Finance Homework: Money Multiplier, Interest Rates, and Bonds

This finance homework assignment presents a series of problems covering key concepts in financial economics and investment analysis. The assignment begins with questions on the money multiplier and the impact of government securities purchases on the money supply. It then delves into macroeconomic topics, including the effects of tax cuts, interest rate parity, and the impact of inflation expectations on real and nominal interest rates. The assignment further explores investment strategies, including bond valuation, yield to maturity calculations, and the analysis of commercial paper and stock valuation using dividend discount models. Finally, it covers portfolio management, including the differences between standard deviation and beta coefficients and the calculation of expected portfolio returns and beta coefficients.

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Complete 11 of the 12 problems below:
1. The required reserve ratio is given as rr.
a. (7 pts) Show that the money multiplier, , is equal to ; where rr is
the required, reserve ratio, DD is the demand deposit. (HINT: begin with
MS = tDD). MS is defined as the money supply.
Answer:
MS is equal to Deposit(DD) + Currency (C )
If Time is Equal to 1 then ,
MS = (1-rr)DD >> rr = (DD-MS)/DD
So,
1/rr = DD/(DD-MS) where MS = DD + C
So,
1/rr = DD/ (DD-DD + C ) >> DD/C which is also known as multiplier
Hence, Money Multiplier = 1/rr
b. (3 pts) If the FED buys $1,000,000 of government securities, what is the
net effect on the money supply? (Be sure to specify if your answer is a net
increase or net decrease of the money supply).
Answer:
If FED buys government securities than it leads to increase in money
supply in the economy. So, FED buying $1,000,000 of government
increase will lead to net increase in money supply in economy.
2. (10 pts) President Trump promises cuts to the wealthy and corporations. His
claim will be that additional tax cuts will continue to stimulate economic growth
(reduce unemployment and increase real output) and place downward pressure on
interest rates? Argue in support or against President Bush economic stimulus. Be
thorough in your analysis.
Answer:
My view is against the Tax cuts proposed by President Trump.
A) It will reduce federal revenues by a huge amount
B) It will lead to increase in federal deficit which is already very high currently
C) Decrease in fed revenues will lead to delay in payment of debt owned by
American government
D) Such reduction in revenues will lead to reduce allocation to Healthcare and
child care and also spending on poor sections of society

E) Reducing interest will again lead increase in borrowing of funds and such
cheaper borrowing can again lead to housing crisis as happened in 2008.
3. The first period spot interest rate is ti1, the expected interest rate in the second time
period is t+1i1e, and the two-year (annual interest rate, for two years) spot interest
rate is ti2.
a. (5 pts) Show that ti2 = [(1 + ti1)(1 + t+1i1e)]1/2 - 1
b. (5 pts) If the one-year spot rate is 4% and the 2-year spot interest rate is
2%, what is the expected interest rate for time period 2?
c. (5 pts) Is the yield curve upward-sloping or downward-sloping? Why?
4. (10 pts) If market participants fully expect inflation in the next year to increase, what
is the net effect on the real interest rate, nominal interest rate and the quantity of
loanable funds?
Answer:
Inflation is difference between nominal and real interest rates. So, if inflation is
tended to increase next year then nominal interest rate will remain constant but real
interest will decrease. Demand for loanable funds will decrease due to increasing
interest rates.
5. As a portfolio manager for an insurance company, you are about to invest funds in
one of three possible investments: (1) 10-year coupon bonds issued by the U.S.
Treasury, (2) 20-year zero-coupon bonds issued by the U.S. Treasury, or (3) one-
year Treasury securities. Each possible investment is perceived to have no risk of
default. You plan to maintain this investment over a one-year period. The return of
each investment over a one-year horizon will be about the same if interest rates do
not change over the next year. However, you anticipate that the U.S. inflation rate
will decline substantially over the next year, while most of the other portfolio
managers in the United States expect inflation to increase slightly.
(a.) (5) If your expectations are correct, how will the return of each investment be
affected over the one-year horizon?
Answer:
Decrease in inflation leads to increase in net returns from bonds. Impact of inflation
on different securities is as follows:
1) Net returns after inflation will increase in this case
2) As zero coupon bonds pay interest at maturity so there will be no change
3) Net returns after inflation will increase in this case
(5 pts) If your expectations are correct, which of the three investments should have
the highest return over the one-year horizon? Why?
Answer:
Increase in inflation leads to decrease in net returns from bonds. Impact of inflation
on different securities is as follows:
1) Net returns after decrease will increase in this case
2) As zero coupon bonds pay interest at maturity so there will be no change
3) Net returns after decrease will increase in this case
6. (10 pts) Calculate the yield to maturity on a 10 percent coupon bond (paid semi-
annually), with a $1000 face value and 20 years remaining to maturity. The bond is
selling at $950.

