Question

LP Bean Company, an all equity company, has an EBIT of $1,200,000 that it expects it will earn forever, and it pays all of its earnings as dividends to shareholders (i.e., no growth). The firm has a corporate tax rate of 45% and has an un-levered beta of 1.25. In the market, you observe that Government T-bills are being sold to yield 3% and the market risk premium is 6%. Assume a world of taxes and a cost for the risk of default.

a) Calculate the value of the firm.

b) Calculate the WACC for the firm.

c) What is the value of the firm if the firm issues $1,500,000 of bonds at par with a coupon rate of 5%? The beta for the equity of the leveraged firm is 1.6.

d) What is the value of the firm if the firm issues $2,000,000 of bonds at par with a coupon rate of 7%? The beta for the equity of the leveraged firm is 1.95.

e) What is the optimal level of debt $0, $1,500,000 or $2,000,000? Explain.

f) What is the WACC for the firm at the optimal level of debt?

g) What are the financial distress costs when the firm as $2,000,000 in debt?

Answer 1

Tax Rate = 45% or 0.45

EBIT = $1,200,000

Unlevered Beta = 1.25

Market Risk Premium = 6%

Government T- Bill yield(Risk-free rate) = 3%

Unlevered Cost of Equity = Risk-free rate + Market Risk Premium * Beta

= 3% + 6%*1.25 = 3% + 7.5 % = 10.5 %

Unlevered Cost of Equity = 10.5% or 0.105

Answer a.

Value of the firm = EBIT * (1- Tax Rate)/Unlevered cost of Equity

= $1200000 *(1-0.45)/0.105

= $1200000*0.55/0.105 = $ 6285714.29

Value of the firm = $ 6285714.29

Answer b.

In the case of Unlevered firm WAAC = Unlevered Cost of Equity = 10.5%

Answer c.

Total Debt = $1500000

Cost of Debt = 5% or 0.05

Beta for the equity of the leveraged firm = 1.6

Unlevered Beta = Levered Beta / ((1 + (1 – Tax Rate) * (Debt / Equity))

= 1.6/((1+(1-0.45)*(1500000/$ 6285714.29)) = 1.6/(1+0.55*0.23864) = 1.6/1.13125 = 1.41436

Unlevered Cost of Equity = Risk-free rate + Market Risk Premium * Beta

= 3% + 6%*1.41436 = 3% + 8.48616 % = 11.48616 %

Value of the firm = EBIT * (1- Tax Rate)/Unlevered cost of Equity

= $1200000 *(1-0.45)/0.1148616

= $1200000*0.55/0.1148616 = $ 5746045.68

Value of the firm = $ 5746045.68

WACC = Cost of equity * Weight of Equity + Cost of Debt * Weight of Debt

= 11.48616 % *(5746045.68/5746045.68+1500000) +5%(1500000/5746045.68+1500000)

= 11.48616 % * 0.79299 + 5% * 0.20700

= 9.10841% + 1.035% = 10.14341%

Answer d.

Total Debt = $2,000,000

Cost of Debt = 7% or 0.07

Beta for the equity of the leveraged firm = 1.95

Unlevered Beta = Levered Beta / ((1 + (1 – Tax Rate) * (Debt / Equity))

= 1.95/((1+(1-0.45)*(1500000/$ 6285714.29)) = 1.95/(1+0.55*0.23864) = 1.95/1.13125 = 1.72376

Unlevered Cost of Equity = Risk-free rate + Market Risk Premium * Beta

= 3% + 6%*1.72376 = 3% + 10.34254 % = 13.34254 %

Value of the firm = EBIT * (1- Tax Rate)/Unlevered cost of Equity

= $1200000 *(1-0.45)/0.1334254

= $1200000*0.55/0.1334254 = $ 4946584.38

Value of the firm = $ 4946584.38

WACC = Cost of equity * Weight of Equity + Cost of Debt * Weight of Debt

= 13.34254  % *(4946584.38/4946584.38+2,000,000 ) +7%(2,000,000 /4946584.38+2,000,000 )

= 13.34254 % * 0.71209 + 7% * 0.28791

= 9.50109% + 2.01538% = 11.51674%

Answer e.

From the above calculation, we get below information and we analyze that on level of debt is $1500000 at which cost of capital is lower.

Debt is $0, WACC = 10.5%

Debt is 1500000, WACC = 10.14341%

Debt is 2000000, WACC = 11.51674%

Answer f.

So, the Optimal level of Debt is 1500000 and WACC is 10.14341%.

Answer g.