1
−(
)20 )
1+5%
+
1000
(1+5%)20
Why there is a $25 payment? Since it’s a semiannual coupon payment, that is
5%*1000/2=$25.
• The first part in the bracket is the annuity that we can figure out with the formula
• The second part is the discounted cash flow (or present value of the face value (or
the denomination) of the bond.
Example
• Now as before, we set the discount rate as 12% per year, then the bond’s
valuation will be
•
25
1
(1 − (
)20 )
(6%)
1+6%
+
1000
(1+6%)20
• Now, one can see that if the discount rate is greater than the coupon rate, the
bond’s value is less than the face value is called discount bond.
• If the discount rate is equal to the coupon rate is called par bond.
• If the discount rate is less than the coupon rate is called premium bond.
Yield to Maturity
• Expected return of the bond holders to hold the bond until maturity of the
bond.
• Or, it be called as the discount rate that makes the bond’s present value
equal to its current bond price. That is, suppose you have a bond with 5%
coupon rate in two years, paid semiannually with face value as $1000, the
current market price is $850, the yield to maturity of the bond can be
calculated as
• 850 =
25
1 4
(1 − ( ) )
𝑖
1+𝑖
1000
+
(1+𝑖)4
• Notice that this is a complicated 4degree polynomial. It is very complicated
to solve it manually.
Hence, we can solve it with the help of Excel
• We can solve it as using the IRR function in Excel where
• We set the initial outlay as $850,
• Set the following cash flows as 25, 25, 25 and 1025 (face value
+coupon),
• It will give you 6.92%, which is 2*6.92%=13.84% annually.
Excel Spreadsheet
• 1. Go to Excel spreadsheet
• Click the function wizard
• Go to the “financial”.
• Make the initial cost of bond as 850 (negative since it’s considered as
cash outflow)
• The coupon payments are 25 25, 25, 1025. Key in theses numbers.
• Notice that since the bond is semiannual, the coupon payment is
5%*1000/2=25.
• The last payment is 1000+25=1025.
• Go to a empty cell and click IRR function.
The Excel Result
• The result will indicate that the IRR is equal to 6.92%.
• Since the bond is semiannual, and all the interest rates are reported in
the annual basis, the yield to maturity is reported as 2*6.92% =
13.84%
• That is, the expected rate of return for the bond investor is around
13.84%
Yield to Call
• Not every bond will exist until the maturity,
• The company or issuing entity can have the right to call back (or
retire) the bond before the maturity if they have notified the bond
buyers.
• The Yield to Call is the discount rate of the bond if it’s called before
the maturity
• Example: If the earlier bond is called back in one year, and suppose
the call price is $900 per bond then the problem becomes
• 850 =
25
𝑖
1−
1
1+𝑖 2
900
+
(1+𝑖)2
Notice that
• The frequency that discounted is in the semiannual basis
• There is no default and prepayment penalty
• The solution can be done with the earlier fashion in Excel,
• With IRR function, the solution is discount rate is
2*5.799%=11.598%.
Why do we discount?
1.
2.
3.
4.
5.
Time Preferences
Financing Cost
Opportunity Cost
Risk
The major difference between finance and accounting:
Time Value of Money
Discount Rate
• The discount rate applied must contain the above reasons.
• The Single Cash Flow
• Suppose you have a single cash flow in the future,
• The net worth of the cash flow must consider the Present Value
• Present Value
𝑪
PV=
(𝟏+𝒊)
where C stands for the future cash flow.
• And i represents the discount rate applied.
The Future Value
• It represents the amount of cash flow may be worth in terms of the
value it may have in the future.
• In the earlier notation, FV=PV(1+i).
• However, these only represent a single period for the cash flow. If the
cash flow requires several periods (say n periods) to get, then
•
𝐶
PV=
(1+𝑖)𝑛
• And the future value is equal to
• FV=PV(1 + 𝑖)𝑛
• That is, the cash flow requires n periods of compounding.
The Example for a bond valuation
• Suppose you own a treasury bond that lasts for 30 years with 3%
interest and face value $1,000. (face value means its denomination
• amount) and paid semiannual interest
•
PV=σ60
1
3%(1000)
2
3%
(1+ 2 )𝑡
+
1000
(1+3%)30
• This is difficult to figure the terms one by one since it involves a
stream of payments.
• Hence, we introduce the following “Annuity”
Annuity
• Definition: A stream of (constant) payments for a finite number of
periods of time.
• Key feature:
• 1. Some finite payments
• 2. A finite number of periods of time.
• 3. Assuming there’s no default.
• 4. The discount rate for the stream of payments is identical
Ordinary Annuity
• Key Feature: Each payment is done at the end of each period.
• The present value and future value
• Present value of the ordinary annuity
𝐶
𝑖
1
)𝑛 )
(1+𝑖)
• PV= (1 − (
• where C is the cash flow per period and i is the discount rate.
•
𝐶
FV= ((1 +
𝑖
𝑖)𝑛 − 1)
Annuity due
• The payments ae carried out at the beginning of each period.
• The Present Value and Future Value
•
𝐶(1+𝑖)
PV=
(1
𝑖
−
1 𝑛
( ) )
1+𝑖
• And the Future Value (at the end of the entire stream)
•
𝐶 1+𝑖
FV=
𝑖
((1 + 𝑖)𝑛 − 1)
Excel Application
• One can use the Excel spreadsheet to do the above problem without using
the given formula
• 1. Turn on the Excel spreadsheet
• 2. use an open blank sheet
• 3. Go click the function wizard 𝑓𝑥
• 4. use the PV function in the list. The function may ask you several things.
• “Rate” shows the discount rate per period (say monthly rate)
• “NPER” shows how many periods are included.
• “Pmt” asks you the payment per period.
• The “Type” question is asking if it’s the begining or ending of each period.
• The ”0” shows that it is at the end of each period, and “1” is at the
beginning.
