NAME: ____________________________
PERCENT
________POINTS _______
5 problems on FUTURE VALUE and PRESENT VALUE (2 points each) (show work for
possible partial credit)
1.
PRESENT VALUE of $10,000, at 2.3%, 2 years
2.
FUTURE VALUE of $10,000, at 1.25%, 1 year
3.
FUTURE VALUE of $1,000, at 3.5%, 4 years
4.
PRESENT VALUE of $1,000,000, at 0.5%, 6 months
5.
FUTURE VALUE of $750, at 0.75%, 9 months
6.
This graph shows an initial equilibrium in the Market for Loanable Funds.
a.
Show the changes in the graph if the fiscal authorities (i.e. Congress and
President) increase government spending substantially. (6 points)
the
b.
In this case the equilibrium interest rate (choose one) . . .
i.
increases
ii.
decreases
c.
In this case the equilibrium quantity of loans (choose one) . . .
i.
increases
ii.
decreases
7.
If the Market for Loanable Funds shows a nominal interest rate of 7%, use the
Fisher Equation -- inominal = E(INF) + rreal -- to find the real rate of
interest if
expected inflation is 3%. (2 points)
8.
For each of the following, indicate whether it takes place in the primary market
or the secondary market for securities. (circle the correct answers) (2 points)
a.
the first
b.
exchange
A successful startup corporation decides to issue shares to the public for
time. (primary/secondary)
You buy 100 shares of Apple Inc., which is listed on the NASDAQ
(primary/secondary)
Unit II: Markets
Interest Rates; Securities
Unit II: Markets
Basic principles of interest rates & fixed-income
markets:
▪time preference
▪ time-value of money
▪ future value (compounding)
▪ present value (discounting)
Unit II: Markets
You will use compounding (future value) and
discounting (present value) in all financial applications
FOREVER.
Unit II: Markets
“. . . the European philosophical tradition . . .
consists of a series of footnotes to Plato”
-- Alfred North Whitehead
“All finance is a series of footnotes to
compounding and discounted present value”.
--Lawrence Morgan
Unit II: Markets
People prefer consumption now to consumption later.
So, if they are to defer consumption – that is, if they are to
save – they require getting something additional in the future.
That is the rate of interest.
e.g. to forego $1.00 now you require $1.10 one year from
now.
That is a 10% (= 0.10) rate of interest. And $1.10 is the
future value of $1.00.
Future Value of $1 for 1 year = $1.10
𝐹𝑉 $1,1 𝑦𝑒𝑎𝑟, 𝑖 = $1 × 1 + 𝑖 1
𝐹𝑉 $𝑥, 1 𝑦𝑒𝑎𝑟, 𝑖 = $𝑥 × 1 + 𝑖 1
𝐹𝑉 $100,1 𝑦𝑒𝑎𝑟, 10% = $100 × 1 + 𝑖 1 = $110
Unit II: Markets
The same principle works for periods longer or shorter than 1
year:
𝐹𝑉 $𝑥, 𝑇𝑦𝑒𝑎𝑟𝑠, 𝑖 = $𝑥 × (1 + 𝑖)𝑇
e.g. for $100 for 2 years at 5%
FV($100, 2 years, 5%) =
e.g. for $100 for 6 months (= 0.5 year), at 5%
FV($100, 0.5 years, 5%) =
Unit II: Markets
Present value
If you turn future value around, you get present value
𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 = $1.10 = 1.10 × $1
divide both sides of the equation by 1.10
𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒
1.10
=
$1.10
1.10
=
1.10
×
1.10
$1 = $1 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒
In general
𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 × (1 + 𝑖)𝑇
𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 =
𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒
1+𝑖 𝑇
Unit II: Markets
Present value
So Present Value of $x to be paid in T years discounted at r is
...
