Titan Mining Corporation has 8.5 million shares of common stock outstanding, 250
ID: 2713209 • Letter: T
Question
Titan Mining Corporation has 8.5 million shares of common stock outstanding, 250,000 shares of 5 percent preferred stock outstanding, and 135,000 7.5 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $34 per share and has a beta of 1.25, the preferred stock currently sells for $91 per share, and the bonds have 15 years to maturity and sell for 114 percent of par. The market risk premium is 7.5 percent, T-bills are yielding 4 percent, and Titan Mining’s tax rate is 35 percent.
What is the firm’s market value capital structure? (Round your answers to 4 decimal places. (e.g., 32.1616))
1) Debt ______
2) Preferred Stock_______
3) Equity______
If Titan Mining 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 round your final answer to 2 decimal places. (e.g., 32.16))
a.What is the firm’s market value capital structure? (Round your answers to 4 decimal places. (e.g., 32.1616))
1) Debt ______
2) Preferred Stock_______
3) Equity______
Explanation / Answer
Answer (a)
Market value capital structure
Debt = 0.3305
Preferred stock = 0.0489
Equity = 0.6206
Answer (b)
Discount rate = 9.87%
Bonds
Number outstanding = 135000
Current Market Price = $1000 * 114% = $ 1140
Market Value of bonds = 135000 * 1140 = $153,900,000
Preferred stock
Current Market Price = $ 91
Number of Shares outstanding = 250,000
Market Value of Preferred stock = 250000 * 91 = $22,750,000
Common Stock
Current Market Price = $ 34
Number of shares outstanding = 8.5 Million
Market value of common stock = 34 * 8500000 = $ 289,000,000
Total Market Value of Company = $ 153,900,000 + $ 22,750,000 + $ 289,000,000
= $ 465,650,000
Weight of Debt in Market Capital Value = $ 153,900,000/$465,650,000 = 0.3305
Weight of Preferred stock in Market Capital Value = $ 22,750,000/$465,650,000 = 0.0489
Weight of common stock in Market Capital Value = $ 289,000,000/$465,650,000 = 0.6206
Calculation of cost of equity
Current Price = $34
Beta = 1.25
Market risk premium = 7.5%
T-Bill rate = 4% (risk-free rate)
As per CAPM, expected return on a stock
re = risk-free rate + Beta * risk premium
re = 4% + 1.25 * 7.5%
re = 4% + 9.375% = 13.375% or 13.38% (rounded off)
Calculation of Cost of Preferred stock
Current Price =$ 91
Dividend = 5%
Dividend Amount = $ 5
Cost of preferred stock = $ 5 / $ 91 = 0.05494 or 5.49%
Calculation of Cost of Debt
Par Value = 1000
Coupon rate = 7.5% semi annual
Semi-annual coupon amount = 1000 * 7.5% * 0.5 = 37.5
Time to maturity = 15 years = 15*2 = 30 semi-annual periods
Current Price = 114% of Par = 1000 * 114% = $ 1140
Let r be the rate of return, then
1140 = 37.5 * (1-(1/(1+r/2)^30))/(r/2)) + 1000/(1+r/2)^30
1140 - 37.5 * (1-(1/(1+r/2)^30))/(r/2)) - 1000/(1+r/2)^30 = 0
Let r = 6% or r/2 = 3%, then LHS will be
= 1140 - 37.5 * (1-(1/(1.03)^30))/(0.03)) - 1000/(1.03)^30
= 1140 – 37.5 * (1-(1/(2.427262)/(0.03)) - 1000/2.427262
= 1140 – 37.5* (1-0.411987)/0.03 – 1000 * 0.411987
= 1140 – 37.5 * 0.588013/0.03 – 411.9868
= 1140 – 37.5 * 19.60044 – 411.9868
= 1140 – 735.0166 – 411.9868
= -7.00331
Let r = 6.1% or r/2 = 3.05%. LHS will be
= 1140 - 37.5 * (1-(1/(1.0305)^30))/(0.0305)) - 1000/(1.0305)^30
= 1140 – 37.5 * (1-(1/(2.462861)/(0.0305)) - 1000/2.462861
= 1140 – 37.5* (1-0.406032)/0.0305 – 1000 * 0.406032
= 1140 – 37.5 * (0.593968/0.0305) – 406.0319
= 1140 – 37.5 * 19.47437 – 406.0319
= 1140 – 37.5 * 730.2887 – 406.0319
= 3.679444
r = 0.06 + (-7.00331 * (0.06-0.061)/(3.679444-(-7.00331))
r = 0.06 + 0.00700331/10.682754 = 0.03 + 0.0006555
r = 0.0606555 or 6.07% (rounded off)
Tax rate = 35%
After-tax cost of debt = 6.07% * (1-tax rate) = 6.07 * (1-0.35) =6.07 * 0.65 = 3.94%
Weighted Average cost of capital WACC = weight of debt * after tax cost of debt + weight of preferred stock * cost of preferred stock + weight of equity * return on equity
WACC = 0.3305 * 3.94% + 0.0489 * 5.49% + 0.6206 * 13.38%
WACC = 1.30217% + 0.268461% + 8.303628%
WACC = 9.874259% or 9.87% (rounded off)
The firm should use the rate of 9.87% as discount rate to evaluate the projects which has the same risk as firm’s current risk.
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