Example: mortgage calculation
Suppose you bought a house that costs $520,000 and you paid 20%
down payment. Let the rest go to mortgage with 3% interest in 30 years.
How much is the monthly payment?
Go to the function wizard 𝑓𝑥
Click the “PMT” function. This is the function that will figure out the
payment amount per month. (that means there are $416,000 you need to
finance)
The payment function will be able to give you $1753.87 which is your
monthly payment for the mortgage.
Leftover Balance
• Suppose you stay in the house for 10 years, you plan to sell it soon.
How much is the bottomline balance for the house?
• Incorrect way to solve the problem; say 10 years of mortgage
payments is 10*12*(1753.87)=210464.40
• So the balance is 416,000210.464.40=205,535.6
• Why?
• You forgot that each payment contains the payment for the
principal and the interests. After 10 years, the monthly mortgage
payment may be more toward the principal.
The correct way for the balance
• You have 30 years of loan. After 10 years of staying, you still have 20
years of mortgage payments owed. That is,
• PV= Use the PMT function with Rate = 3%/12
• The “NPER” is 240
• “PMT” is 1753.87
• The balance is $316,241.90
• That means if you want to sell the house, you need to sell it more than
320,000 if you do not want to lose money.
Amortization
• This is an alternative method. That is, the balance letover needs to
take interest payment and payment for the principal into account.
• For example, the balance is
• Interest payment 416,000*(3%/12)=1040
• Monthly payment =1753.87
• Payment for the principal =713.87
• The balance of the mortgage after the first month
• =416,000713.87=415,286.13
Balance after the first month
• Residual Balance = 415,286.13
• Interest Payment = (415,286.13)*(3%/12)=1038.22
• The Monthly mortgage payment = 1753.87
• Balance paid for the principal = 715.65
• Balance leftover after two months = 415,286.13715.65=414,570.48
• This will keep on for the rest of payments
• The process is called amortization.
Excel application
• The amortization schedule with manual calculation is tedious. Hence,
we cam use the Excel spreadsheet to do so.
• The details can be found in the amortization table sent to you
separately
Financial Ratio Analysis
Activity Analysis (for salesoriented firm)
Salesoriented firm
1. Account Receivable Turnover
= Sales/Account Receivable
2. Inventory Turnover
= Cost of Goods Sold/Inventory
3. Account Payable Turnover
= Purchase/Account Payable
Days of Operating Activity (for salesoriented firm)
• Days of account receivable still outstanding
• = 365/account receivable turnover
• Days of account payable still outstanding
• = 365/account payable turnover
• Days of inventory still unsold
• = 365/inventory turnover
ServiceOriented Industry (need to design differently)
• For example,
• Miles per Passenger (e.g. Airline Industry)
•
= Mileage per flight/Number of Passengers
• Expense per flight = Cost/Number of Flights
• Passengers per flight = Number of passengers/Number of flights
Cycle of Business (salesoriented industry)
• Operating Cycle =Days of Account Receivable oustanding
•
+Days of Inventory Turnover
• Cash Cycle = Operating Cycle –Days of Account Payable
• For different industry, the ratios must be readjusted.
Liquidity Analysis
.
1. Current Ratio = Current Asset/Current Liabilities
2. Quick Ratio = (Current Asset – Inventory)/Current Liabilities
3. Cash Ratio =(Cash + Cash Equivalent)/Current Liabilities
• These ratios work for all industries.
Solvency Analysis
• These ratios are for the firm’s capital structure
• Debt Ratio = (Total Debt )/(Total Capitalization)
• Equity Ratio = (Total Equity )/(Total Capitalization)
• DebttoEquity Ratio = (Total Debt)/(Total Equity)
• Interest Coverage Ratio
•
= (Earning before Interest and Tax)/(Interest Expense)
Profitability Analysis
• Return on Asset (ROA)= (Net Income)/(Total Asset)
• Return on Sales (ROS)= (Net Income)/(Total Net Sales)
• Return on Equity (ROE) = (Net Income)/(Total Equity)
• Return on Common Equity
•
= (Net Income – Prefer Dividends)/Total Common Equity)
Balance Sheet (in millions)
2014
2015
2016
Assets
Cash
Marketable securities
Accounts Receivable
Inventory
Plant, Building, and Equipments (net)
Investments in affiliates
230
50
1420
1230
1873
0
210
100
1350
1578
1305
430
970
0
1300
1450
990
1329
Total Assets
4803
4973
6039
Liabilities
Shortterm debts
Advances from customers
Accounts payable
Interest payable
Tax payable
Other Accrued Expenses
Bonds payable
107
421
685
75
117
20
2025
130
326
792
98
120
15
2076
1030
534
657
62
128
35
1450
Stockholders' Equity
Common stock
Additional paidin capital
Retained earning
1001
74
278
1201
156
59
1875
144
124
Income Statement(in millions)
2014
2015
2016
Net Sales
4629
4418
4983
Cost of Goods Sold
2215
3109
2310
Selling and General Expenses
771
812
759
Depreciation Expense
210
298
284
97
109
121
175
137
254
1161
47
1255
Interest Expense
Income Tax Expense
Net Income
Financial Ratios
1. Activity Analysis
A/R turnover
Inv turnover
A/P turnover
n.a.
Working Capital Turnover
Total Asset Turnover
Assuming that marketable securities are cash equivalent
2. Liquidity Analysis
Current ratio
Quick ratio
Cash ratio
Working Capital ratio
Operating cycle
n.a.
Cash cycle
n.a.
