P6-13 Valuation of assets Using the information provided in the following table, find the value of each asset.
|
Cash flow |
|
| Asset |
End of year |
Amount |
Appropriate required return |
| A |
1 |
$5,000 |
18% |
|
2 |
5,000 |
|
| |
3 |
5,000 |
|
| B |
1 through ∞ |
$300 |
15% |
| C |
1 |
$0 |
16% |
|
2 |
0 |
|
|
3 |
0 |
|
|
4 |
0 |
|
| |
5 |
35,000 |
|
| D |
1 through 5 |
$1,500 |
12% |
| |
6 |
8,500 |
|
| E |
1 |
$2,000 |
14% |
|
2 |
3,000 |
|
|
3 |
5,000 |
|
|
4 |
7,000 |
|
|
5 |
4,000 |
|
|
6 |
1,000 |
|
P6-17 Bond value and changing required returns Midland Utilities has outstanding a bond issue that will mature to its $1,000 par value in 12 years.
The bond has a coupon interest rate of 11% and pays interest annually.
a. Find the value of the bond if the required return is (1) 11%, (2) 15%, and (3) 8%.
b. Plot your findings in part a on a set of "required return (x axis)-market value of bond (y axis)" axes.
c. Use your findings in parts a and b to discuss the relationship between the coupon interest rate on a bond and the required return and the market value of the bond relative to its par value.
d. What two possible reasons could cause the required return to differ from the coupon interest rate?
P6-18 Bond value and time: Constant required returns Pecos Manufacturing has just issued a 15-year, 12% coupon interest rate, $1,000-par bond that pays interest annually.
The required return is currently 14%, and the company is certain it will remain at 14% until the bond matures in 15 years.
a. Assuming that the required return does remain at 14% until maturity, find the value of the bond with (1) 15 years, (2) 12 years, (3) 9 years, (4) 6 years, (5) 3 years, and (6) 1 year to maturity.
b. Plot your findings on a set of "time to maturity (x axis)-market value of bond (y axis)" axes constructed similarly to Figure 6.5 on page 252.
c. All else remaining the same, when the required return differs from the coupon interest rate and is assumed to be constant to maturity, what happens to the bond value as time moves toward maturity? Explain in light of the graph in part b.
P6-19 Bond value and time: Changing required returns Lynn Parsons is considering investing in either of two outstanding bonds. The bonds both have $1,000 par values and 11% coupon interest rates and pay annual interest. Bond A has exactly 5 years to maturity, and bond B has 15 years to maturity.
a. Calculate the value of bond A if the required return is (1) 8%, (2) 11%, and (3) 14%.
b. Calculate the value of bond B if the required return is (1) 8%, (2) 11%, and (3) 14%.
c. From your findings in parts a and b, complete the following table, and discuss the relationship between time to maturity and changing required returns.
d. If Lynn wanted to minimize interest rate risk, which bond should she purchase? Why?
P6-22 Yield to maturity Each of the bonds shown in the following table pays interest annually.
a. Calculate the yield to maturity (YTM) for each bond.
b. What relationship exists between the coupon interest rate and yield to maturity and the par value and market value of a bond? Explain.
P7-6 Common stock value: Zero growth Kelsey Drums, Inc., is a well-established supplier of fine percussion instruments to orchestras all over the United States.
The company's class A common stock has paid a dividend of $5.00 per share per year for the last 15 years. Management expects to continue to pay at that amount for the foreseeable future.
Sally Talbot purchased 100 shares of Kelsey class A common 10 years ago at a time when the required rate of return for the stock was 16%. She wants to sell her shares today. The current required rate of return for the stock is 12%. How much capital gain or loss will Sally have on her shares?
P7-8 Common stock value: Constant growth Use the constant-growth model (Gordon growth model) to find the value of each firm shown in the following table.
| Firm |
Dividend expected next year |
Dividend growth rate |
Required return |
| A |
$1.20 |
8% |
13% |
| B |
4.00 |
5 |
15 |
| C |
0.65 |
10 |
14 |
| D |
6.00 |
8 |
9 |
| E |
2.25 |
8 |
20 |
P7-9 Common stock value: Constant growth McCracken Roofing, Inc., common stock paid a dividend of $1.20 per share last year.
The company expects earnings and dividends to grow at a rate of 5% per year for the foreseeable future.
a. What required rate of return for this stock would result in a price per share of $28?
b. If McCracken expects both earnings and dividends to grow at an annual rate of 10%, what required rate of return would result in a price per share of $28?
P7-14 Common stock value: Variable growth Lawrence Industries' most recent annual dividend was $1.80 per share (D0 = $1.80), and the firm's required return is 11%.
Find the market value of Lawrence's shares when:
a. Dividends are expected to grow at 8% annually for 3 years, followed by a 5% constant annual growth rate in years 4 to infinity.
b. Dividends are expected to grow at 8% annually for 3 years, followed by a 0% constant annual growth rate in years 4 to infinity.
c. Dividends are expected to grow at 8% annually for 3 years, followed by a 10% constant annual growth rate in years 4 to infinity.
P7-15 Common stock value: All growth models You are evaluating the potential purchase of a small business currently generating $42,500 of after-tax cash flow (D0 = $42,500).
On the basis of a review of similar-risk investment opportunities, you must earn an 18% rate of return on the proposed purchase. Because you are relatively uncertain about future cash flows, you decide to estimate the firm's value using several possible assumptions about the growth rate of cash flows.
a. What is the firm's value if cash flows are expected to grow at an annual rate of 0% from now to infinity?
b. What is the firm's value if cash flows are expected to grow at a constant annual rate of 7% from now to infinity?
c. What is the firm's value if cash flows are expected to grow at an annual rate of 12% for the first 2 years, followed by a constant annual rate of 7% from year 3 to infinity?
P7-16 Free cash flow valuation Nabor Industries is considering going public but is unsure of a fair offering price for the company. Before hiring an investment banker to assist in making the public offering, managers at Nabor have decided to make their own estimate of the firm's common stock value. The firm's CFO has gathered data for performing the valuation using the free cash flow valuation model.
The firm's weighted average cost of capital is 11%, and it has $1,500,000 of debt at market value and $400,000 of preferred stock at its assumed market value. The estimated free cash flows over the next 5 years, 2016 through 2020, are given below. Beyond 2020 to infinity, the firm expects its free cash flow to grow by 3% annually.
| Year (t) |
Free cash flow (FCFt) |
| 2016 |
$200,000 |
| 2017 |
250,000 |
| 2018 |
310,000 |
| 2019 |
350,000 |
| 2020 |
390,000 |
a. Estimate the value of Nabor Industries' entire company by using the free cash flow valuation model.
b. Use your finding in part a, along with the data provided above, to find Nabor Industries' common stock value.
c. If the firm plans to issue 200,000 shares of common stock, what is its estimated value per share?