Question

12. Finding the WACC Makai Metals Corporation has 9.1million shares of common stock outstanding and 230,000   6.2 percent semiannual bonds outstanding, par value $1000 each.  The common stock currently sells for $41 per share and has a beta of 1.20, and the bonds have 20 years to maturity and sell for 104 percent of par.  The market risk premium is 7 percent, T-bills are yielding 3.1 percent, and the tax rate is 35 percent.  

a. What isthe firm's market value capital structure?

b.  If the company is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows?  

Answer 1

Requirement (a) – Firm’s Market Value Capital Structure

Capital	Calculation	Market Value Capital Structure Weights
Debt	[$23,92,00,000 / $61,23,00,000]	0.3907
Common Stock	[$37,31,00,000 / $61,23,00,000]	0.6093

Market Value of Capital

Market Value of Debt = $23,92,00,000 [230,000 Bonds x ($1,000 x 104%)]

Market Value of Common Stock = $37,31,00,000 [91,00,000 Shares x $41 per share]

Total Market Value = $61,23,00,000

Requirement (b) – The rate use to Discount the Project’s cash flows.

After-Tax Cost of Debt

After-Tax Cost of Debt is the After-Tax Yield to Maturity (YTM) of the Bond

Par Value = $1,000

Semi-annual Coupon Amount = $31 [$1,000 x 6.20% x ½]

Bond Price = $1,040 [$1,000 x 104%]

Maturity Period = 40 Years [20 Years x 2]

Therefore, Yield to Maturity [YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [(Par Value + Bond Price)/2]

= [$31 + {($1,000 – $1040) /40 Years)] / [($1,000 + $1040) / 2}]

= [($31 - $1) / $1020]

= 0.0293 or

= 2.93%

Semi-annual YTM = 2.93%

Therefore, the annual YTM = 5.86% [2.93% x 2]

After Tax Cost of Debt = Bond’s YTM x [ 1 – Tax Rate]

= 5.86% x (1 – 0.35)

= 5.86% x 0.65

= 3.81%

Cost of Equity

Cost of Equity = Rf + [B x Risk Premium]

= 3.10% + (1.2 x 7%)

= 3.10% + 8.40%

= 11.50%

Therefore, Discount Rate = [After Tax Cost of Debt x Weight of Debt] + [Cost of equity x Weight of Equity

= [3.81% x 0.3907] + [11.50% x 0.6093]

= 1.49% + 7.01%

= 8.50%

“Therefore, the rate to be used to Discount the Project’s cash flows = 8.50%”