Question

Adjusted WACC. Thorpe and Company is currently an​ all-equity firm. It has three million shares selling for $22 per share. Its beta is 0.7​, and the current​ risk-free rate is 2.3​%. The expected return on the market for the coming year is 10.6​%. Thorpe will sell corporate bonds for $22,000,000 and retire common stock with the proceeds. The bonds are​ twenty-year semiannual bonds with a 9.3​% coupon rate and 1,000 par value. The bonds are currently selling for $923.83 per bond. When the bonds are​ sold, the beta of the company will increase to 0.9.

What was the WACC of Thorpe and Company before the bond​ sale? What is the adjusted WACC of Thorpe and Company after the bond sale if the corporate tax rate is 15 %​?

Hint​: The weight of equity before selling the bond is​ 100%.

Answer 1

WACC of Thorpe and Company before the bond sale
Cost of Equity					Amount of Equity
	Riskfree rate		2.30%			Shares		3,00,00,000.00
	Beta		0.70			Price		22
	Market return		10.6%			Value		66,00,00,000.00
	Cost of Equity (Ke) = Rf+β(Rm-Rf)
	Rf - Risk free return
	β - Beta of the stock
	Rm - Market Return
	Ke = 2.3+.7(10.6-2.3)
	Ke = 8.11 %
Weighted Average Cost of Capital (WACC)
Ke * Pe + Kd (1 - t) * Pd
Pe + Pd (1 - t)
Ke - Cost of Equity
Kd - Cost of debt
Pe - Proportion of Equity
t - Tax rate
(Note: Cost of debt will be zero, since it is a full equity company before issue of bond)
WACC =	8.11 * 66 million + 0 * 0
	66 million + 0
=	8.11%
(Note: If company is a full equity company its WACC will be equal to Cost of equity ) WACC of Thorpe and Company After the bond sale Equity share capital before bond issue 66 million Less: Bonds isued (22 million) Current Equity share capital 44 million Equity Beta before issue of bond = .7 Beta of company before issue of Bond = .7 Beta of Company = Be * Pe + Bd * Pd (1 - t ) Pe + Pd ( 1 - t ) Be - Beta of equity Bd - Beta of Debt Pe - Proportion of equity Pd - Proportion of debt T   - Tax rate .9   =     Be * 44 million + 0 * 22 ( 1 -.15 )      44 million + 22 milion ( 1- .15)      Be = 1.28 Cost of Equity Cost of Equity (Ke) = Rf+β(Rm-Rf)             =   2.3+1.28(10.6-2.3)             = 12.92% Cost of Debt Coupon Rate 9.30% Taxrate 15% Semi annual interest payment 46.50 ( 1000 * 9.3 % ) / 2 Market value of bond 923.83 Cost of debt before tax semi annually (46.5/923.83) * 100 5.03% Cost of debt before tax annually 10.06% Cost of debt after tax annually 8.55% ( 5.03 * 2 )* ( 1 - .15 ) Cost of Debt (Kd) = I (1 - t ) WACC Amount of Equity 44 million Amount of Equity 22 million Total 66 million WACC        = 12.92 * 44 miilion + 10.06 * 22 million ( 1 - .15 ) 44 million + 22 million ( 1 - .15 )        = 12.07%