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# Variable growth, Preferred stock, market value, bond coupon rate

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1. Common stock value-Variable growth

Newman Manufacturing is considering a cash purchase of the stock of Grip's Tool. During the year just completed, Grips earned \$4.25 per share and paid cash dividends of \$2.55 per share (D0 = \$2.55). Grip's earnings and dividends are expected to grow at 25% per year for the next 3 years, after which they are expected to grow at 10% per year to infinity. What is the maximum price per share that Newman should pay for Grips if it has a required return of 15% on investments with risk characteristics similar to those of Grips?

2. Common stock value - Constant growth

Use the constant-growth model (gordon 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

3. Preferred stock valuation Jone Design wishes to estimate the value of its outstanding preferred stock. The preferred issue has an \$80 par value and pays an annual dividend of \$6.40 share. Similar-risk preferred stocks are currently earning a 9.3% annual rate of return.

a. What is the market value of the outstanding preferred stock?
b. If an investor purchases the preferred stock at the value calculated in part a, how much does she gain or lose per share if she sells the stock when the required return on similar-risk preferred has risen to 10.5%? Explain.

4. Authorize and available shares Aspin Corporation's charter authorizes issuance of 2,000,000 share of common stock. Currently, 1,400,000 shares are outstanding and 1,000,000 shares are being held as treasury stock. The firm wishes to raise \$48,000,000 for a plant expansion. Discussion with its investment bankers indicate that the sale of new common stock will net the firm \$60 per share.

a. What is the maximum number of new shares of common stock that the firm can sell without receiving further authorization from the shareholder?
b. Judging on the basis of the data given and your finding in part a, will the firm be able to raise the needed funds without receiving further authorization?
c. What must the firm do to obtain authorization to issue more than the number of shares found in part a.

Bond value and changing required returns Midland Utilities has outstanding a bonds 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 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 finding in 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 different from the coupon interest rate?

Yield to maturity The Salem Company bond currently sells for \$955, has a 12% coupon interest rate and a \$1000 par value, pays interest annually, and has 15 years to mature.

a. Explain the relationships that exist between the coupon interest rate and yield to maturity and the par value and market value of a bond.

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#### Solution Preview

Please see attachment for format of tables and graphs.

1. COMMON STOCK VALUE-VARIABLE GROWTH
Newman Manufacturing is considering a cash purchase of the stock of Grip's Tool. During the year just completed, Grips earned \$4.25 per share and paid cash dividends of \$2.55 per share (D0 = \$2.55). Grip's earnings and dividends are expected to grow at 25% per year for the next 3 years, after which they are expected to grow at 10% per year to infinity. What is the maximum price per share that Newman should pay for Grips if it has a required return of 15% on investments with risk characteristics similar to those of Grips?

NOTE: Double click the table to see the formulas used.

2. COMMON STOCK VALUE - CONSTANT GROWTH
Use the constant-growth model (Gordon model) to find the value of each firm shown in the following table.
Firm Dividend expected next year Growth rate Required return Value of firm
A \$1.20 (A) 8% (B) 13% (C) \$24.00 =A/(C - B)
B \$4.00 5% 15% \$40.00
C \$0.65 10% 14% \$16.25
D \$6.00 8% 9% \$600.00
E \$2.25 8% 20% \$18.75

3. PREFERRED STOCK VALUATION.
Jones Design wishes to estimate the value of its outstanding preferred stock. The preferred issue has an \$80 par value and pays an annual dividend of \$6.40 share. Similar-risk preferred stocks are currently earning a 9.3% annual rate of return.
a. What is the market value of the ...

#### Solution Summary

Variable growth, preferred stock, market value and the bond coupon rate is examined.