3. Solvency Analysis
Debt ratio
Equity ratio
Debttoequity ratio
Liabilitiestoequity ratio
2014
2015
2016
3.260
1.801
3.273
1.970
4.364899
1.364
0.888
3.833
1.593
3.321157
1.340
0.825
4.277372263
2.481751825
0.408759124
3.277372263
4.088384
2.09596
0.391414
3.088384
296.7913
213.1697
5.6621
3.455099
1.476408
4.6621
324.3363
214.4348
0.443889236
0.281698938
1.575757576
0.974131559
0.443595
0.284738
1.55791
0.954096
0.410664
0.35486
1.157256
0.660756
1.580
0.964
And
Profitability Analysis
Return on assets
0.241723923
0.00945
0.207816
Return on sales
0.25081011
0.01064
0.251856
Return on invested capital
0.619861185
0.02709
0.541182
Return on equity
0.858093126
0.03319
0.585628
Introduction
• The Purpose of Financial Statements:
• 1) to summarize the transactions the entity has (potentially) accomplished,
• 2) to identify the essential activities the entity is doing,
• 3) to point out the current financial status of the entity,
• 4) to describe the cash position they entity has achieved,
• 5) to provide the investors the information for their investments.
• Unfortunately, the statements may be stated, in terms of convenience of
accounting practice, all are stated by the (current) or historical value of the items.
Hence, the values of net income in (say) income statement, are reported in the
money in a particular period. So, comparison across the periods, may not be
entirely justifiable when comparison is done with many periods together.
Asset: 1. Ownership: It indicates that the entity has the ownership for the benefit and economic
resources of doing so.
2. Economic Resources: It is valuable and recognizable in the market.
3. for Future Growth and Prosperity: the purpose is to generate the benefit for the future.
It has the potential or productivity to become more in return.
Liability: obligation that one needs to retire in a short run or long terms. These obligations might
include the employee payroll, bonds issued, customer pay inadvance…etc.
Equity: the residual of the firm’s value after paying all the obligations. That’s why, based on this
definition, the accounting identity such as Total Assets = Total Liability + Equity will hold in any
case.
Financial Asset: Different from the usual concept, these assets emphasize on the transferring the
cash flows (or capitals) from sectors to other sectors. Hence, the value of them, depending on the
future cash flows that they can provide from such provision in return.
Financial Market: (what is a market?)
Balance Sheet (or called Statement of Financial Position)this is the financial
statement that contains the information for the sources and usages of funding.
Income statement (or called Statement of Operations)this is the statement for the
firm’s performance within the defined period. It is a subject to the concept of flows.
Statement of Cash Flows this is the statement of the firm’s performance in the cash
basis.
Some concepts:
• Accrual Basis: The transactions are recognized as if the transactions are likely to
accomplished with certain degree of confidence, complete the transactions and
render the payments accordingly. In other words, the potential cash flows (inward
or outward) will be provided successfully. Yet, the entire transaction may not
necessarily finish in the cash flow transferred.
• Cash Basis: The transactions are recognized and recorded only if the cash flows
are involved. In other words, the transactions in the financial statements are
reported only when cash flows are done. That means, the statements are reported
with actual payments are completed.
Financial Ratio Analysis
Limitations of financial ratios:
1. There is a linear relationship between the numerator and
denominator2. There is the possibility that the information for either the
numerator or denominator is unavailable.
3. The financial ratios can only represent the information up to
the present if the information is available. The ratios can be
used as the indicators for the institution of interest.
4. The accounting policy of the entity will influence the financial
ratios calculated.
Usage of Financial Ratios
• 1. To identify the proportional relationship among certain items of financial
reports.
• 2. To possibly consider the relationship identified over different periods,
• 3. To compare the identified relationship with the benchmark(s) chosen.
•
•
•
•
To compare to the benchmarks for the ratios:
1. Compare to the industrial average,
2. Compare to the peer group,
3. Compare to the individual history.
• *One must be careful in choosing the benchmark(s) to compare.
CORPORATE FINANCE
TU @ 12:50 2:15PM  MEET ONCE A WEEK
Textbook
Essentials of corporate finance
FLOW OF CLASS
MAJOR ASSIGNMENTS
 Discussions
 Quizzes
 Homework:
 MIDTERM: ch 18
 Final: comprehensive
WEEK 1 LECTURE 1
1/14/21
THE PURPOSE OF FINANCIAL STATEMENT
 To summarize the transactions the entry has (profitability) accomplished
 To identify the essential activities the entity is doing
 Point out the current financial status of the entry
 Describe the cash position the entity has achieved
 To describe the information for their investments
ASSET
 Something of value that the company OWNS
 Economic resources: valuable and possibly recognizable in the market
 Future growth and prosperity: the purpose is to generate the benefit for the future
LIABILITY
 Obligation that needs to retire in short or long term. YOU OWE. Ex payroll. Bonds
issued, customer pay inadvance
EQUITY: the residual (whats left over) of the firms value after paying obligations. EQUATION:
TOTAL ASSETS= TOTAL LIABILITY + EQUITY
FINANCIAL ASSETS
 This is transferring the cash flows (or capitals) from sectors to other sectors. IN OTHER
WORDS, its the transferring of $$ or capital to elsewhere for MORE assets
FINANCIAL MARKET: providing capital and asking for a bigger return than the one you
contributed.
FINANCIAL STATEMENTS
 BALANCE SHEETS assets= total liabilities + equity
 Also known as statement of financial position
 A snapshot of the financial position
 This is the financial statement that contains the information for the sources and
usages of funding
 Contains the asset side, showing the firms usage of the capital obtained and how
they make it grow
 The opposite of asset is liability, which indicates the sources of financial
obligations that need to be retired in the ST or LT
 The equity is called the residual claim that the firm pays off the liability and the
leftover amount

INCOME STATEMENT (statement of operations)

Shows the firms performance within the defined period ( operations of the
institution, a more detailed)
Shows you what is a PERIODIC TRANSACTION that can possibly be
accomplished
Concept of the transition for the firm, and how well they perform for this goal.
STATEMENT OF CASH FLOW
 Every transaction in terms of cash
 Every transaction that CAN actually happen
 Is represented in 3 different areas: operating cash flows, investing cash flows,
and financing cash flows
 How the business obtains and dispenses cash flows
CONCEPTS
ACCRUAL BASIS
 Transactions as they are accrued, NOT paid.