Answer:
Approx YTM : [Coupon + (Face Value – Price)/Number of Years] / {(Face Value +
Price)/2 }
YTM : [ 100 + (1000-950)/40 ] / { (1000 + 950) / 2 } = 10.54%
7. (10 pts) A bond’s yield to maturity is less than its coupon. Assuming no change in
interest rates, would you expect its price in one year to be higher, lower, or
unchanged? Explain why.
Answer:
YTM can be less than coupon only when the bond is selling at premium as compared
to its price.
If interest rates remain unchanged then price of bond will be lower as compared to
previous years. Because YTM will increase in next year and consequently price will
decrease.
8. (10 pts) A $1 million commercial paper issue sold at a discounted price of $982,000.
It matures in 100 days. Calculate its annual rate of return.
Answer:
Annual Rate of Return is:
Start
Value
End
Value
Period in
Years Annual Rate of Return
Values 982000 1000000 0.273972603 6.8546%
Remarks (100/365)
=((End Value/Start Value)^(1/Periods)
-1
9. (10 pts) Traditional Film is a company in a declining business. Dividends are
expected to decrease at a 10% rate. Last year’s dividend was $3 per share. The
required return for Traditional Film is 25%. What would you pay for a share of the
stock?
Answer:
The above question can be solved using Dividend Discount Model:
Price = Dividend of Next Year / (Cost of Capital – Growth Rate )
So, Price = 2.7 / { 25% - ( - 10%)} = 2.7/0.35 = $7.71

10. (10 pts) An analyst has made the following explicit estimates of EkG stock’s future
dividends:
T 1 2 3 4 5
Div $1.25 $1.37 $1.40 $1.40 $1.50
After 5 years the stock is expected to quit growing and pay a constant dividend of
$1.50 forever. If investors require a 10% return from the stock with EkG’s risk, what
should be the stock’s price?
Answer:
T 1 2 3 4 5 After 5
Years
Stock Price is
Sum of all
Dividends
Div $1.25 $1.37 $1.40 $1.40 $1.50 $1.50
Return $1.14 $1.13 $1.05 $0.96 $0.93 $15.00 $20.21
Annuity
Factor 1.1 1.21 1.331 1.4641 1.61051 0.1
11. (10 pts) What is the difference between the standard deviation of a stock’s return and
a stock’s beta coefficient?
Answer:
Standard Deviation (SD):
SD is also referred as volatility of a stock i.e. measure of dispersion of its return.
SD is calculated as square root of variance of stock from its mean.
High SD means returns of a stock vary largely and are spread out compared to
mean returns.
Low SD means returns of a stock are very close or near to its mean.
SD measures total risk of a stock.
Beta:
Beta in simple terms is volatility of a stock as compared to market index. For
example: Apple’s Beta is 1.5 it means if S&P500 rises by 1% then apple is
expected to rise 1.5%.
Beta measures systematic risk of stock.
Higher beta means the stock is more volatile compared to index.
Lower beta means the stock is less volatile compared to index.
12. (10 pts) Provide an algebraic expression for the expected return of an N-asset
investment portfolio and its beta coefficient. The expected return on each asset is

defined as Ri and its beta coefficient is βi; where i =1, 2, …, N. Explain these
expressions.
Answer:
Algebraic expression for calculating Expected return of N-asset Investment
portfolio is as follows:
Here,
Bportfolio: Beta of porfolio calculated using weight of stocks and their individual
betas.
Expected Return Market: It is expected return of market calculated using previous
datas of makret
Risk free rate: It is rate of government securities i.e. rate of US government
treasury bonds.