1. Suppose A-rated bonds were trading in the market at a YTM of 10% on all maturities, and you bought an A-rated, 10-year, 9% coupon bond with face value of $1,000 and annual coupon payments. Suppose that immediately after you bought the bond the yield on such bonds dropped to 8% on all maturities and remains there until you sold the bond at your horizon date at the end of four years.
What price did you pay for the 10-year, 9% coupon bond?
Show in a flow matrix the coupons you received on the bond and their values at your horizon date from reinvesting.
What is the price of the original 10-year bond at your horizon date?
What is your horizon date value and total return?
2. Given a 10-year, 10% coupon bond with semiannual payments, $1,000 face value, and currently trading at par, calculate the total return for an investor with a 5-year horizon date, given the following interest rate scenarios:
Yields on such bonds stay at 10% on all maturities until the investor sells the bond at her horizon date.
Immediately after the investor buys the bond, yields on such bonds drop to 8% on all maturities and remain there until the investor sells the bond at her horizon date.
Immediately after the investor buys the bond, yields on such bonds increase to 12% on all maturities and remain there until the investor sells the bond at her horizon date.
Comment on the relation between total return and interest rates.
3. Given the following spot rates on 1-year to 4-year zero coupon bonds:
Year Spot Rate
1 8.0%
2 8.5%
3 9.0%
4 9.5%
a. What is the equilibrium price of a four-year, 9% coupon bond paying a principal of $100 at maturity and coupons annually?
b. If the market prices the four-year bond such that it yields 10%, what is the bond's market price?
c. What would arbitrageurs do given the prices you determined in (a) and (b)? What impact would their actions have on the market price?
d. What would arbitrageurs do if the market price exceeded the equilibrium price? What impact would their actions have on the market price?
4. Bond X is a one-year zero with face value of 1,000 trading at $945 and Bond Y is a two-year zero with a face value of 1,000 trading at $870.
a. Determine algebraically the implied forward rate f11.
b. Explain how the forward rate can be attained by a locking-in strategy.
5. Suppose an investor is planning to buy a stock currently priced in the market at $200 and expected to pay an annual dividends of $20 in each of the next three years and to sell for $100 at end of the third year. Assuming the investor can reinvest her dividends at 10%, what is the investor's expected total return on the stock?
6. Suppose a well-established company is expected to have a constant growth rate in dividends of 5% for a very long time. What is value of the company's stock, if its current dividends are $1 per share and the discount rate investors require on the stock is 10%? What would be the value of the stock if it were expected to grow at 7% for three years and then 5% thereafter?