The Imaginary Products Co. currently has debt with a market value of $250 millio

Question

The Imaginary Products Co. currently has debt with a market value of $250 million outstanding. The debt consists of 9 percent coupon bonds (semiannual coupon payments) which have a maturity of 15 years and are currently priced at $983.90 per bond. The firm also has an issue of 2 million preferred shares outstanding with a market price of $20. The preferred shares pay an annual dividend of $1.20. Imaginary also has 14 million shares of common stock outstanding with a price of $20.00 per share. The firm is expected to pay a $2.20 common dividend one year from today, and that dividend is expected to increase by 5 percent per year forever. If Imaginary is subject to a 40 percent marginal tax rate, then what is the firm’s weighted average cost of capital?

a.Debt=?

b.Preferred equity=?

c.Common equity=?

d. The best method to use when estimating a firm’s discount rate is the=? capital asset pricing model. or weighted avg cost of capital approach

Explanation / Answer

Solution:

Step 1: Total amount of debt, common equity, and preferred equity:

                        Debt = $250,000,000 (given)

                        Preferred equity = $20 x 2,000,000 = $40,000,000

                        Common equity = $20 x 14,000,000 = $280,000,000

                        Total capital = $570,000,000

                        xDebt = 250/570 = 0.4385

                        xps = 40/570 = 0.0701

                        xcs = 280/570 = 0.4912

Step 2: Cost of capital components:

                        Cost of debt:

$983.90 = $45 x PVIFA(30, YTM/2) + $1,000 x PVIF(30, YTM/2)

                         Solving, we find that YTM = 0.0920 (this is a pretax number)

N = 15 x 2 = 30
PV = -$983.90
PMT = (.09 x $1,000) / 2 = 45
FV = 1000
I/YR = 4.60 x 2 = 9.20

Cost of preferred equity:

Cost of common equity:

Step 3: Combine using the WACC formula.

=

WACC = (0.4385 * 0.092 * (1 – 0.4)) + (0.0701 * 0.06) + (0.4912 * 0.16) = 0.1070032 0r 10.70%

The best method to use when estimating a firm’s discount rate is “WACC” as it corporates all the component of the capital, i.e. debt & equity, in its implied proportions, while CAPM represents the cost of equity, which is generally higher that the debt & hence doesn’t give the correct figure.

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