Part I Bonds

Assume that all bonds have a face value of $1,000 unless otherwise noted.

1. What is the price of a 30-year, zero coupon bond with a YTM of 5%?

2. Take the bond above and add an annual coupon of 4.8%. Now what is the price?

3. A semiannual coupon bond has a 5.8% annual coupon rate, a semiannual YTM of 3%, and a price of $950. What are the bond equivalent yield, effective annual yield, and current yield?

4. What is the YTM of a semiannual coupon bond that matures in 30 years with an annual coupon rate of 5% and a price of $1,050? What if instead the coupons were quarterly? Annual?

5. Consider 3 Treasury bonds, which pay semi-annual coupons. Each bond has a face value of $1,000. Bond A has 5 years remaining to maturity and a coupon rate of 10%. Bond B has 20 years remaining to maturity and a coupon rate of 10%, and Bond C has 20 years remaining to maturity and a coupon rate of 4%.

(a.) If all bonds provided a 10% return (APR, compounded semiannually) if they were purchased today and held to maturity, what is the price today of each of the bonds? Essentially, what is the price of each bond if the YTM is 10%?

(b.) What is the price of each bond if the YTM was 4%? What if it was 16%?

6. Two years ago Gadget Geek Inc. (GG) issued a high-yield (or junk) bond with a coupon rate of 20%, paying semi-annual coupons. When originally issued the bond was sold at par and had four years until maturity. Currently, GG bonds have a yield-to-maturity of 15%. By how much is the duration of GG bonds higher than that of an AAA rated zero-coupon bond with an interest rate of 7% (EAR) and 23 months until maturity? (Report a negative number if GG has the lower duration of the two.)

7. Consider again the 3 Treasury bonds that pay semi-annual coupons. Each bond has a face value of $1,000. Bond A has 5 years remaining to maturity and a coupon rate of 10%. Bond B has 20 years remaining to maturity and a coupon rate of 10%, and Bond C has 20 years remaining to maturity and a coupon rate of 4%.

(a) Using Excel, create a single graph showing the price of Bonds A & B for varying YTMs. Let YTM range from 0.5% to 18% per year (compounded semi-annually) in increments of 50 basis points (1 basis point is 1/100 of a percent thus examples of a 50 basis point change would be a change from 4.5% to 5% or 11.2% to 11.7%). Is the graph linear? If not, what shape is it? Does a change in YTM affect the price of each of the two bonds the same way? Why or why not?

(b) Create a similar graph for Bonds B & C. Is the graph linear? If not, what shape is it? Does a change in YTM affect the price of each of the two bonds the same way? Why or why not?

Part II Stocks

1. Datacorps most recent dividend (D₀) was $2.50; its growth rate is 5% and its cost of capital is 10%.

a. What is the value of Datacorps stock according to the constant growth DDM model?

b. What is the percentage price change in Datacorps price if the cost of capital increases to 11%?

c. What is the percentage price change in price if the growth rate falls to 4.5% (assume the cost of capital remains at 10%)?

2. You expect Nokia to pay dividends of $1, $2, and $3 over the next three years. Beginning in year 3, you expect Nokias dividend to grow at a constant rate of 7% per year. If your required return on Nokia is 12%, what is the intrinsic value of this stock based on the DDM model?

3. Using the constant DDM model, what must be the growth rate of a stock that is selling for $50, has a cost of capital of 12%, and just paid a dividend (D₀) of $2?

4. GMs stock price is $32.18. The expected dividend next year (D₁) is $1.52. Assume GM has a discount rate of 11%

(a) According to the constant growth DDM, what is GMs expected growth rate?

(b) If GMs expected earnings per share is $6, what is the present value of its growth opportunities (PVGO)? Explain what your answer means.

(c) What do you expect GMs stock price to be in 5 years?

5. QuickStart is growing at a rapid pace of 20% per year. Analysts expect growth to slow to 10% after 5 years and then finally reach a perpetual rate of 2% after 10 years. QuickStart recently paid a dividend of $5 per share. The cost of capital is 8%.

(a) What is the stock price?

(b) If QuickStarts earnings are expected to be $7 per share, what are the values of its assets in place and growth opportunities, i.e., its No Growth Value and the Present Value of its Growth Opportunities?

6. Beth Knight, CFA, and David Royal, CFA, are independently analyzing the value of Bishop, Inc. stock. Bishop paid a dividend of $1 last year. Knight expects the dividend to grow by 10% in each of the next three years, after which it will grow at a constant rate of 4% per year. Royal also expects a temporary growth rate of 10% followed by a constant growth rate of 4%, but he expects the supernormal growth to last for only two years. Knight estimates that the required return on Bishop stock is 9%, but Royal believes the required return is 10%.

(a) Without doing any computations, which analyst has a higher estimate of value?

(b) Compute the two estimates of the stock price.