\$2.19

## Cost Of Capital and WACC

Chapter 9 p382
P9-1, P9-5, P9-7, P9-10, P9-14
P9-1: Concepts of cost of capital: Mace Manufacturing is in the process of analyzing its investment decision making procedures. Two projects evaluated by the firm recently involved building new facilities in different regions; North and South. The basic variables surrounding each project analysis and the resulting decision actions are summarized in the following table.
Basic variables North South
cost \$6 million \$5 million
life 15 years 15 years
expected return 8% 15%
least-cost financing 7%
source debt equity
cost (post tax) 7% 15%
decision
action invest don't invest
reason 8%>7% cost 12%<16% cost
A. An analyst evaluating the North facility expects that the project will be financed by debt that costs the firm 7%. What recommendations do you think this analyst will make regarding the investment?
B. Another analyst assigned to study the South facility believes that funding for the project will come from the firm's retained earnings at a cost of 16%. What recommendation do you expect this analyst to make regarding the investment?
C. Explain why the decision in part A and B may not be in the best interest of the firm's investors? North is 8% >7% and South is 12%<16%
D. If the firm maintains a capital structure containing 40% debt and 60% equity, find its weighted average cost using the data in the table.
E. If both analysts had used the weighted average cost calculated in part D, what recommendations would they recommendations would they have made regarding the North and South facilities?
F. Compare and contrast the analyst's initial recommendations with your findings in part E. Which decision method seems more appropriate? Explain why?
P9-5 the cost of debt:
Gronseth Drywall Systems, Inc. is in discussions with its investment bankers regarding the issuance of the bonds. The investment banker has informed the firm that different maturities will carry different coupon rates and sell at different prices. The firm must choose among several alternatives. In each case, the bonds will have a \$1000.00 par value and floatation costs will be \$30 per bond. The company is taxed at a rate of 40%. Calculate the after-tax cost of financing with each of the following alternatives:
Alternative Coupon rate Time to maturity (years) Premium or discount
A 9% 16 \$250.00
B 7% 5 50
C 6% 7 PAR
D 5% 10 -75
A.
B.
C.
D.

P9-7 Cost of preferred stock:
Taylor Systems has just issued preferred stock. The stock has 12% annual dividend and a \$100 par value and was sold at \$95.50 per share. In addition, floatation costs of \$2.50 per share must be paid.
A. Calculate the cost of the preferred stock.
\$12.00
A rp= \$95.00 = 12.63%

B. If the firm sells the preferred stock with a 10% annual dividend and nets \$90.00 after floatation costs, what is its cost?
B rp= \$10.00
\$90.00 = 11.11%

P9-10 Cost of common stock equity: kn=D1+g /Nn
Ross textiles wish to measure its cost of common stock equity. The firm's stock is currently for \$57.50. The firm expects to pay a \$3.40 dividend at the end of the year (2016). The dividends for the past 5 years are shown in the following table:
Year Dividend
2015 \$3.10
2014 \$2.92
2013 \$2.60
2012 \$2.30
2011 \$2.12

After underpricing and flotation costs, the firm expects to net \$52 per share on a new issue.
A. Determine the growth rate of dividends from 2011-2015
N=4 (2011-2015) PV (initial value) = -\$2.12 FV (terminal value) = \$3.10 solve for I (growth rate)
=9.97%
B. Determine the net precedes Nn that the firm will actually receive.
Nn=\$
C. Using the constant growth variation model, determine the cost of retained earnings, Rr.
Rr= (next dividend / Current price) + growth rate
(3.40/57.50) +0.0997
0.0591 + 0.0997= 0.1588 =15.88%
D. Using constant growth valuation model, determine the cost of new common stock, Rn.
(3.40 / \$52.00) + 0.0997
0.0654 + 0.0997= 0.1651 =16.51%
P9-14 WACC: book weights and market weights
Webster Company has compiled the information shown in the following table.
Source of Capital Book value Market value After-tax cost
Long-term debt \$4,000,000 \$3,840,000 6.00%
Preferred stock 40,000 60,000 13
Common stock equity 1,060,000 3,000,000 17
totals 5,100,000 6,900,000

A. Calculate the weighted average cost of capital using the book value weights.
WACC = r(E) × w(E) + r(D) × (1 - t) × w(D)
B. Calculate the weighted average cost of capital using the market value weights.
WACC = r(E) × w(E) + r(D) × (1 - t) × w(D)
C. Compare your answers obtained in part A and B. explains the differences.

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