Meaning the underlying transaction in which it will be accomplished with a high
likelihood to succeed.
CASH BASIS (you can see this is the statement of cash flows)
 Recognizing the transaction only when physical cash is involved (in other words,
only when the cash flows are done). ** reported with actual payments are
completed**
FINANCIAL RATIO ANALYSIS
Is used to reflect the truth and condition of the institution, the performance of the firm such as
profitgenerating activity in sales (ex: accounts receivable turnover rate= sales (or revenue)/
average (depends on the firm) account receivable.)
 LIMITATIONS
 Linear relationships between the numerator and denominator
 Possibility that the information for either the numerator and denominator is
unavailable
 The financial ratios can only represent the information up to the present if
the information is available. The ratios can be used as the indicators for the
institution of interest.
 Accounting policy of the entity will influence the financial ratios calculated
(meaning that if the accounting rules change for the organization, so will the ratio
calculations)

USAGE OF FINANCIAL RATIOS
Need to identify which kind of industry and their activities to:
 Identify the proportional relationship among certain items of financial reports
 To possibly consider the relationship identified over different periods
 To compare the identified relationship between the benchmark(s) chosen
 TO COMPARE THE BENCHMARKS FOR THE RATIOS:
 Compare the industrial average
 Compare the peer group
 Compare the individual history
FINANCIAL RATIOS  SALES INDUSTRY
1. Accounts receivable turnover
a. Sales (or revenue) / average account receivable
i.
AVERAGE account receivable depends on the industry
2. Inventory turnover
a. COGS/ Average level of inventory
i.
This tells you how much is sold compared to what isnt
ii.
The more efficient the sales are functioning the faster they can get the
inventory down
3. Accounts payable turnover
a. Lets you know the amount of inventory that has actually been paid to the firm
b. COGS= beginning inventory + purchase  ending inventory
c. In this, the beginning inventory can be considered as the ending inventory, which
shows the amount of credit the firm is using to PURCHASE inventory.
i.
The more inventory is purchased on credit the better
ii.
The less the ratio is, the better because it is interpreted as a credit + cash
purchase
4. Days of accounts receivable still standing
a. Ratio that tells how many days the firm is about tti switch the accounts that are
collectible to cash, namely
b. Days of account receivable still outstanding= (365 days)/(account receivable
turnover)
5. Days of account payable still outstanding
a. 365 days/ account payable turnover
b. This shows how many days the the firm can wait before paying a bill
c. Interest free
6. Days of inventory still unsold
a. 365 days/ inventory turnover
b. How many days before the firm sells its product
c. The shorter the better
7. Operating cycle
a. Days of inventory still unsold + days of account receivable still outstanding
8. Cash cycle
a. Operating cycle  days of account payable outstanding
FINANCIAL RATIOS ALL INDUSTRIES
1. Liquidity analysis
i.
The area the firm is about to solve shortterm obligations for
ii.
The faster = better
b. Current ratio= current assets / current liabilities
i.
Current assets includes cash + cash equivalents + marketable securities
+ accounts receivable + inventories
c. Quick ratio = current assets  inventories/ current liabilities
d. Cash ratio= cash and cash equivalents/ current liabilities
2. Solvency analysis
i.
Is the analysis for the firms ability for retirement of longterm financial
obligations
b. Debt ratio= total debts/ total capitalization
c. Equity ratio= total equity/ total capitalization
d. Equity is usually both common stock and preferred stock, but most analyses
focus on common SO THE ALTERNATIVE WOULD BE total equity ratio=
common equity/ total capitalization
e. Debt to equity ratio= total debts/ total equity
f. Interest coverage ratio= earnings before interest and taxes/ interest
expense
3. Profitability analysis:
i.
Is to investigate if the firm earned enough for their capital providers
b. Return to asset= total net income/ total assets
c. Return to sales= total net income/ total sales
d. Return to equity= total net income/ total equity
WEEK 2 LECTURE 1
1/19/21
Financial statements only give:
1. Estimates for most likely amounts of the transactions
2. To provide the general activities the firm has accomplished
3. When the accounting policy for the firm changes, the underlying amount (or transaction)
will be reported differently
4. The numbers of the transactions are usually not subject to any adjustment for the
inflation (MEANING that the transaction amount will not be the same today as it was
tomorrow)
FINANCIAL RATIO ANALYSIS
(activity analysis for salesoriented firms)
Sales oriented firm
1. Accounts receivable turnover
a. sales/ accounts receivable
i.
MEANING if you’ve received the $$ that is owed to you (something that
you expect to receive)
ii.
SALES through credit
iii.
When this ratio is big, this means that your cash sales is lower, meaning
that there are a lot of people (or accounts) that still need to pay you.
2. Inventory turnover
a. Cost of goods sold/ inventory
i.
ii.
(COGS= beginning inventory + purchase  inventory)
Purchase will most likely not told, so you have to figure it out based on
everything else thats provided
1. How much something in terms of inventory is able to be sold.
3. Accounts payable
a. purchase/ account payable
i.
I can buy something, but i don't have to pay it immediately. THIS IS
WHAT WE (YOU) OWE to others.
ii.
Smaller ratio= better
Days of operating activity (for sales oriented firms)
1. Days of accounting receivable still outstanding
 365/ accounts receivable turnover
 Tells you the days it takes for you to get the money people owe you
2. Days of accounts payable still outstanding
 365/ account payable turnover
 Tells the days in which you need to pay someone else
 The longer= the better
3. Days of inventory still unsold
 365/ inventory turnover
 The shorter= the better because it shows that your inventory is being sold
at a fast rate
SERVICE ORIENTED INDUSTRY
For example:
1. Miles per passenger (an airline industry)
a. = miles per flight/ number of passengers
2. Expense per flight= cost/ number of flights
3. Passengers per flight= number of passengers/ number of flights
CYCLE OF BUSINESS (SALES ORIENTED)
1. Operating cycle= days of account receivable outstanding + days of inventory turnover
 You sold something between the # of days to receive the money and the # of
days with raw materials
2. Cash cycle
a. = operating cycle days of account payable
i.
