Question

DecourcyW Inc. recently hired you as a consultant to estimate the company’s WACC. You have obtained the following information.

• The firm's noncallable bonds mature in 12 years. The bonds have a 10.50% annual coupon rate, a par value of $1,000, and a market price of $1,180.00. The bonds pay coupon payments semi-annually. The firm has 600,000 bonds outstanding.
• Common equity investors’ bond-yield risk premium is 5.5%.
• The risk-free rate is 1.85%, the market risk premium is 12.00%, and the common stock’s beta is 1.15.
• The firm has 40 million shares outstanding of common stocks that sell at $27 per share. The firm just paid a dividend of $2.30 per share, and the constant growth rate is expected to be 5.75%.
• The firm would like to use the median (i.e. mid-point) of the three methods (i.e. Bond-yield-risk premium method, CAPM, and DCF) to estimate the cost of equity, and it does not expect to issue any new common stock.
• The firm has 6.5%, $100 par value preferred stocks. There are 3 million shares outstanding. The preferred stock currently sells at $90 per share.
• The company’s tax rate is 21%.

What is its WACC? Do not round your intermediate calculations.

Answer 1

WACC = (weight of debt * cost of debt) + (weight of preferred stock * cost of preferred stock) + (weight of equity * cost of equity)

market value of debt = bonds outstanding * price per bond = 600,000 * $1,180 = $708,000,000

market value of preferred stock = shares outstanding * price per share = 3 million * $90 = $270,000,000

market value of equity = shares outstanding * price per share = 40 million * $27 = $1,080,000,000

total market value = $708,000,000 + $270,000,000 + $1,080,000,000 = $2,058,000,000

weight of debt = $708,000,000 / $2,058,000,000 = 0.344

weight of preferred stock = $270,000,000 / $2,058,000,000 = 0.131

weight of equity = $1,080,000,000 / $2,058,000,000 = 0.525

cost of debt = YTM of bond * (1 - tax rate)

YTM is calculated using RATE function in Excel with these inputs :

nper = 12*2 (12 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 10.5% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -1180 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

the RATE is calculated to be 4.06%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 8.12%

cost of debt = YTM * (1 - tax rate)

cost of debt = 8.40% * (1 - 21%) ==> 6.42%

cost of preferred stock = dividend / current price = (6.5% * 100 / 90) = 7.22%

cost of equity (CAPM) = risk free rate + (beta * market risk premium)

cost of equity (CAPM) = 1.85% + (1.15 * 12%) ==> 15.65%

cost of equity (Gordon model) = (next year dividend / current share price) + constant growth rate

cost of equity (Gordon model) = (($2.30 * (1 + 5.75%)) / $27) + 0.0575 = 14.76%

cost of equity (bond yield plus risk premium approach) = risk free rate + risk premium

cost of equity (bond yield plus risk premium approach) = 1.85% + 5.5% = 7.35%

cost of equity = median of three methods = 14.76%

WACC = (0.344 * 6.42%) + (0.131 * 7.22%) + (0.525 * 14.76%) ==> 10.90%