Question

 Maria​ Gonzalez, Ganado's Chief Financial​ Officer, estimates the​ risk-free rate to be 3.30 %​, the​ company's credit risk premium is 4.40​%, the domestic beta is estimated at 0.97​, the international beta is estimated at 0.71​, and the​ company's capital structure is now 70​% debt. The​ before-tax cost of debt estimated by observing the current yield on​ Ganado's outstanding bonds combined with bank debt is 8.30​% and the​ company's effective tax rate is 38​%. Calculate both the CAPM and ICAPM weighted average costs of capital for the following equity risk premium estimates. a. 7.80​% b. 6.70​% c. 4.70​% d. 3.80​%

Answer 1

Assumption	CAPM	ICAPM
beta	0.97	0.71
risk free interest rate,Rrf	3.30%	3.30%
company credit risk premium	4.40%	4.40%
cost of debt before tax Kd	8.30%	8.30%
corporate income tax	38%	38%
optimal capital structure proportion of debt D/V proportion of equity	70% 30%	70% 30%

now we assume that,

If we are simply talking about the stock market (a = m), then R_a = R_m. The beta coefficient is a measure of a stock's volatility, or risk, versus that of the market; the market's volatility is conventionally set to 1, so if a = m, then β_a = β_m = 1. R_m - R_f is known as the market premium; R_a - R_f is the risk premium. If a is an equity investment, then R_a - R_f is the equity risk premium; if a = m, then the market premium and the equity risk premium are the same.

so here we take Rm = equity risk premium

The equation for the equity risk premium, then, is a simple reworking of the CAPM:

Equity Risk Premium = R_a - R_f = β (R_m - R_f)

where:

R_a = expected return on investment in "a"

R_f = risk-free rate of return

R_m = expected return of market

now we want to find CAPM & ICAPM from the given equity risk premium.

so 1)R_m= 7.80%

a) Trident's cost of equity CAPM   ICAPM

ke = Rrf + ( Rm - Rrf ) β 7.665% 6.495%

b) Trident's weighted average cost of capital 5.902% 5.5507%

WACC = [ ke x E/V ] + [ ( kd x ( 1 - t ) ) x D/V ]

2) R_m=6.70%

a) Trident's cost of equity CAPM   ICAPM

ke = Rrf + ( Rm - Rrf ) β 6.598% 5.714%

b) Trident's weighted average cost of capital 5.582% 5.3164%

WACC = [ ke x E/V ] + [ ( kd x ( 1 - t ) ) x D/V ]

3)R_m​​​​​​​= 4.70%

a) Trident's cost of equity CAPM   ICAPM

ke = Rrf + ( Rm - Rrf ) β 4.258% 4.294%

b) Trident's weighted average cost of capital 5.00% 4.89%

WACC = [ ke x E/V ] + [ ( kd x ( 1 - t ) ) x D/V ]

4)R_m​​​​​​​= 3.80%

a) Trident's cost of equity CAPM   ICAPM

ke = Rrf + ( Rm - Rrf ) β 3.785% 3.655%

b) Trident's weighted average cost of capital 4.738% 4.69%

WACC = [ ke x E/V ] + [ ( kd x ( 1 - t ) ) x D/V ]