Cash cycle represents the # of days you have to maintain(or reserve) that
internal cash flow.
ii.
The shorter= the better you are
iii.
Example: someone pays you within a 30 day period and you have 90
days to pay someone else back.
LIQUIDITY ANALYSIS
 Wanting to get enough cash to be able to retire the obligation that is still within a shirt
term period (APPLIED TO ALL INDUSTRIES)
1. Current ratio= current assets/ current liabilities
a. Current assets= cash + cash equivalents + marketable securities + accounts
receivable + inventory
b. Current liabilities=something you have to retire, an obligation within a year…
account payable (debt) + overhead fees +
c. CURRENT RATIO… THE BIGGER OR HIGHER THE BETTER YOU ARE.
2. Quick ratio= (current assets  inventory)/ current liabilities
a. We take out inventory because we dont always sell our inventory quickly
3. Cash ratio= (cash + cash equivalents)/ current liabilities
SOLVENCY ANALYSIS
These ratios are for the firms capital structure
1. Debt ratio= (total debt)/ (total capitalization)
a. Total debt= everything, total obligation that needs to retire. INTEREST BARRING
2. Equity ratio= total equity/ total capitalization
3. Debt to equity ratio= total debt / total equity
4. Interest coverage ratio= earnings before interest and tax/ interest expense
a. Ex: boing
b. EBIT = earnings prior to interest they have to pay
c. The higher the better you are
PROFITABILITY ANALYSIS
1. Return on assets (ROA)= net income/ total assets
2. Return on sales (ROS)= net income/ total net sales
a. Net sales= total sales  sales subsidies
3. Return on equity (ROE)= net income/ total equity
4. Return on common equity= net income  prefer dividends / total common equity
LOOKING AHEAD:
1. GETTING AN EMAIL LATER ON TODAY WITH QUIZ 1. THIS IS DUE NEXT TUESDAY.
WEEK 3 LECTURE 1
I.
II.
III.
1/26/21
Why do we discount?
A. To have the product now
B. When we wait, we have financing cost + opportunity cost (the cost associated
with making a decision over something else) + risk (the cost of having an
uncertain outcome)
Finance vs accounting: time value of money.
A. Finance talks about time value of money
B. Accounting talks about the transaction of the money
The discount rate makes a net worth as present value
IV.
A. When you are in accounting, you are considering present value (PV=C/1+i),
where c stands for the future cash flow.
The future value
A. Represents the amount of cash flow may be worth in terms of value it may have
in the future
1. FV= PV(1+i)
2. ** however that is only for a single value. If its multiple periods: PV=
C/(1+i)^n
a) Future value = PV=(1+i)^n
b) N = the period
B. EXAMPLE: suppose you own a treasury bond that lasts for 30 years with 3%
interest and face value $1,000 (face value means its denomination amount) and
paid semianual interest
1. PV= ∑^60((3%*1000)/2)
1000
 + ______
(1+ 3%/2)^t
(1+3%)^30
*** use fx in excel, choose PV + insert: rate (which is 3%/2 periods since its semi annual)
VII. ANNUITY
A. DEFINITION: A stream of (constant) payments for a finite number of periods of time
B. Key features: (ex paying rent, tuition)
a. Some finite payment
b. A finite number of periods of time (something is fixed)
c. Assuming theres no default
d. The discount rate for the stream of payments is identical
C. ANNUITY DUE
a. The payment are carried out at the beginning of each period
b. The present value and future value
i.
VIII. ORDINARY ANNUITY
A. Key feature: each payment is done at the end of each period (ex paychecks, after
youve done the work)
a. The present value and future value
b. Present value of the ordinary annuity
i.
PV= C/I(1(1/(1+i)^n)
1. Where c is the cash flow per period and i is the discount rate
IN EXCEL:
WEEK 4 LECTURE 1
I.
02/01/21
Perpetuity and stock valuation
A. Perpetuity is similar to annuity, but refers to infinite periods of cash flows
B. PV OF A PERPETUITY= C/ i
1. c= the perperiod cash flow and i= the discount rate or rate of return
C. You can use this form to infer several things:
1. The stock value (using past history of stock prices to predict the stock
price)
2. Rate of return
a) Denominator is the possible rate of return for one to invest the
money TODAY
3. DRAWBACKS FROM FORMULA @ B:
a) The expected cash flows never grow over time. There is
generalization that it incurs some growth rate of the cash flows
socalled constant growth rate model of stock valuation
b) PV OF STOCK=
(1) C= cash flow per period and the cash flow are subject to
constant growth rate over time
(a) THIS CAN BE USED FOR INFER THE REQUIRED
RATE OF RETURN
c) Can be used used to assess the stock valuation in justifying the
corporate finance decision
(1) Assumptions implied in the equation above:
(a) The expected cash flows in the numerator are not
necessarily the genuine divided payment. They
represent the expected cash flows the investor may
get from the company’s earning in their operations
**the format simply considers that the investor is
entitled to get the earnings of the firm.
(b) The DISCOUNT RATE is constant over time which
means that the costs for the investor to buy the
stock remains the same over time
(c) Formula assumes that there are HIGH number of
periods, and the entire infinite sum can be
approximated by the perpetual model with a
negligible error (INVESTOR BELIEVES THAT THE
BUSINESS WILL ONLY LAST SO LONG)
d) Application of the PV STOCK
can be used to
obtain the possible discount rate (or rate of return) the investors
intended to have
e)
pv can be
substituted for the current stock proce for the equation and abstain
the possible rate of return of the stock from using the above
equation
(1) EXAMPLE  Suppose the current stock price is $20.00
and the expected growth rate of earnings is 5%,let the
expected cash flow is $2.00 currently, the equation will give
us
meaning that the markets expected rate of return is 15.5%
(2) By the same token, if the rate of return is 15%, the growth
rate of the dividend (or expected earning) is 5%, the
current dividend is $2.00, the possible stock valuation is
then,
(3)
TEST 2 WILL BE SENT OUT WEDNESDAY AND IT MUST BE TURNED IN BY NEXT
WEDNESDAY AT 1 PM FOR TEST: NAME + CLASS YOU ARE IN
WEEK 5 LECTURE 1
02/09/21
CAPITAL BUDGETING
I.
