Titan Mining Corporation has 8.3 million shares of common stock outstanding and
ID: 2759349 • Letter: T
Question
Titan Mining Corporation has 8.3 million shares of common stock outstanding and 270,000 5 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $31 per share and has a beta of 1.15, and the bonds have 15 years to maturity and sell for 112 percent of par. The market risk premium is 7.1 percent, T-bills are yielding 4 percent, and the company’s tax rate is 30 percent.
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.) Discount rate %
Explanation / Answer
Solution:
The firm should use the Weighted Average Cost of Capital (Overall Cost of Capital) as a discounting rate to evaluate the new investment project.
1) Cost of Debt after tax (Kd)
Annual Interest = $1000 x 5% = $50
Redemption value = At par $1,000
Net Proceed = Current Market Value $1,000 x 112% = $1,120
Life = 15 Years
Cost of Debt after tax (Kd) = [Annual Interest + (Redemption Value – Net Proceeds)/life] / (Redemption Value + Net Proceeds)/2 x (1-Tax Rate)
= [$50 + ($1000 - $1,120) / 15] / ($1000 + $1,120)/2 x 0.70
= ($50 - $8) / $1,060 x 0.70 = 2.7736%
2) Cost of Equity (ke) as per CAPM Model
Risk Free Rate = T-bill rate = 4%
Market Risk Premium = 7.1%
Stock Beta = 1.15
Cost of Equity (ke) as per CAPM Model = Risk Free Rate + Market Risk Premium x Stock Beta
= 4% + 7.1% x 1.15 = 12.165%
3) Calculation of WACC (Weighted Average Cost of Capital)
Capital Structure (At Book Value)
Value
Weight
Cost of Capital (%)
WACC (Weight x Cost of Capital)
Common Stock (8.3 Million Share @ $10 Par Value each)
$83,000,000
0.24
12.165
2.86
5% Bonds Payable (270,000 bonds @ $1000 par value each)
$270,000,000
0.76
2.7736
2.12
Total
$353,000,000
4.98 or 5%
WACC = 4.98% or 5%
The firm should use 5% (Overall Cost of Capital) as a discounting rate to evaluate the new investment project.
However, WACC may be calculated at Market Value as follows:
3) Calculation of WACC (Weighted Average Cost of Capital) at Market Value
Capital Structure (At Market Value)
Value
Weight
Cost of Capital (%)
WACC (Weight x Cost of Capital)
Common Stock (8.3 Million Share @ $31 Market Value each)
$257,300,000
0.46
12.165
5.59
5% Bonds Payable (270,000 bonds @ $1,120 Market Value each)
$302,400,000
0.54
2.7736
1.50
Total
$559,700,000
7.09 or 7.10%
In this case WACC at market value will be 7.10%
Capital Structure (At Book Value)
Value
Weight
Cost of Capital (%)
WACC (Weight x Cost of Capital)
Common Stock (8.3 Million Share @ $10 Par Value each)
$83,000,000
0.24
12.165
2.86
5% Bonds Payable (270,000 bonds @ $1000 par value each)
$270,000,000
0.76
2.7736
2.12
Total
$353,000,000
4.98 or 5%
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