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# Price of stocks

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1) Price a stock that pays a dividend of \$3 for the next ten years and then \$2 forever after that. Assume the discount rate is 20%. Show in dollars and percent what you would earn if you held this stock for three years.

2) Price a stock that pays no dividend for five years, then pays a \$1 dividend in year 6 after which the dividend grows by 10% annually. Assume the discount rate is 15%. Show in dollars and percent what you would earn if you held this stock for two years.

3) XYZ Corp. has earnings per share of \$4, a payout ratio of 50% and a return on equity of 10%. This company's stock has a discount rate of 15%. Calculate the price of its stock. What change in the payout ratio would make the price of this stock increase? Intuitively, why?

https://brainmass.com/economics/finance/price-of-stocks-135178

#### Solution Preview

Note: the abbreviations have the following meanings

PVIF= Present Value Interest Factor
PVIFA= Present Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations
PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
PVIF( n, r%)= =1/(1+r%)^n

1) Price a stock that pays a dividend of \$3 for the next ten years and then \$2 forever after that. Assume the discount rate is 20%. Show in dollars and percent what you would earn if you held this stock for three years.

METHOD 1

Step 1: Calculate the present value of \$ 3 per year for next 10 years

n= 10
r= 20.00%
PVIFA (10 periods, 20.% rate ) = 4.192472

Annuity= \$3.00
Therefore, present value= \$12.58 =3x4.192472

Step 2: Calculate the present value of a perpetuity of \$ 2 per year from 11th year forever

Perpetuity= \$2.00
r= 20.00%
Therefore value of perpetuity in year 10= \$10.00 =2/20.%

PV of this amount at time t=0 is calculated using PVIF

n= 10
r= 20.00%
PVIF (10 periods, 20.% rate ) = 0.161506

Future value= 10
Therefore, present value= \$1.62 =10x0.161506

Therefore, value of the stock= \$14.20 =12.58+1.62

Alternatively;
We have a perpetuity of \$ 2 and additional \$1 for the first 10 years

Step 1: Calculate the present value of \$ 1 per year for next 10 years

n= 10
r= 20.00%
PVIFA (10 periods, 20.% rate ) ...

#### Solution Summary

The solution calculates price of stocks for different growth rates of dividends.

\$2.19

## After-Tax Cost of Debt Cost of Preferred Stock with Flotation Costs Cost of Equity: DCF Bond Yield and After- Tax Cost of Debt What would your estimate be for the divisions cost of capital What are three types of project risk? How is each type of risk used? Explain in words why new common stock that is raised externally has a higher percentage cost than equity that is raised internally by reinvesting earnings. o. (1) Harry Davis estimates that if it issues new common stock, the flotation cost will be 15%. Harry Davis incorporates the flotation costs into the DCF approach. What is the estimated cost of newly issued common stock, taking into account the flotation cost? (2) Suppose Harry Davis issues 30- year debt with a par value of \$ 1,000 and a coupon rate of 10%, paid annually. If flotation costs are 2%, what is the after- tax cost of debt for the new bond issue? p. What four common mistakes in estimating the WACC should Harry Davis avoid?

See attached file.

After-Tax Cost of Debt

Calculate the after- tax cost of debt under each of the following conditions:
a. Interest rate, 13%; tax rate, 0%.
b. Interest rate, 13%; tax rate, 20%.
c. Interest rate, 13%; tax rate, 35%.

(10-2) After-Tax Cost of Debt
LL Incorporated's currently outstanding 11% coupon bonds have a yield to maturity of 8%. LL believes it could issue at par new bonds that would provide a similar yield to maturity. If its marginal tax rate is 35%, what is LL's after- tax cost of debt?

(10-4) Cost of Preferred Stock with Flotation Costs
Burnwood Tech plans to issue some \$ 60 par preferred stock with a 6% dividend. The stock is selling on the market for \$ 70.00, and Burnwood must pay flotation costs of 5% of the market price. What is the cost of the preferred stock?

(10-5) Cost of Equity: DCF
Summerdahl Resorts common stock is currently trading at \$ 36 a share. The stock is expected to pay a dividend of \$ 3.00 a share at the end of the year (D1 \$ 3.00), and the dividend is expected to grow at a constant rate of 5% a year. What is the cost of common equity?

(10-9) Bond Yield and After- Tax Cost of Debt
A company's 6% coupon rate, semiannual payment, \$ 1,000 par value bond that matures in 30 years sells at a price of \$ 515.16. The company's federal plus state tax rate is 40%. What is the firms component cost of debt for purposes of calculating the WACC? (Hint: Base your answer on the nominal rate.)

