Question

Finding the WACC [LO3] Titan Mining Corporation has 9 million shares of common stock outstanding, 250,000 shares of 6 percent preferred stock outstanding, and 105,000 7.5 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $34 per share and has a beta of 1.25, the preferred stock currently sells for $91 per share, and the bonds have 15 years to maturity and sell for 93 percent of par. The market risk premium is 8.5 percent, T-bills are yielding 5 percent, and Titan Mining's tax rate is 35 percent.

 a. What is the firm's market value capital structure?

 b. If Titan Mining is evaluating a new investment project that has the same risk as 16. 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	[$9,76,50,000 / $42,64,00,000]	0.2290
Preferred Stock	[$2,27,50,000 / $42,64,00,000]	0.0534
Equity	[$30,60,00,000 / $42,64,00,000]	0.7176

Market Value of Capital

Market Value of Debt = $9,76,50,000 [105,000 Bonds x ($1,000 x 93%)]

Market Value of Preferred Stock = $2,27,50,000 [250,000 Shares x $91]

Market Value of Equity = $30,60,00,000 [90,00,000 Shares x $34]

Total Market Value = $42,64,00,000

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 = $37.50 [$1,000 x 7.50% x ½]

Bond Price = $930 [$1,000 x 93%]

Maturity Period = 30 Years [15 Years x 2]

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

= [$37.50 + {($1,000 – $930) / 30 Years)] / [($1,000 + $930) / 2}]

= [($37.50 + $2.33) / $965]

= 0.04165

= 4.165%

Semi-annual YTM = 4.165%

Therefore, the annual YTM = 8.33% [4.165% x 2]

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

= 8.33% x (1 – 0.35)

= 8.33% x 0.65

= 5.41%

Cost of Preferred Stock

Cost of Preferred Stock = [Preferred Dividend / Selling Price] x 100

= [$6.00 / $91.00] x 100

= 6.59%

Cost of Equity

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

= 5% + [1.25 x 8.50%]

= 5% + 10.63%

= 15.63%

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

= [5.41% x 0.2290] + [6.59% x 0.0534] + [15.63% x 0.7176]

= 1.24% + 0.35% + 11.22%

= 12.81%

“Therefore, the rate to be used to Discount the Project’s cash flows would be 12.81%”