II.
Capital budgeting
A. CONCEPT: The allocation process for the capital obtained for the purpose of te
firm investments
B. OBJECTIVE: the optimality for the firms growth (using the $$ or capital of the
business to get the most growth)
C. CRITERIA: none of the criteria will overwhelm the others. Need to investigate
them all
D. ASSUMPTIONS:
1. the projects expected cash flows are forecasted or predetermined
2. The discount rate is given. That is, the rate is PREDETERMINED
3. The project is assumed as when one has started will continue until its
done
4. No deferment, choice or change of mind is considered
5. All projects are considered manually exclusive
E. IT IS TRYING TO ALLOCATE THE LIMITED CAPITAL YOU OBTAIN FROM THE
INVESTOR
THE DECISION RULES
A. NET PRESENT VALUE (NPV): the present value of the project net of the initial
outlay or present value of the entire costs
1. Choose the projects with positive NPV
2. Start with the project that has the highest NPV
B.
1. Initial outlay (c1/1+i) is the initial cst of the present vakye of the cost
involved over the years
2.
a) This shows 3 different projects, with 3 different initial outlay values
& the amount of money you would get back from it. YOU CAN DO
THIS ON EXCEL TO FIND OUT WHICH PROJECT WILL GIVE
MORE TO YOU. in this example, interest rate is 12% (0.12)
b)
150
60
80
180
300
80
120
100
100
70
90
100
=NPV(0.
12)(150
:180)
250
=NPV(0.
12)(300
:250)
=NPV(0.
12)(100
:100)
c) ACCORDING TO THE NVP RULE, you would choose project 3. If
you have any $$ left over, you would do project 2. LAST would be
project 1.
3.
a) ^^ how to calculate by hand on calculator
C.
1. NEW EXAMPLE^^
2. In this example, NVP does not work because it requires different cash
flows throughout the years. So, if the year is bad, the company has the
option to discontinue the project.
3.
a) Notice how 300, 400, 500 comes from “good” year
b) 260, 160, 220= the amount of $$ you will get back
c)
so you insert those values into the equation^^
D.
WEEK 6 LECTURE 1
I.
02/16/21
Capital Budget PT 2
Internal Rate of Return (IRR)
A. The discount rate sets the dicounted cash flows of the project equal to the
internal outlay. (IN OTHER WORDS, the disount rate that sets the net preent
vaue of the project equal to zero).
B. It is a breakeven rate of the project
C. It is the WORSE CASE SCENARIO, which indicated the highest disount rate that
the project can undertake
D. Decision rule:
II.
1. Choose the projects that the IRR exceeds the actual financing costs
2. Start with the project of the highest IRR
3. Go to the 2nd best project if capital leftover
4. Go to the rest if additional capital is available
Example: suppose you have three projects:
A.
B. TO DO ON EXCEL:
1.
a) IRR1= 39.68%
IRR2: 24.12%
IRR3: 62.92%
C. Now suppose the actual cost for financing is 20% then, all projects are double.
Bug you will go with project 3, project 1, the project 2.
1. SOME LIMITATIONS
a)
2. The decisions based on NVP and IRR may not be the same. Hense,
simply use one decision rule to determine the capital budget is dangerous
a)
3. OTHER DECISION RULES
a)
b) Discounted cash flows of the project breakeve with its initial
payment
(1) Suppose you have a discount rate of 12%
(a) Discounted payback period for project 1=3
(b) ‘’Project 2= 4
(c) ‘’ project 3=3
(i)
Decision: do 1 and 3, project 2 only if there
is value left over
(2) LIMITATIONS
(a)
D. WEIGHTED COST OF CAPITAL
1. Weighted average cost of capital (WACC) is the rate of financing the firms
operation which represents the “minimum” requirement the investor may
with respect to the portions of their contribution
a) This is NOT the profibalility index. It does NOT represent the firm’s
rate of return.
2. CALCULATION FORMAT
a) WACC= (Debt ratio) * Cost of Debt * (1TC) + (Equity Ratio) * Cost
of Equity
(1) IF THE FIRM IS FINANCED WITH DEBT AND EQUITY
ONLY
(a) Notice that the case debt + equity ration= 1
(b) TC is the corporate tax rate (because the debt
payments are taxdeductible)
b) WACC= (debt ratio)*Cost of Debt*(1TC)+(common equity
Ratio)*(cost of common equity)+(preferred equity ratio)*(cost of
preferred Equity)
(1) If the firm has issued preferred stock
3. The format
a) The cost of debt and cost of equity are the required rates of return
to return to the investors. “Required” means requirement to satisfy
the said investors
(1) If the firm issued bonds, the required rate of return for the
firm is the bond’s yield
(2) Cost of equity represents the rate that makes the investors
in equity would consider the rate is fair enough for them to
investigate in the stocks
(a) EXAMPLE
E. weighted average cost of capital
1. Discount rate is normally given, but the discount rate should consider the
rate should suffice to cover what the investor may want
2. WACC is the rate of financing the firms operation which represents the
minimum requirement the investor may with respect to the portion of their
contribution (ex: 20% contribution from parents & 40% from your in laws,
20% from padrinos. The biggest is the 60% so because of that, it matters
more).
a) WACC is not the firms profitability index. It does not represent the
firm rate of return, but the minimum the firm should obtain.