(10-10) Cost of Equity
The earnings, dividends, and stock price of Shelby Inc. are expected to grow at 7% per year in the future. Shelby's common stock sells for \$ 23 per share, its last dividend was \$ 2.00, and the company will pay a dividend of \$ 2.14 at the end of the current year.

a. Using the discounted cash flow approach, what is its cost of equity?
b. If the firms beta is 1.6, the risk- free rate is 9%, and the expected return on the market is 13%, what will be the firms cost of equity using the CAPM approach?
c. If the firms bonds earn a return of 12%, what will rs be using the bond yield plus risk premium approach? (Hint: Use the midpoint of the risk premium range.)
d. On the basis of the results of parts a through c, what would you estimate Shelby's cost of equity to be?

During the last few years, Harry Davis Industries has been too constrained by the high cost of capital to make many capital investments. Recently, though, capital costs have been declining, and the company has decided to look seriously at a major expansion program that has been proposed by the marketing department. Assume that you are an assistant to Leigh Jones, the financial vice president. Your first task is to estimate Harry Davis's cost of capital. Jones has provided you with the following data, which she believes may be relevant to your task:

(1) The firm's tax rate is 40%.
(2) The current price of Harry Davis's 12% coupon, semiannual payment, non-callable bonds with 15 years remaining to maturity is \$ 1,153.72. Harry Davis does not use short- term interest-bearing debt on a permanent basis. New bonds would be privately placed with no flotation cost.
(3) The current price of the firms 10%, \$100 par value, quarterly dividend, perpetual preferred stock is \$116.95. Harry Davis would incur flotation costs equal to 5% of the proceeds on a new issue.
(4) Harry Davis's common stock is currently selling at \$ 50 per share. Its last dividend (D0) was \$ 3.12, and dividends are expected to grow at a constant rate of 5.8% in the foreseeable future. Harry Davis's beta is 1.2, the yield on T- bonds is 5.6%, and the market risk premium is estimated to be 6%. For the bond-yield- plus-risk premium approach, the firm uses a 3.2% point risk premium.
(5) Harry Davis's target capital structure is 30% long- term debt, 10% preferred stock, and 60% common equity.

a. (1) What sources of capital should be included when you estimate Harry Davis's weighted average cost of capital (WACC)?
(2) Should the component costs be figured on a before- tax or an after-tax basis?
(3) Should the costs be historical (embedded) costs or new (marginal) costs?
b. What is the market interest rate on Harry Davis's debt and its component cost of debt and what is the component cost of this debt for WACC purposes?
c. (1) What is the firms cost of preferred stock?
(2) Harry Davis's preferred stock is riskier to investors than its debt, yet the preferred yield to investors is lower than the yield to maturity on the debt. Does this suggest that you have made a mistake? (Hint: Think about taxes.)
d. (1) What are the two primary ways companies raise common equity?
(2) Why is there a cost associated with reinvested earnings?
(3) Harry Davis doesn't plan to issue new shares of common stock. Using the CAPM approach, what is Harry Davis's estimated cost of equity?
e. (1) What is the estimated cost of equity using the discounted cash flow (DCF) approach?
(2) Suppose the firm has historically earned 15% on equity (ROE) and has paid out 62% of earnings, and suppose the investors expect similar values to obtain in the future. How could you use this information to estimate the future dividend growth rate, and what growth rate would you get? Is this consistent with the 5.8% growth rate given earlier?
(3) Could the DCF method be applied if the growth rate was not constant? How?
f. What is the cost of equity based on the bond- yield- plus- risk- premium method?
g. What is your final estimate for the cost of equity, rs?
h. What is Harry Davis's weighted average cost of capital (WACC)?
i. What factors influence a company's WACC?
j. Should the company use the composite WACC as the hurdle rate for each of its divisions?
k. What procedures are used to determine the risk- adjusted cost of capital for a particular division? What approaches are used to measure a division's beta?
l. Harry Davis is interested in establishing a new division, which will focus primarily on developing new Internet- based projects. In trying to determine the cost of capital for this new division, you discover that stand- alone firms involved in similar projects have on average the following characteristics:
&#61607; Their capital structure is 10% debt and 90% common equity.
&#61607; Their cost of debt is typically 12%.
&#61607; The beta is 1.7.

Given this information, what would your estimate be for the divisions cost of capital?
m. What are three types of project risk? How is each type of risk used?
n. Explain in words why new common stock that is raised externally has a higher percentage cost than equity that is raised internally by reinvesting earnings.
o. (1) Harry Davis estimates that if it issues new common stock, the flotation cost will be 15%. Harry Davis incorporates the flotation costs into the DCF approach. What is the estimated cost of newly issued common stock, taking into account the flotation cost?
(2) Suppose Harry Davis issues 30- year debt with a par value of \$ 1,000 and a coupon rate of 10%, paid annually. If flotation costs are 2%, what is the after- tax cost of debt for the new bond issue?
p. What four common mistakes in estimating the WACC should Harry Davis avoid?

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