Question

KKK Co has $500m Debt with the coupon rate of 7%. The current stock price is $50 and 10 million shares are outstanding. Suppose E(rm) = 10%, rf = 4%, βd = 0.5, βU = 1.5 and tax rate is 50%. What are WACC, re and rd?

Answer 1

WACC = (Weight of Debt times cost of debt) + (Weight of equity times cost of equity)

WACC = Wd*Kd +WeKe

Explaining notations used in question:

E(rm) = Expected Market return

rf = risk free rate

βd = Debt beta (It is assumed that coupon rate considers the systematic risk of debt)

βU = Unlevered beta (we will have to find levered beta for CAPM formula)

re = return on equity or cost of equity

rd = return on debt or cost of debt

tax rate will be denoted by t

D/E = debt upon equity

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rd = coupon rate * (1-t)

rd = 7% * (1- 50%)

rd = 7%*50%

rd = 3.5%

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For re calculation we will use CAPM approach which uses levered beta, however in question we are provided with unlevered beta so let us first find lever beta:

βL = βU + ( βU - βd ) (1 - t) D/E

βL = 1.5 + (1.5 - 0.5) ( 1 - 50%) 500/500

solving this we will get

βL = 2

Now to find re,

re = rf + βL [ E(rm) - rf ]

re = 4% + 2 [ 10% - 4%]

re = 4% + 12%

re = 16%

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WACC = (Weight of Debt times cost of debt) + (Weight of equity times cost of equity)

So let us first find the weights of debt and equity

Total Capital = Debt + Equity

1000 = 500 + 500 ($50 stock price * 10 Million shares)

Weight of Debt = 500/1000 = 50%

Weight of Equity = 500/1000 = 50%

WACC = (50%* 3.5%) + (50%*16%)

WACC = 1.75% + 8%

WACC = 9.75%

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Therefore, WACC = 9.75%

re = 16%

rd = 3.5%