3. WACC CALCULATION FORMAT
a) = (debt ratio)*Cost of Debt*(1TC)+( equity Ratio)*(cost of
common equity) ////// **** if the firm is financed by DEBT ONLY**
(1) TC is the corporate tax rate
b) WACC= (debt ratio)*Cost of Debt*(1TC)+(common equity
Ratio)*(cost of common equity)+(preferred equity ratio)*(cost of
preferred Equity) /////// ******* If the firm has issued preferred
stock
(1) WHEN YOU CALCULATE WACC, IT IS a %.
F. The format
1. The cost of debt and cost of equity are the required rates of return to
returns to the investors. “Required” means minimal requirement to satisfy
the said investors
2. If the firm issued bonds, the required rate of return for the firm is the
bond’s yield. (the yield to maturity at least)
3. Cost of equity represents the rate ohat makes the investors in equity
would consider the rate is fair enough for them to investigate in the
stocks.
a) EXAMPLE: suppose the firm has issued 200,000 share of
common stock, no tax rate is given. In addition, they did 50,000
preferred stock, $400,000 in bonds. The value for each is:
(1) Common stock $25
(2) Preferred stock price $15
(3) Cost of common stock= 25%
(4) Cost oc preferred stock = 10%
(5) Cost of debt= 5%
(a) SO: total capital=
(200,000*25)+(50,000*15)+400,000= 6,150.00
(b) WACC=
(i)
The 21.87% is the minimum requirement to
satisfy equity, bond, and other shareholders.
WEEK 7 LECTURE 1
02/23/21
RATE OF RETURN AND RISK
I.
rate of return and risk
A. So far, we assume the discount rate is given. BUT IN REALITY: THIS IS THE
SUBJECT TO ESTIMATION AND ASSESSMENT
B. Two types of risk:
1. Systemanic  when the risk may affect all the securities in the capital
market (ex: COVID, ALL BUSINESSES)
2. Idiosyncratic  when the risk is confined to a certain securities, certain
industries and certain sectors
C. How to estimate the systematic risk and its relationship with systematic risk
1. The capital asset pricing model (CAPM): The tradeoff between the
(required) expected rate of return and the socalled systematic risk
a) It is a simple linear model
b) It is feasible to calculate the expected rate of return once one can
easily obtain with the market as a whole
2. EXAMPLE
State of the world probability rate of return
Recession
¼
10
Recovery
½
20%
Boom
¼
14
THE STATISTICS
I.
The expected rate of return (according to the assessment
from the probability distribution assessment perhaps
subjectively) is:
A. ¼ (10) + ½ (20%) + ¼ (14) = 11% ***** THIS IS
WRONG BECAUSE YOU DID NOT TAKE INTO
ACCOUNT HOW MUCH RISK YOU ARE
UNDERTAKING***
B. Standard deviation:
3. EXAMPLE:
WEEK 8 LECTURE 1
03/02/21
RATE OF RETURN AND RISK
RATE OF RETURN & RISK
The rate of return is usually subject to estimation & assessment. There are 2 types of risk:
1. Systematic  when the risk may affect the risky securities in the capital market. THIS
AFFECTS THE ENTIRE INDUSTRY, OR PERSON
2. Idiosyncratic : when the risk is confined to a certain securities, certain industries and
certain sectors. ONLY HAPPENS TO A CERTAIN SECOR.
HOW TO ESTIMATE THE SYSTEMATIC RISK AND ITS RELATIONSHIP WITH SYSTEMATIC
RISK. you can use:
1. The capital asset pricing model (CAPM)
a. The tradeoff between the (required) expected rate of return and the socalled
systematic risk
b. It is a simple linear model
c. It is feasible to calculate the expected rate of return once one can easily obtain
the assessment that how sensitive the asses will be associated with the market
as a whole
Example found on next page
EXAMPLE
STATE OF THE WORLD
PROBABILITY
RATE OF RETURN
RECESSION
1/4
10%
RECOVERY
1/2
20%
BOOM
1/4
14%
The expected rate of return )according to the assessment from probability assessed perhaps
subjectively) is:
 1/4(10%)+ ½(20%)+¼(14%)= 11%

Standard deviation as
 REPRESENTS YOUR UNDERTAKING OF UNDERTAKING RISK
 THIS IS NOT SYSTEMATIC RISK
ANOTHER EXAMPLE
Suppose there are 2 assets of portfolio
STATE OF THE
WORLD
PROBABILITY
RATE OF RETURN
(1)
RATE OF RETURN
(2)
RECESSION
1/4
10%
4%
RECOVERY
1/2
20%
12%
BOOM
1/4
14%
8%
Rate of return is: 9% (calculate like this: 1/4(4%)+ ½(12%)+¼(8%)= 9% )
& the variance of asset 2 is: 44%
The covariance of these 2 assets then:
cov(r1,r2)=¼(10%115)(4%9%)+½(20%11%)(12%9%)+¼(14%11%)(8%9%)=156%^2
REMEMBER: the covariance is defined with “two arguments only. That is, the covariance
must explain the association between 2 arguments only. If one has more than 2 assets, one can
only explain among all arguments in one covariance alone.
MEAN VARIANCE ANALYSIS
 For any riskaverse investor, suppose there are only 2 assets, the objective is to:
 MaxE(Rp) subject to:
 W1+W2=1
 Rp=W1R1+W2R2,
 Var(Rp)=W1Var(R1)+W^2v1(R1)+W^2v2Var(r2)+2W1W2COV(R1R2)
 WHERE: E(Rp)=W1E(R1)+W2E(R2)

The problem is to maximize the expected rate of return & is subject to the constrains for
the choice variables are the “weights”
SYSTEMATIC RISK
β𝑖 =
𝑐𝑜𝑣(𝑅𝑖,𝑅𝑚)
2
σ𝑚
where Rm represents the rate of return for the market portfolio which can be
2
approximated by the market index’s rate of return σ 𝑚is the variance of the rate of return for the
market portfolio
 The numerator represents the correspondence with the market altogether, while the
denominator represents the vavolarity of the entire market. In other words, it shows how
sensitive the rate of return for asset is within
THE CAPITAL ASSET PRICING MODEL (CAPM)
The model describes the “equilibrium” expected rate of return for a risky asset as:
E(Ri)=
EXAMPLE
Suppose the stock with beta risk around 1.2 and the market index’s rate of return as 12% on the
average. Let the basically
EXAMPLE
Suppose the firm’s stock jas the required rate of return as 12% and the Tbill rate as 2% and the
market index’s rate of return as 10%, then we can find the firm’s stock is subject to the
β𝑖=(12%2%)
that ism the firms stock is somewhat more responsive than the market index in the impact from the systematic news
 = 1.25
(10%2%)
SO SINCE β𝑖= 1.25 IT IS RISKIER THAN THE MARKET, because the market is at (1).
