FINA1310, Spring 2023 Problem Set 2
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Problem Set 2
FINA1310, Spring 2023
1. (25 points) A bond with face value of $1,000 is currently traded at $1,050. It matures in 10 years. Its coupon rate is 20%, paid quarterly.
(a) (5 points) What is its current yield?
(b) (5 points) What is its YTM?
(c) (5 points) What is EAR?
(d) (10 points) Suppose that you decided to sell this bond 2 years later (after eight coupon pay- ments). After selling it, you have realized a capital gain of 10%. What is YTM of the bond at the moment of selling?
2. (15 points) After negative news about corporation’s A earnings, its credit rating was reduced from Aaa to Baa. As a result, the yield to maturity of its twenty-year bond with face value of $1,000, coupon rate of 10% and semiannual payments, increased from 6% to 8%. As a result of the down- grade, what is the capital gain of your portfolio that consists of 100 of such bonds?
3. (15 points) A stock has just paid a dividend of $20. For the coming four years, it is expected to increase its dividends at 5% per year. After that, the growth rate is going to slow down to 2%. Suppose that required rate of return is 10%.
(a) (10 points) Compute the price of the stock.
(b) (5 points) Suppose that you hold the stock for one year. Compute your holding period return.
4. (25 points) Consider a stock that has just paid a dividend $2 per share. Going forward, it is expected to increase its dividend payment at 2% per year (dividends are paid annually). Current stock price is $51.
(a) (5 points) What is the rate of return required by investors?
(b) (5 points) Suppose that the economy is hit by a recession. During the recession, you expect
the company to stop paying dividends. The recession is expected to last for two years. After the recession is over, you expect the dividend growth rate to return to 2% per year (that is, the first dividend payment after recession is going to be $2 × 1.02). Using the same required rate of return as in (a), compute the new stock price.
(c) (5 points) Now suppose that with probability 20% the company is going to go bankrupt (in which case it will stop pay dividends forever) after the recession. With probability 80%, it is going to survive and return to 2% annual dividend growth rate after the recession. Suppose that the required rate of return is the same as in (a). What is the stock price then?
(d) (10 points) Now suppose that recessions happen on average once every 10 years. That is, you expect the economy to be in recession in the coming 2 years, then the economy is expected to stay in the normal stage for 8 years, then a new 2-year recession is expected to occur, and so on. Assuming that the company is not going to pay any dividends during recessions (but also is not going to default) and is going to pay increasing dividends during non-recession years (with annual growth rate of 2%), compute the stock price. In particular, starting from next year, dividends are expected to be $0, $0, $2 × 1.02, $2 × 1.022 , . . . , $2 × 1.028 , $0, $0, $2 × 1.029 , $2 ×
1.0210 , . . . , $2 × 1.0216 , $0, $0, . . . . Assume that the required rate of return is the same as in (a).
5. (20 points) Suppose that project’s cash flows are C0 = $82, C1 = −$30, C2 = −$100, C3 = −$100, C4 = $150. Required rate of return is 10%.
(a) (5 points) Compute NPV. Should you take the project based on the NPV rule?
(b) (5 points) Suppose that the project generate an additional cash flow C5 at the end of year 5.
What is the size of C5 that makes you indifferent between implementing the project and not taking it?
(c) (5 points) Suppose again that there is no additional cash flows after year 4. Compute IRR of this project. What would be an appropriate IRR rule for this project (i.e., for which required rates of return the project should be accepted)?
(d) (5 points) Suppose now that signs of cash flows are flipped, i.e., C0 = −$82, C1 = $30, C2 = $100, C3 = $100, C4 = −$150. What is IRR rule now?
2023-03-09