Question

titan mining corporation has 14 million shares of common stock outstanding 900,000 shares of 9 percent preferred stock outstanding and 210,000 ten percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $34 per share and has a beta of 1.15, the preferred stock currently sell for $80 per share, and the bonds have 17 years to maturity and sell for 91 percent of par. The market risk premium is 11.5 percent, T-bills are yielding 7.5 percent, and the firm's tax rate is 32 percent. What discount rate should the firm apply to a new projects cash flows if the project has the same risk as the firm's typical project?

Answer 1

Answer :- Discount Rate = 16.41%

Calculation of Weighted Cost of Capital (WACC)

WACC = (Cost of Equity * Weight of Equity) + (Cost of Preferred Stock * Weight of Preferred stock) + (Cost of Debt * Weight of Debt)

Calculations of Weights

Market value of Equity shares = Number of shares * Market Price per share

= 14,000,000 * $ 34

= $ 476,000,000

Market value of Preferred Stock = Number of shares * Market Price per share

= 900,000 * $ 80

= $ 72,000,000

Market value of Debt = Number of Bonds * Market Price per bond

= 210,000* (1000 * 91 %)

= 210,000 * 910

= 191,100,000

Assuming Par value of Bond as $1000.

Total Value = Market value of Equity + Market value of Preferred Stock + Market value of Debt

= 476,000,000 + 72,000,000 + 191,100,000

= $ 739,100,000

Weight of Equity = Market value of Equity / Total Value

= 476,000,000 / 739,100,000

= 0.644027

Weight of Preferred Stock= Market value of Preferred stock / Total Value

= 72,000,000 / 739,100,000

= 0.097416

Weight of Debt = Market value of Debt / Total Value

= 191,100,000 / 739,100,000

= 0.258558

Cost of Equity = Risk free rate + Beta * Market Risk Premium

= 7.5 % + 1.15 * 11.5%

= 20.725 %

Cost of Preferred Stock = (Dividend / Price) * 100

= (100 * 9%) / 80

= (9 / 80) *100

= 11.25%

Cost of Debt( Before Tax)={ Coupon +[( Face value - Market Price ) / No.of years]} / (Face Value + Market price) / 2

where Semiannual coupon = 1000 * 10%/ 2 =$ 50

Years to maturity = 17.*2 =34

= { 50 + [(1000 - 910 ) / 34]} / [ (1000 + 910) / 2]

= { 50 + [90 / 34]} / [ 955 / 2 ]

= 11.20% (approx.)

Cost of Debt (after Tax ) = 11.20 (  1-tax rate)

= 11.20 (1-0.32)

= 7.616 %

WACC = (20.725 % * 0.644027) + (11.25% * 0.097416) + (7.616 % * 0.258558)

= 13.34746 % + 1.09593 % + 1.969178

= 16.41 %