𝑃𝑉 $𝑥, 𝑇 𝑦𝑒𝑎𝑟𝑠, 𝑖 =
examples:
𝑃𝑉 $1, 2 𝑦𝑒𝑎𝑟𝑠, 10% =
𝑃𝑉 $1, 0.5 𝑦𝑒𝑎𝑟𝑠, 10% =
$𝑥
(1+𝑖)𝑇
Unit II: Markets
Present value
Note: as r rises, PV falls; as i falls, PV rises
Bond prices: the price of a bond is the Present value of the
payments it will make
For short-term instruments (e.g. Treasury bills) there is only
one payment; for long-term bonds there are many payments
(interest payments, and eventually the “face value” of the
bond). The price or PV of the bond is the sum of the PVs of all
those payments.
Unit II: Markets
Present value
Note: as i rises, PV falls; as i falls, PV rises.
Compare PV of $100 to be received in 2 years at (a) 10% and
(b) at 5%:
𝑃𝑉 $100,2 𝑦𝑒𝑎𝑟𝑠, 10% =
𝑃𝑉 $100,2 𝑦𝑒𝑎𝑟𝑠, 5% =
Unit II: Markets
The Rate of Interest (continued)
Where does “the interest rate” come from? (actually many interest
rates)
LOANABLE FUNDS THEORY
Unit II: Markets
The Rate of Interest (continued)
LOANABLE FUNDS THEORY is basic supply and demand theory
DEMAND FOR LOANABLE FUNDS (demand for credit) from . . .
a) Households (for car, house, appliances, . . . )
b) Businesses (for investment, trade finance, inventory finance, . . . )
c) Government (for infrastructure, uneven tax receipts, general
spending)
d) Foreign sources (all of the above)
Unit II: Markets
The Rate of Interest (continued)
Interest Rate r
LOANABLE FUNDS THEORY is basic supply and demand theory
Demand for loanable funds
Quantity of Loans
Unit II: Markets
The Rate of Interest (continued)
LOANABLE FUNDS THEORY is basic supply and demand theory
SUPPLY OF LOANABLE FUNDS (supply of credit) from . . .
a)
b)
c)
d)
Households from savings (directly or indirectly)
Business (retained earnings)
Government (budget surplus, tax receipts)
Foreign supply (all of the above).
Unit II: Markets
The Rate of Interest (continued)
Interest Rate r
LOANABLE FUNDS THEORY is basic supply and demand theory
Supply of loanable funds
Quantity of Loans
Unit II: Markets
The Rate of Interest (continued)
LOANABLE FUNDS THEORY is basic supply and demand theory
Equilibrium determination of interest rate
Interest Rate r
S
D
Quantity of Loans
Unit II: Markets
The Rate of Interest (continued)
This is supply and demand for credit.
It determines an interest rate (the price of credit).
Once you know the interest rate, you can calculate the price
of a bond or loan (more about this later).
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
a) Economic growth
generally, strong growth will shift the demand for credit
-- and probably the supply of credit – to the right.
This tends to push interest rates higher.
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
Interest Rate r
S
S´
r2
r1
D
Quantity of Loans
D´
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
b) Inflation
Distinguish nominal interest rates and real interest rates.
1. the nominal rate is that actual rate that borrowers
pay and lenders receive.
2.
if there is inflation, the dollars that a borrower pays
back and a lender receives are worth less than
when the loan was made, so the real rate of
interest is lower.
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
b) Inflation (continued)
The difference between nominal and real rates is the
rate of inflation. If the borrower receives 5% interest
but inflation has been 4%, the real rate is 1%. (actually
expected inflation)
i = E(INF) + rR or
rR = i – E(INF)
(called the “Fisher effect”)
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
b) Inflation (continued)
Unit II: Markets
Figure 4.5 Expected Inflation and Interest Rates (ThreeMonth Treasury Bills), 1953–2013
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
c) Monetary policy
basically, if the central bank increases the rate of growth
of the money supply, that will lower short-term interest
rates
-- unless the money supply grows so rapidly that
expected inflation increases.
