Questions:
QUESTION 1
On September 1, 2012, Al buys a bond for $15,000 that makes coupon payments of $750 after each of following three years and returns its principal of $15,000 at the end of the three years. In other words, it is a standard coupon bond with a 5 percent annual interest rate making payments once each year.
On September 1, 2013, Al receives his first coupon payment of $750. At that time, the market interest rate on bonds like Al's has risen to 6 percent. Al sells his bond to Biff at that time, for a price equal to the present value of the bond's payments.
a. How much does Biff pay Al for the bond?
b. Calculate Al's current yield, capital-gains yield, and total return for the year. On September 1, 2014, Biff receives a coupon payment of $750. The market interest rate on bonds like his remains 6 percent. Biff sells his bond to Cass at that t me, for a price equal to the present value of the bond's payments.
c. How much does Cass pay Biff for the bond?
d. Calculate Biff's current yield, capital-gains yield, and total return for the year.
On September 1, 2015, Cass receives a coupon payment of $750 and the principal of $15,000. Over the course of the year (between September 1, 2014, and September 1, 2015), the market interest rate on bonds like his rose to 7 percent. But Cass decided to keep the bond.
e. What is Cass's total return for the year?
Explain and show all your work for each part.
QUESTION 2 (6 marks)
Consider the bond market to be in equilibrium according to our complete theory of the term structure of interest rates. The current interest rate on one-year bonds is 2 percent, and you believe, as does everyone in the market, that in one year the interest rate on one-year bonds will be 3 percent, and in two years, the interest rate on one-year bonds will be 4 percent. That is, using our standard notation,
= 2%, = 3%, and = 4%.
Assume that there is no term premium on a one-year bond.
a. According to the expectations theory of the term structure of interest rates, what will the interest rate be today on a two-year bond and a three-year bond? That is, what is and Suppose the term premium equals 0.75 percent the number of years to maturity, for the 2-year bond and the 3-year bond.
b. Calculate the interest rate today on the two-year bond and the three-year bond, incorporating the term premium.
c. Draw the yield curve for today, using the values you calculated in part b. Your drawing ould show three points and should be drawn reasonably to scale, showing the values on each axis of each point plotted. Explain briefly (in one or two sentences) why the yield curve
has the shape it does.
QUESTION 3
Loretta buys a one-year debt security on December 31, 2013, for $10,000, which will pay her a nominal interest rate of 5% percent. From December 31, 2013, to December 31, 2014, the inflation rate is 2 percent.
Loretta has a tax rate of 40 percent.a. How much nominal interest (in dollars) does Loretta earn during the year? Show your calculations.
b. How much (in dollars) does Loretta pay in taxes on her interest income? Show your calculations.
c. How much (in dollars) is Loretta's after-tax nominal income? Show your calculations.
d. How much principal (in dollars) does Loretta lose because of inflation? Show your calculations.
e. How much real interest income (in dollars) does Loretta earn? Show your calculations.
f. How much (in dollars) is Loretta's after-tax real interest income? Show your calculations.
g. What percent of Loretta's nominal interest income goes to: (1) her, in the form of after tax real interest income; (2) the government, in the form of taxes; and (3) inflation, in the form of lost principal value? Show your calculations.
QUESTION 4
Suppose the following version of the APT is a good model of risk in the stock market. There are three factors: (1) the stock market's excess return, in percentage points; (2) the change over the last year in the inflation rate, in percentage points; and (3) the spread between ten-year Treasury bonds and three-month Treasury bills, in percentage points. Suppose the stock market's average excess return is 7 percentage points and the average risk-free interest rate is 1 percent, the average change in the inflation rate is 0 percentage points, and the average spread between ten-year Treasury bonds and three-month Treasury bills is 2 ercentage points. Each of the following stocks has the beta coefficients shown in the table below:
Microsoft
Goldcrafters
State Farm
a.
1i
2
3
0
2i
1
2
2
3i
1
1
0
What is the expected return to each of the three stocks? Show your calculations.
b. If the market's excess return were to rise 10 percentage points in a particular year (that is, instead of the average of 7 percent, the market's excess return will be 17 percent), what would you expect the effect to be on the return to each of the three stocks? Show your calculations.
c. If the inflation rate was expected to rise 2 percentage points in a particular year (that is, instead of the average of 0 percent, the inflation rate will rise by 2 percentage points), what would you expect the effect to be on the return to each of the three stocks?
d. If the interest-rate spread rose 2 percentage points in a particular year (that is, instead of the average of 2 percentage points, the interest-rate spread will be 4 percentage points), what would you expect the effect to be on the return to each of the three stocks?