Question

[Please use the data for this problem on the next few problems - aka save your work!] Suppose a firm has 24 million shares of common stock outstanding at a price of $14.5 per share. The firm also has 100,000 bonds outstanding with a current price of $1057.5. The outstanding bonds have yield to maturity 7.8%. The firm's common stock beta is 1.2 and the corporate tax rate is 35%. The expected market return is 13% and the T-bill rate is 1.5%.

a. What is the weight of equity used in the WACC for this firm? (Show your answer to 3 decimals.)

b. What is the weight of debt used in the WACC for this firm? (Show your answer to 3 decimals.)

c. Cost of equity (3 decimal places)?

d. After tax cost of debt? (4 decimal places)

e. What is the weighted average cost of capital (WACC)? (4 decimals)

Answer 1

Total value of equity= 24,000,000*$14.5= $348,000,000

Total value of debt= 100,000*$1,057.5= $105,750,000.

Total firm value= $348,000,000 + $105,750,000 = $453,750,000.

a.Weight of equity= $348,000,000/ $453,750,000

= 0.7669*100 = 76.69%.

b.Weight of debt= $105,750,000/ $453,750,000

= 0.2331*100 = 23.31

c.The cost of equity is calculated using the Capital Asset Pricing Model (CAPM) which is calculated using the formula below:

Ke=Rf+b[E(Rm)-Rf]

where:

Rf=risk-free rate of return

Rm=expected rate of return on the market.

b= stock’s beta

Ke= 1.5% + 1.2*(13% - 1.5%)

= 1.5% + 13.80%

= 15.30%.

d.After tax cost of debt= Before tax cost of debt*(1 - tax rate)

= 7.8%*(1 - 0.35)

= 5.07%.

e.The weighted average cost of capital is calculated using the below formula:

WACC=Wd*Kd(1-t)+We*Ke

where:

Wd= Percentage of debt in the capital structure.

Kd= The before tax cost of debt

We=Percentage of equity in the capital structure

Ke= The cost of common equity.

T= Tax rate

WACC= 0.2331*5.07% + 0.7669*15.30%

= 1.1818% + 11.7336%

= 12.9154%.

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