In: Finance
DIY also had three bond issues outstanding. The first bond issue would mature in 8 years. It had $750,000 face value, 10% coupon rate and was trading at YTM of 9.5%. The second bond issue, with original maturity of 20 years, was issued 10 year ago. It had $800,000 face value and 8% coupon rate, and was trading at 103.5% of par. The third one was a perpetual bond that had $600,000 face value, 7% coupon rate and 7.5% YTM. All bonds paid semi-annual coupons. DIY had 35,000 shares of outstanding common stock, currently trading at $65 per share with beta of 1.35. The risk-free rate is 5% and the market risk premium is 9%. The tax rate is 40%.
The cost of equity, Ke = Rf + Beta x Rmp = 5% + 1.35 x 9% = 17.15%
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All bonds paid semi-annual coupons.
Bond 1: The first bond issue would mature in 8 years. It had $750,000 face value, 10% coupon rate and was trading at YTM of 9.5%.
Current market value = D1 = -PV(Rate, Nper, PMT, FV) = - PV (9.5%/2, 2 x 8, 10%/2 x 750000, 750000) = 770,687.30
Pre tax cost of debt = Kd1 = YTM = 9.5%
Bond 2: The second bond issue, with original maturity of 20 years, was issued 10 year ago. It had $800,000 face value and 8% coupon rate, and was trading at 103.5% of par.
Market value = D2 = 103.5% x 800,000 = 828,000
Pre tax cost of debt = Kd2 = YTM = 2 x Rate (Nper, PMT, PV, FV) = 2 x Rate (2 x (20 -10), 8%/2 x 800000, -828000, 800000) = 7.50%
Bond 3: The third one was a perpetual bond that had $600,000 face value, 7% coupon rate and 7.5% YTM.
Market value = D3 = Annual cash flows / discount rate = 600,000 x 7% / 7.5% = 560,000
Pre tax cost of debt = Kd3 = YTM = 7.5%
Total debt = D = D1 + D2 + D3 = 770,687 + 828,000 + 560,000 = 2,158,687
Wd1 = D1/D = 770,687 / 2,158,687 = 35.70%
Wd2 = D2 / D = 828,000 / 2,158,687 = 38.36% and Wd3 = D3 / D = 560,000 / 2,158,687 = 25.94
Hence, pre tax cost of debt = Wd1 x Kd1 + wd2 x Kd2 + Wd3 x Kd3 = 35.70% x 9.5% + 38.36% x 7.50% + 25.94% x 7.5% = 8.21%
Hence, the after-tax cost of debt, Kd = Pre tax cost of debt x (1 - tax rate) = 8.21% x (1 - 40%) = 4.93%
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Market value of equity, E = P x N = 65 x 35,000 = 2,275,000
Wd = D / (D + E) = 2,158,687 / (2,158,687 + 2,275,000) = 48.69%
We = 1 - Wd = 1 - 48.69% = 51.31%
Hence, WACC = Wd x Kd + We x Ke = 48.69% x 4.93% + 51.31% x 17.15% = 11.20%
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Project cost, C = 80,000
D = Wd x C = 48.69% x 80,000 = 38,950.65
E = We x C = 51.31 x 80,000 = 41,049.35
Hence, total cost of the project = D / (1 - Fd) + E / (1 - Fe) = 38,950.65 / (1 - 5%) + 41,049.35 / (1 - 7%) = $ 85,140