Question

Titan Mining Corporation has 7.1 million shares of common stock outstanding, 255,000 shares of 4.3 percent preferred stock outstanding, and 140,000 bonds with a semiannual coupon rate of 5.6 percent outstanding, par value $1,000 each. The common stock currently sells for $66 per share and has a beta of 1.10, the preferred stock has a par value of $100 and currently sells for $90 per share, and the bonds have 19 years to maturity and sell for 108 percent of par. The market risk premium is 7.6 percent, T-bills are yielding 2.9 percent, and the company’s tax rate is 25 percent.

a. What is the 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	[$15,12,00,000 / $64,27,50,000]	0.2352
Preferred Stock	[$2,29,50,000 / $64,27,50,000]	0.0357
Equity	[$46,86,00,000 / $64,27,50,000]	0.7291

Market Value of Capital

Market Value of Debt = $15,12,00,000 [140,000 Bonds x ($1,000 x 108%)]

Market Value of Preferred Stock = $2,29,50,000 [255,000 Shares x $90]

Market Value of Equity = $46,86,00,000 [71,00,000 Shares x $66]

Total Market Value = $64,27,50,000

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 = $28 [$1,000 x 5.60% x ½]

Bond Price = $1,080 [$1,000 x 108%]

Maturity Period = 38 Years [19 Years x 2]

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

= [$28 + {($1,000 – $1080) / 38 Years)] / [($1,000 + $1080) / 2}]

= [($28 - $2.11) / $1,040]

= 0.02475

= 2.475%

Semi-annual YTM = 2.475%

Therefore, the annual YTM = 4.95% [2.475% x 2]

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

= 4.95% x (1 – 0.25)

= 4.95% x 0.75

= 3.71%

Cost of Preferred Stock

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

= [$4.30 / $90] x 100

= 4.78%

Cost of Equity

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

= 2.90% + (1.10 x .60%)

= 2.90% + 8.36%

= 11.26%

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

= [3.71% x 0.2352] + [4.78% x 0.0357] + [11.26% x 0.7291]

= 0.87% + 0.17% + 8.21%

= 9.25%

“Therefore, the rate to be used to Discount the Project’s cash flows = 9.25%”