Question

1. Tri Co. has the following cost of debt structure: Please show all work.

wd	0%	20%	30%	40%	50%
rd	0.0%	9.0%	10.0%	11.0%	12.0%

The market risk premium is 4.5%, the risk free rate is 5%, beta of unleveraged firm is 1.20, Hamada’s equation b= b_U [1 + (1 - T)(w_d/w_e)]. Tax rate T = 40%.

Please use the above information to answer following questions:

a. If the firm uses 40% debt, what is the cost of equity of the firm, based on CAPM model?

b. What is WACC of the firm?

c. If FCF₀ = 150 million, g=3%, what is the firm value?

Answer 1

Answer :

(a.) Calculation of Cost of Equity of the firm

Cost of Equity = Risk free Rate + (Beta * Market Risk Premium)

If Firm uses 40% debt we need to calculate Levered Beta

Beta = Beta unlevered  [1 + (1 - Tax Rate )(weight of debt / weight of equity)]

Given

Beta unlevered = 1.20

Tax Rate = 40% or 0.40

Weight of Debt = 40% or 0.40

Weight of Equity = 60% or 0.60

Beta = Beta unlevered  [1 + (1 - Tax Rate )(weight of debt / weight of equity)]

= 1.20 [ 1 + (1 - 0.40) (0.40 / 0.60 )

= 1.20 [ 1 + (0.60 * 0.67)]

= 1.20 * 1.40

= 1.68

Cost of Equity = Risk free Rate + (Beta * Market Risk Premium)

= 5% + (1.68 * 4.5%)

= 5% + 7.56%

= 12.56%

(b.) WACC = (Cost of Equity * Weight of Equity) + (Cost of Debt after tax * Weight of Debt)

= (12.56% * 0.60) + [11% (1 - 0.40) * 0.40]

= 7.536% + [6.6% * 0.40]

= 7.536% + 2.64%

= 10.176%

(c.) Firm Value = [FCF0 * (1 + growth rate)] / (WACC - Growth rate)

= [150 * ( 1 + 0.03) ] / (0.10176 - 0.03)

= 154.5 / 0.07176

= $2,153.01 million