Question

BEA

is considering a change in its capital structure. BEA currently has $20 million in debt

carrying a rate of 8%, and its stock price is $40 per share with 2 million shares outstanding.

BEA is a zero

-

growth firm and pays out all its earnings as dividends. Th

e firm’s EBIT is

$14.933 million, and it faces a 40% federal

-

plus

-

state tax rate.

The market risk premium is 4% and the risk

-

free rate is 6%. BEA is considering increasing

its debt level to a capital structure with 40% debt, based on market values, and

repurchasing

shares with the extra money that is borrows. BEA will have to retire the old debt in order

to issue new debt, and the rate on the new debt will be 9%. BEA has a beta of 1.00

i.

What is BEA’s current WACC?

ii.

What is BEA’s unlevered beta?

(Hint: use

market values of debt to equity when

un

-

levering, which is the same as using

iii.

What’s BEA’s new beta and cost of equity?

iv.

What’s BEA’S new WACC

(after the change in capital

structure)

?

v.

What’s BEA’s total value of the firm with 40% debt? (after the recapitalization is

fully completed).

vi.

What’s BEA’S value of equity and debt, when debt is 40% of the capital structure?

vii.

What’s the value of a share before the repurchase?

viii.

After retiring the old debt, how much cash is left to repurchase shares?

ix.

How many shares will be outstanding after the rep

urchase?

x.

What will the price of a share be after the repurchase?

Answer 1

i). Current WACC = (weight of debt*cost of debt*(1-Tax rate)) + (weight of equity*cost of equity)

Cost of equity = risk-free rate + beta*market risk premium = 6% + 1*4% = 10%

Current WACC = (20/(20+80)*8%*(1-40%)) + (80/(20+80)*10%) = 8.96%

ii). Unlevered beta = beta/(1 + (1-Tax rate)*D/E)) = 1/(1+(1-40%)*20/80) = 0.8696

iii). New capital structure: D/Capital = 40% so, D/E = 40/60 = 2/3 0.667

Relevered beta = unlevered beta*(1+(1-Tax rate)*D/E) = 0.8696*(1+(1-40%)*0.667) = 1.217

New cost of equity = 6% + 1.217*4% = 10.87%

iv). New WACC = (40%*9%*(1-40%)) + (60%*10.87%) = 8.68%

v). Value of the firm (V) = FCF/WACC = EBIT*(1-Tax rate)/WACC = 14.933*(1-40%)/8.68% = 103.20 million

vi). Debt value = 40%*firm value = 40%*103.20 = 41.28 million

Equity value = 103.20 -41.28 = 61.92 million

vii). Share value before the repurchase = equity value/shares O/S = 61.92/2 = $30.96

viii). After retiring the old debt, cash left for the repurchase will be new debt - old debt = 41.28 - 20 = 21.28 million

ix). Shares O/S after repurchase = old number of shares - shares bought back

Shares bought back = cash/price = 21.28/30.96 = 0.69 million

Shares O/S after repurchase = 2 - 0.69 = 1.31 million or 1,312,644

x). Price per share after repurchase = equity value/shares O/S = 61.92/1.31 = $47.17