Managerial Finance (MGMT 221)
Solution to Securities Practice Problems
- A 4-year, $1,000 face value bond has a coupon rate of 12% (paid annually) and sells for $1,097.19. What is the yield-to-maturity of the bond? Hint: The answer is an integer percentage.
Answer: Since the price is above $1,000, we know that the interest rate must be below 12%. Trial and error, a financial calculator, or Excel will show that
PV = $120 PVIFA9%,4 + $1,000/1.094 = $1,097.19. So, the yield-to-maturity is 9%. - A bond with an 8.6% coupon rate sells at par. What is the yield-to-maturity of the bond? Suppose that the yield-to-maturity is still the same after one year. What would the capital gains yield be over that year? What would the coupon yield be over that year?
Answer: Since the bond sells at par, the yield-to-maturity must be equal to the coupon rate. So, the yield-to-maturity is 8.6%. If the yield-to-maturity is still equal to the coupon rate in a year, then the bond will still sell for $1,000. This implies that the capital gains yield will be zero. The coupon yield will be $86/$1000 = 8.6%.
- A bond has a face value of $1,000, a coupon rate of 10% with the coupons paid semi-annually, and four years to maturity. If the yield-to-maturity is 9%, what is the value of the bond today? Is the bond a discount bond, a par bond, or a premium bond?
Answer: PV = $50 PVIFA4.5%,8 + $1,000/1.0458 = $1,032.98. Notice that we use the semi-annual interest rate (which is half the yield-to-maturity) because we have semi-annual cash flows. The bond is a premium bond because it sells for more than $1,000. - A stock does not pay dividends, but reported earnings-per-share of $4 this past year. The expected earnings growth is 7% per year for the next 4 years. The average historical P/E ratio in the industry is 18. The stock has an expected return of 11%. What is the stock worth today?
Answer: Since there are no dividends, we need to use the Malkiel Model. The expected earnings per share in four years is $4 1.074 = $5.243. The expected price in four years is $5.243 18 = $94.38. So, P0 = $94.38 / 1.114 = $62.17 - A stock maintains a dividend payout ratio of 40% and has expected earnings-per-share of $3 this coming year. The expected earnings growth is 6% per year for each of the following 3 years (after this year). The average historical P/E ratio in the industry is 20. The stock has an expected return of 14.8%. What is the stock worth today?
Answer: Since the growth rate is good only for a few years, we cannot use the Gordon Model. We can instead use the Malkiel Model. The expected dividend this year is D1 = 40%$3 = $1.20. Dividends for the subsequent years are expected to be D2=D1(1+g) = $1.20 1.06 = $1.272, D3=D1(1+g)2 = $1.20 1.062 = $1.348, and D4=D1(1+g)3 = $1.20 1.063 = $1.429. The expected earning per share in four years is E4 = E1(1+g)3 = $31.063 = $3.573. The expected price in four years is 20$3.573=$71.46. So, the current value of the stock is P0 = $1.20/1.148 + $1.272/1.1482 + $1.348/1.1483 + $1.429/1.1484 + $71.46/1.1484 = $44.87. - An all-equity firm currently has the following income statement.
Income Statement
Sales / $3,650,180
Costs / $3,134,566
Depreciation / $678,153
Interest / 0
Taxes / 0
Net Income / ($162,539)
Dividends / 0
Retained Earnings / ($162,539)
The required return on the company’s stock is 12%. You believe that the company’s sales will grow at 8% per year for the next four years. You believe industry conditions are such that the average firm in the industry will have a P/E ratio of 18 in four years and a P/Sales ratio of 4 in four years. Estimate the value of the company today.
Answer: Sales4 = $3,650,180 1.084 = $4,966,030.
V4 (value of the stock in four years) = $4,966304 = $19,864,118
V0 (value of the stock today) = $19,864,118/1.124 = $12,624,006