Titan Mining Corporation has 14 million shares of common stock outstanding, 900,

Question

Titan Mining Corporation has 14 million shares of common stock outstanding, 900,000 shares of 9 percent preferred stock outstanding and 220,000 ten percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $42 per share and has a beta of 1.15, the preferred stock currently sells 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 project's cash flows if the project has the same risk as the firm's typical project?

Explanation / Answer

The discount rate will be the WACC of the firm:

Total Capital = (14,000,000 x $42) + (900,000 x $80) + (220,000 x $910) = $860,200,000

Weight of Equity = (14,000,000 x $42) / $860,200,000 = 0.6836
Weight of Preferred Stock = (900,000 x $80) / $860,200,000 = 0.0837
Weight of Debt = (220,000 x $910) / $860,200,000 = 0.2327

Cost of Equity = 7.5% + 1.15*(11.5% - 7.5%) = 12.1%
Cost of Preferred Equity = 9%
Cost of Debt = After-tax YTM of the bond = 11.2% x (1-tax rate) = 7.616%

YTM:

Bond Value = C/2 {[1-(1+(YTM/2))-2t/(YTM/2)] + [F / (1+ (YTM/2))2t]

B0 = $910
C = $1,000 x 10% = $100
F = $1,000
YTM = the yield to maturity on the bond
t = 17

$910 = $100/2 {[1-(1+(YTM/2))-34/(YTM/2)] + [$1,000 / (1+ (YTM/2))34] = 11.2%

WACC = (12.1% x 0.6836) + (9% x 0.0837) + (7.616% x 0.2327) = 10.796%

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