Question

Titan Mining Corporation has 7.2 million shares of common stock outstanding, 260,000 shares of 4.4 percent preferred stock outstanding, par value $2,000 each. The common stock currently sells for $65 per share and has a beta of 1.15, the preferred stock has a par value of $100 and currently sells for $91 per share, and the bonds have 15 years to maturity and sells for $105 percent of par . The market risk premium is 7.5 percent, T-bills are yielding 3.1 percent, and the company's tax rate is 21 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 Components	Calculation	Market Value Capital Structure Weights
Debt	[$304,500,000 / $796,160,000]	0.3825
Preferred Stock	[$23,660,000 / $796,160,000]	0.0297
Equity	[$46,80,00,000 / $796,160,000]	0.5878

Calculations

Market Value of Debt = $304,500,000 [145,000 Bonds x ($2,000 x 105%)]

Market Value of Preferred Stock = $23,660,000 [260,000 Shares x $91 per share]

Market Value of Equity = $468,000,000 [72,00,000 shares x $65 per share]

Total Market Value = $796,160,000

Requirement (b) – Discount Rate to be used by the firm to discount the project's cash flows

After-tax Cost of Debt

The After-Tax Cost of Debt is the After-Tax Yield to maturity of (YTM) of the Bond and is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Face Value [$2,000]	FV	2,000
Coupon Amount [$2,000 x 11% x ½]	PMT	110
Yield to Maturity [YTM]	1/Y	?
Time to Maturity [15 Years x 2]	N	30
Bond Price [-$2,000 x 105%]	PV	-2,100

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the yield to maturity (YTM) on the bond = 10.34%

The After-tax Cost of Debt is the after-tax Yield to maturity of the Bond

After Tax Cost of Debt = Yield to maturity x (1 – Tax Rate)

= 10.34% x (1 – 0.21)

= 10.34% x 0.79

= 8.17%

Cost of Preferred Stock

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

= [($100 x 4.40%) / $91] x 100

= [$4.40 / $91] x 100

= 4.84%

Cost of Equity

As per CAPM Approach, the Cost of Equity = Risk-free Rate + [Beta x Market Risk Premium]

= Rf + [B x Risk Premium]

= 3.10% + [1.15 x 7.50%]

= 11.73%

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

= [8.17% x 0.3825] + [4.84% x 0.0297] + [11.73% x 0.5878]

= 3.12% +0.14% + 6.90%

= 10.16%

“Hence, the Discount Rate to be used by the firm to discount the project's cash flows will be 10.16%”