Question

Finding the WACC
Titan Mining Corporation has 6.4 million shares of common stock outstanding and 175,000 6.2 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $53 per share and has a beta of 1.15; the bonds have 25 years to maturity and sell for 106 percent of par. The market risk premium is 6.8 percent, T-bills are yielding 3.1 percent, and the company's tax rate is 22 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?
(Do not round your intermediate calculations.)

Answer 1

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

Capital	Market value
Debt	0.2872
Equity	0.6548

Capitals	Number of Bonds/Shares	Market Value per Bond/Share	Market Value [ Number of Bonds or Shares / Market Value per Bond or Share]	Weight to total market value Market value / Total market value]
Bond	1,75,000	1,060	18,55,00,000	0.3535
Common Stock	64,00,000	53	33,92,00,000	0.6465
TOTAL			52,47,00,000	1.0000

Requirement (b) - Rate 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 the Bond

The Yield to maturity of (YTM) of the Bond 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
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 6.20% x ½]	PMT	31
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [25 Years x 2]	N	50
Bond Price/Current Market Price of the Bond [-$1,000 x 106%]	PV	-1,060

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 = 2.87%.

The semi-annual Yield to maturity = 2.87%.

Therefore, the annual Yield to Maturity = 5.74% [2.87% x 2]

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

= 5.74% x (1 – 0.22)

= 5.74% x 0.78

= 4.48%

Cost of Equity

As per Capital Asset Pricing Model [CAPM], the cost of equity is calculated by using the following equation

Cost of equity = Risk-free Rate + [Beta x Market Risk Premium]

= 3.10% + [1.15 x 6.80%]

= 3.10% + 7.82%

= 10.92%

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

= [4.48% x 0.3535] + [10.92% x 0.6465]

= 1.58% + 7.06%

= 8.64%

“Hence, the rate to discount the project’s cash flows will be 8.64%”