Ec 1745 Problem Set 6

Tarun Singh Worked with Richard Gong Ec 1745 Problem Set 6 1. A) p0= (p10)/((1.10)^10) B) rate of earnings growth for first 10 yrs: 15% e10 = e1((1.15)9) → $69(1.15)9= $242.73 C) kt+1 = kt(1+λROE); λ=1 for years 1-10 $69 = k0(ROE) → k0 = $69/.15 = $460 k10 = k0(1+λROE)9 → k10 = $460(1.15)9 = $1618.22 D) e11 = ROE(k10) = .08($1618.22) = $129.46 E) D11 = (1-λ)e11 = (1-0)$129.46 = $129.46 Given that all the earnings are paid out the growth rate of the dividends from year 11 onward are 0%. F) p10 = D11/(r-g)= ($129.46)/(.1-0) = $1294.6 G) p0 = (p10)/((1.10)^10) = ($1294.6)/(1.110) = $499.12 2. A) P/E = (1-λ)/(r-λROE) ΔROE = ((.7 + 50r -1)/(50(.7))) - ((.7 + 30r -1)/(30(.7))) = -(1/75) – (1/35) + (1/21) = .00571429 = .05714% B) r= ((1-λ)/(P/E)) + λROE Δr = ((1-.7)/50)-((1-.7)/30) = -.004 = -.04% C) 1) A firm with P/E = 30: ROE = ((.7+(.1(30))-1)/(.7(30))) = .1286 A firm with P/E = 50: ROE = ((.7+(.1(50))-1)/(.7(50))) = .13429 → Avg ROE = .1314 New P/E = (1-λ)/(r-λROE) = (1-.7)/(.1-.7(.1314)) = 37.5 2) ROE1 = ((.7+(.1(20.5))-1)/(.7(20.5))) = .12195 ROE2 = ((.7+(.1(150))-1)/(.7(150))) = .14 → Avg ROE = .130975 3) Due to convexity of P/E with respect to ROE, the greater the dispersion in ROE across firms the higher the P/E ratio. 3. A) Convertible debt holders convert debt to equity if they can get more than $500,000. By converting the total number of shares doubles to 20,000.

Vs Vc Ve

V= $500,000 $500,000 $0 $0

V=$1,000,0 00 $1,000,000 $0 $0

V=$1,500,0 00 $1,000,000 $500,000 $0

V=$2,000,0 00 $1,000,000 $500,000 $500,000

V=$2,500,0 0 $1,000,000 $750,000 $750,000

C) If the company does poorly senior debt is impacted negatively, equity holders are also impacted negatively but they cannot lose money. If the company does well senior debt doesn’t get an additional pay-off whereas equity holders do. Thus, equity holders want the company to take risky projects with npv=0 but senior debt does not. For convertible debt if the pay-off function is concave then convertible debt holders will prefer risk but if it is convex they will not. 4. A) rate of return required by investors : .07+1.6(.17-.07) = .23 = 23% .20<.23 ; so the excess rate of return is less than that predicted by CAPM so this project is not acceptable. Investor require a 3% excess rate of return above the return B) WACC = wd(Rd) + (1-wd)(Re) Re = Ra+(wd/(1-wd))(Ra-Rd) Rd = .07+.4(.17-.07) = .11 ==11% WACC = wd(Rd) + (1-wd)( Ra+(wd/(1-wd))(Ra-Rd)) = wd(Rd) +(1-wd)Re → WACC = Ra = .23 = 23% According to Modigliani & Miller, WACC=E(Ra) in a frictionless world, meaning there are no transaction costs, no corporate taxes, no differences of opinion and no big players. This means that WACC is not dependent upon leverage. Therefore, neither Alan nor Bruce is correct. C) If corporate taxes are 30% then Bruce is right and the firm can lower the cost of capital by using leverage, meaning it would be possible to make the project viable. WACC = .2 = wd(1-T)(Rd) + (1-wd)(Re) = wd(1-T)(Rd) + (1-wd)(Ra) + w(Ra-Rd) → WACC = .2 = Ra – wd(T)(Rd) → wd = ((.23 - .2)/((.3)(.11))) = .9091 = 90.91% A debt of 90.91% would be required to make this project viable. D) Bruce will still be correct because the personal tax rate on both dividends and interest payments cancel each other out. Therefore the required weight for debt will still be 90.91%. E) If the personal tax applies only to interest payments then the tax on debt is greater than the tax on equity, therefore there is no benefit to increasing leverage. Thus, Alan would be correct in this case. Furthermore, because the tax on debt is greater than the tax on equity this would mean that the firm would not be able to profitably carry out this project.