WEEK 9 LECTURE 1
03/16/21
RATE OF RETURN AND RISK
CAPITAL ASSET PRICING MODEL (CAPM)
a. The model describes equilibrium expected rate of return for a risky asset as
i.
E(Ri)=Rf+Bi(E(Rm)Rf)
1. Where E(Rm) is the expected rate of return for the market portfolio which
is appropriate by the market index’s average rate of return
2. The tem as E(Rm)Rf can be cled the market premium which shows how
the capital market rewards the investor is taking extra risk
ii.
EXAMPLE: suppose there is a stock with beta risk around 1.2 and the market
index’s rate of return as 12% on the average. Let the basically tbill rate be 2%,
the required rate of return for the stock is:
1. E(R)=2%+1.2(12%2%)2%=14%
2.
b. Diversification with he systematic risk and applications in capital budgeting
i.
Asset 1 has the B1=1.5, asset 2 has B2=0.5 and asset 3 has B3=0.9. The
combinations of the assets will have the systematic risk as 1. We are going to
have the portfolio as
1.
ii.
By the capital asset pricing model with Rf=2% E(Rm)=12%
1. We have E(R1)=17%
2. E(R2)
Capital budgeting with option
Capital budgeting has 3 things assumed (so far):
1. The projects future cash flows are determined or assumed
2. The discount rate for the cash flows is given
3. The projects are continued until the projects are done
a. The real time, the projects can be
a. EXAMPLE
b.
c.
project
chance
Year 1
Year 2
Year 3
1
60%
250
300
350
1
40%
100
100
200
2
60%
300
350
450
2
d.
THE USUAL ANALYSIS IS:
Obtain the expected cash flows in the project together and consider whether it pays off.
The expected cash flows are:
THE NET PRESENT VALUE:
QUIZ 4 WILL BE GIVEN ON WEDNESDAY (TOMORROW, 03/17/21)
WEEK 10 LECTURE 1
IF BETA IS NOT KNOWN, YOU CANNOT USE CAPM.
03/23/21
WEEK 13 LECTURE 1
Capital structure theory
04/13/21
Chapter 11
Introduction to Risk, Return, and the Opportunity Cost of Capital
347
11.4 SelfTest
Suppose the probabilities of the recession or boom are each.30, while the probabil
ity of a normal period is.40. Would you expect the variance of returns on these two
investments to be higher or lower? Why? Confirm by calculating the standard devia
tion of the auto stock. (Refer to Section 11.3 if you are unsure of how to do this.)
The gold mining stock offers a lower expected rate of return than the auto stock and
more volatility—a loser on both counts, right? Would anyone be willing to hold gold
mining stocks in an investment portfolio? The answer is a resounding yes.
To see why, suppose you do believe that gold is a lousy asset, and therefore, you
hold your entire portfolio in the auto stock. Your expected return is 5% and your stan
dard deviation is 10.6%. We'll compare that portfolio to a partially diversified one,
invested 75% in autos and 25% in gold. For example, if you have a $10,000 portfolio,
you could put $7,500 in autos and $2,500 in gold.
First, we need to calculate the return on this portfolio in each scenario. The portfo
lio return is the weighted average of returns on the individual assets with weights equal
to the proportion of the portfolio invested in each asset. For a portfolio formed from
only two assets,
Portfolio rate
of return
(fraction of portfolio rate of return
X
in first asset on first asset
(11.4)
(fraction of portfolio rate of return
+
Х
in second asset on second asset
=
For example, autos have a weight of .75 and a rate of return of —8% in the recession,
and gold has a weight of .25 and a return of 20% in a recession. Therefore, the portfo
lio return in the recession is the following weighted average:9
Portfolio return in recession [.75 X(8%)] + 0.25 x 20%)
= 1%
Table 11.8 expands Table 11.6 to include the portfolio of the auto stock and the
gold mining stock. The expected returns and volatility measures are summarized at the
bottom of the table. The surprising finding is this: When you shift part of your funds
from the auto stock to the more volatile gold mining stock, your portfolio variability
actually decreases. In fact, the volatility of the autoplusgold stock portfolio is con
siderably less than the volatility of either stock separately. This is the payoff to
diversification.
We can understand this more clearly by focusing on asset returns in the two extreme
scenarios, boom and recession. In the boom, when auto stocks do best, the poor return
on gold reduces the performance of the overall portfolio. However, when auto stocks
are stalling in a recession, gold shines, providing a substantial positive return that
boosts portfolio performance. The gold stock offsets the swings in the performance of
the auto stock, reducing the bestcase return but improving the worstcase return. The
inverse relationship between the returns on the two stocks means that returns are more
stable when the gold mining stock is added to an allauto portfolio.
'Let's confirm this. Suppose you invest $7,500 in autos and $2,500 in gold. If the recession hits, the rate of
return on autos will be 8%, and the value of the auto investment will fall by 8% to $6,900. The rate of return
on gold will be 20%, and the value of the gold investment will rise 20% to $3,000. The value of the total portfo
lio falls from its original value of $10,000 to $6,900 + $3,000 = $9,900, which is a rate of return of 1%. This
matches the rate of return given by the formula for the weighted average.
Purchase answer to see full
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