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
c) Monetary policy
Interest Rate r
S
S´
r1
r2
D
Quantity of Loans
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
d) Fiscal policy
a budget deficit represents additional demand for credit, so this
raises interest rates; a budget surplus reduces interest rates.
although this is demand from the government (particularly the
national government) all the rates are connected so this will have
an impact on corporate, municipal, and other interest rates.
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
d) Fiscal policy
S
Interest Rate r
r2
r1
D
Quantity of Loans
D´
Unit II: Markets
Factors that affect interest rates (or the price of bonds)
e) Foreign demand for credit
Foreign entities can borrow or lend in our market.
However, even activity in foreign markets affects our domestic
market since the markets are all connected. (This will also affect
the foreign exchange markets.)
Unit II: Markets
Recent history of U.S. short-term interest rate
Unit II: Markets
Securities
These are the basic items which are bought and sold in
financial markets: principally stocks and bonds.
They allow savings to move to investors more-or-less
anonymously and therefore allow investors to mobilize
large amounts of resources.
Unit II: Markets
Securities
❖Primary Market: securities are originally issued or sold
in the primary market (new stock is issued, new bonds
are sold)
– this is typically used to raise capital for an
enterprise.
Unit II: Markets
Securities
❖Secondary Market: after the securities are issued in the
primary market, they can be bought and sold in the
secondary market; the prices of the securities varies
– an investor will be more willing to buy securities
in the primary market if it is possible to liquidate the
investment at will; otherwise the investor would
have to hold shares forever or hold bonds until
maturity.
Unit II: Markets
Securities Valuation (overview)
1. Information (and even misinformation) is key to
valuations.
2. Securities regulation tries to see to it all relevant
information is public.
3. Cash flows are the central to valuation – you will work
with these in detail shortly.
4. Efficient Markets Hypothesis – the hypothesis that the
market price reflects all the information about an
asset so that no one can reliably earn returns higher
than that of the overall market – HIGHLY
CONTROVERSIAL
UNIT II: MARKETS
CLASS OUTLINE
I.
Interest rates
These are the basis of all financial markets
All finance is a series of footnotes to compounding and discounted present value”.
A.
Basic principles of interest rates & fixed-income markets:
1.
Time preference
2.
Time value of money
3.
Future value (compounding)
4.
Present value (discounting)
B.
Time preference and the time value of money
People prefer consumption now to consumption later.
if they defer consumption – if they SAVE – they require something additional in
future THAT IS THE RATE OF INTEREST
REMEMBER THAT 10% MEANS 0.10 – that's what we use in calculations.
C.
Future value (compounding)
If you invest $1 for one year at a rate of r percent, the "future value" of that $1 is
what you get back – the $1 plus interest – after one year.
𝐹𝑉($1,1 𝑦𝑒𝑎𝑟, 𝑖) = $1 × (1 + 𝑖)1
Same thing for $x:
𝐹𝑉($𝑥, 1 𝑦𝑒𝑎𝑟, 𝑖) = $𝑥 × (1 + 𝑖)1
e.g. 𝐹𝑉($100,1 𝑦𝑒𝑎𝑟, 10%) = $100 × (1 + 𝑖)1 = $110
For longer or shorter periods:
𝐹𝑉($𝑥, 𝑇𝑦𝑒𝑎𝑟𝑠, 𝑟) = $𝑥 × (1 + 𝑖)𝑇
e.g. FV($100,2 years,5%) =
FV($100,6 months = 0.5 year,5%) =
D.
Present value (discounting)
This is the INVERSE of future value: If you know you will receive $1.10 one year
from now, and the interest rate is 10%, what is that expected amount worth now?
