Question

Titan Mining Corporation has 9 million shares of common stock outstanding and 340,000 5.7 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $38 per share and has a beta of 1.2; the bonds have 20 years to maturity and sell for 119 percent of par. The market risk premium is 7.8 percent, T-bills are yielding 3 percent, and the company’s tax rate is 25 percent.

  

a.	What is the firm's market value capital structure? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .3216.) Debt=? Equity=?
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 intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

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

Capital	Market value
Debt	0.5419
Equity	0.4581

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	3,40,000	1,190.00	40,46,00,000	0.5419
Common Stock	90,00,000	38.00	34,20,00,000	0.4581
TOTAL			74,66,00,000	1.0000

Requirement (b) - Rate to Discount the Project’s cash flows

After-Tax Cost of Debt

· The Yield to maturity (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value

· The Yield to maturity of (YTM) of the Bond is the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.

· 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 5.70% x ½]	PMT	28.50
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [20 Years x 2]	N	40
Bond Price/Current Market Price of the Bond [-$1,000 x 119%]	PV	-1,190

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 semi-annual yield to maturity on the bond (1/Y) = 2.14%.

The semi-annual Yield to maturity = 2.14%.

Therefore, the annual Yield to Maturity of the Bond = 4.28% [2.14% x 2]

The firm’s after-tax cost of debt on the Bond is the after-tax Yield to maturity (YTM)

The After-tax cost of debt = Annual Yield to maturity on the bond x (1 – Tax Rate)

= 4.28% x (1 – 0.25)

= 4.28% x 0.75

= 3.21%

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]

= 3.00% + [1.20 x 7.80%]

= 3.00% + 9.36%

= 12.36%

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

= [3.21% x 0.5419] + [12.36% x 0.4581]

= 1.74% + 5.66%

= 7.40%

“Hence, the rate to discount the project’s cash flows will be 7.40%”