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Loan Amortization and Positive NPV Exam Notes

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DuPont Equation Chapter 2
ROE = PM * TATO * EM
PM = Profit Margin = Net Income/Sales
TATO = Total Asset Turnover = Sales/Assets (CA+FA)
EM = Equity Multiplier = Assets/Equity
The more debt you use, the more EM increases
ROA=PM*TATO
Highest TA= most efficient and lowest cost
Highest PM= most control over price, monopoly
Highest EM= most debt, interest paid on debt is tax
deductible
NWC (net working capital)=CA-CL
Total Liability=CL+LTD (long-term debt)
Total Equity=TA-TD
Chapter 1
Types of business organizations and their costs and
benefits: proprietorships, partnerships, LLCs,
corporations
Limited liability over firms debt: LLC, corporations,
limited partners (general partners have liability)
Double taxation: C Corp taxed on income/dividends
o Effective tax rate=TaxEarnings...Earnings before
taxes-Regular= Net income - Dividends -
Personal/wage tax
o (Pre-tax amount)(Dividends)*((1-new tax)*(1-old
tax)*(1-individual dividend tax)/#of shares
outstanding
Objective of financial manager: maximize shareholder
wealth
Roles of financial manager: investment decisions,
financing decisions, and (short-term) cash management
Financial markets: primary vs. secondary, dealer vs.
auction
o Secondary is bigger (shareholder-to-shareholder);
Primary=IPO
o Bid (buy) prices and ask (sell) prices; liquidity
lowers transaction costs
Net Income is not a cash flow…includes depreciation,
revenue that hasn’t been received
Financial Institutions: move funds to investors to
companies, move funds through time, spread out risk
Chapter 3
NPV=PV(benefits)>PV(costs)
Valuation Principle: different people/companies value
products differently but price is same in competitive
market
When interest rates go up, PV goes down
Arbitrage and the Law of One Price
o Arbitrage would exist if prices differ in perfectly
competitive market
o Buying low and selling high in different markets
at the same point of time
Concept of time value of money
o Costs and benefits can be compared when cash is
realized at different time periods by measuring
values at the same time period
o TVM equation for a lump sum:
FV = PV(1+r)
N
<--> PV = FV/(1+r)
N
o r is always a periodic rate
Rule of 72: 72/(interest rate)
Discount rate: the interest rate, r.
o The same rate in both compounding and
discounting
Discount factor: the present value of $1 in one year:
1/(1+r)
Chapter 4
Present value of uneven cash flows: PV = C
1
/(1+r) + C
2
/(1+r)
2
+ … + C
N
/(1+r)
N
o NPV(7,0,{100,200,300},{1,2,2})
o NPV(interest rate,PV at 0,{CF1, CF2...CFn},{m1,m2...mn}) where m=times per year
Perpetuities: PV = C/r, where C is a recurring payment every period forever
Annuities: PV = C/r[1-1/(1+r)
N
], where C is a recurring payment every period until N
Growing Perpetuities: PV = C/(r-g), where g is the growth rate in C and C is the period 1 cash flow
Growing Annuities:
o PV = C/(r-g){1-[(1+g)/(1+r)]
N
}
You can only use the growing perpetuities and growing annuities formulas if r > g
Positive NPV indicates favorable investment
Chapter 5
Effective Annual Rate (EAR): EAR = (1+APR/m)
m
1,
where m is the number of compounding periods within
the year
o Periodic rate, r = APR/m
o APR = [(1+EAR)
1/m
1]*m
o Use EAR to compare loans or savings options
o Use EAR to price a security with different number of
periods per year.
o EAR is used to compare alternative investments
o APR is used for time value of money problems (quoted
rate)
Loan Amortization:
o The amount that a loan payment pays down principal is
whatever is left over after paying the interest. If the
loan payment is PMT and the period interest rate is r:
PMT = Interest Portion + Principal Portion
Interest Portion: Total Loan Balance at Beginning
of Period * r
Principal Portion: PMT Interest
New Loan Balance = Loan Balance at Beginning
of Period Principal Portion
o EAR in calc: EFF(10,12) EFF(int rate,m)
o APR in calc: NOM(10.47,2) NOM(EAR,# of
periods)

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Chapter 1 • Types of business organizations and their costs and benefits: proprietorships, partnerships, LLCs, corporations • Limited liability over firms debt: LLC, corporations, limited partners (general partners have liability) • Double taxation: C Corp taxed on income/dividends o Effective ...
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