Page 1 of 6
That is "present value"
𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒
1.10
=
$1.10
1.10
1.10
= 1.10 × $1 = $1 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒
In general:
𝑭𝒖𝒕𝒖𝒓𝒆 𝒗𝒂𝒍𝒖𝒆 = 𝑷𝒓𝒆𝒔𝒆𝒏𝒕 𝒗𝒂𝒍𝒖𝒆 × (𝟏 + 𝒊)𝑻
𝑷𝒓𝒆𝒔𝒆𝒏𝒕 𝒗𝒂𝒍𝒖𝒆 =
𝑭𝒖𝒕𝒖𝒓𝒆 𝒗𝒂𝒍𝒖𝒆
(𝟏+𝒊)𝑻
So, the present value of $x to be received afterT years discounted r%:
𝑃𝑉($𝑥, 𝑇 𝑦𝑒𝑎𝑟𝑠, 𝑟 ) =
$𝑥
(1+𝑖)𝑇
e.g. 𝑃𝑉($1,2 𝑦𝑒𝑎𝑟𝑠, 10%) =
𝑃𝑉($1,6 𝑚𝑜𝑛𝑡ℎ𝑠 = 0.5 𝑦𝑒𝑎𝑟𝑠, 10%) =
Present Value is used to compute the price of all bonds, short-term and long-term.
For short-term markets there is only one payment; for long-term markets there are
many payments of both interest and principal.
NOTE: PV and interest rate move inversely:
as i rises, PV declines; as i declines, PV rises.
compare PV of $100 to be received in 2 years, discounted (a) 10% (b) 5%
𝑃𝑉($100,2 𝑦𝑒𝑎𝑟𝑠, 10%) =
𝑃𝑉($100,2 𝑦𝑒𝑎𝑟𝑠, 5%) =
E.
Where do interest rates come from? LOANABLE FUNDS THEORY
Basic supply and demand:
1.
Demand comes from . . .
Page 2 of 6
Interest Rate r
Quantity of Loans
Supply comes from . . .
Interest Rate r
2.
Quantity of Loans
3.
Equilibrium determination of interest rate
Interest Rate r
S
D
Quantity of Loans
NOTE: this is the supply and demand for credit; its price is the interest rate.
Once that is known, you can calculate the present value of a bond, etc.
F.
Factors that affect interest rates
a.
Economic Growth:
Page 3 of 6
Interest Rate r
S
S´
r2
r1
D
D´
Quantity of Loans
b.
Inflation: if prices are rising
(1) credit demanders (deficit units)
(2) credit suppliers (surplus units
-- together these increase the interest rate
S´
S
Interest Rate r
r2
E(INF)
r1
D´
D
Quantity of Loans
terms:
nominal interest rate : the actual rate in a transaction
real interest rate :
the interest rate adjusted for inflation
if the borrower pays 5% per annum but expected inflation is 4%, the
"real" interest rate is 5% - 4% = 1%
this is the "Fisher Effect":
𝒓𝒏𝒐𝒎𝒊𝒏𝒂𝒍 = 𝒓𝒓𝒆𝒂𝒍 + 𝑬(𝑰𝑵𝑭) or 𝒓𝒓𝒆𝒂𝒍 = 𝒓𝒏𝒐𝒎𝒊𝒏𝒂𝒍 = 𝑬(𝑰𝑵𝑭)
Here, the real interest rate is the difference between the blue and red lines:
Page 4 of 6
c.
Monetary policy:
Interest Rate r
S
S´
r1
r2
D
Quantity of Loans
d.
Fiscal policy:
S
Interest Rate r
r2
r1
D
D´
Quantity of Loans
e.
Foreign demand and supply: the same things but from foreign sources.
Recent history of U.S. short-term interest rates
Page 5 of 6
II.
Securities
A.
Financial markets primarily buy and sell securities
B.
Primary market
C.
Secondary market
After a security is issued in the primary market it can be sold to someone else. (This
is most of what you see in the daily trading of stocks and bonds.)
D.
Valuation of securities
1.
Information is the key.
2.
Securities regulation tries to be sure all relevant information is public.
3.
Cash flows are crucial to valuation.
4.
"Efficient markets hypothesis" – that the market price reflects all relevant
information so no one can reliably earn higher-than-market returns.
HIGHLY CONTROVERSIAL
Page 6 of 6
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