University of CaliforniaWalter A. Haas School of BusinessUGBA 103Introduction to FinanceProf. Dmitry Livdan 2 December 2013Solutions to the Final1. (a) (4 points) The new investment of $8.00 will generate an extra $8.00(125%) = $10.00 inearnings this year, so that E1= 8.00 + 10.00 = 18.00. Since 40% of these earnings willbe reinvested, we have I1= 0.4(18.00) = 7.20 and D1= E1− I1= 10.80.(b) (4 points) In year 2, the initial investment will generate $8.00(25%) = $2.00, and theinvestment made at the end of the first year will generate $7.20(25%) = $1.80. These arein addition to the original (no-growth) earnings of $8.00, so that E2= 8.00+2.00+1.80 =11.80. Again, 40% of these earnings will be reinvested, and the rest will be distributedto shareholders: I2= 0.4(11.80) = 4.72, and D2= E2− I2= 7.08.(c) (7 points) The long-term growth rate in earnings and dividends is g = 25%(0.4) = 0.1. Infact, using the same reasoning as in the first two years, you can verify that the dividendsin year 3 will be D3= D2(1 + g) = 7.788. So the expected dividends that will be paidto the shareholders are as follows:0 1 2 3 4 · · ·↑ 10.80 7.08 7.08(1.1) 7.08(1.1)2· · ·P0The appropriate discount rate r is obtained from the CAPM:r = rf+ (rm− rf)β = 0.06 + (0.14 − 0.06)(1.5) = 18%.Therefore, the value of EY’s stock isP0=10.801 + r+7.08r − g11 + r=10.801.18+7.080.18 − 0.111.18= 84.1525.(d) (5 points) AIP generate AIP =E0r=$8.000.18= $44.44 or a fraction$44.44$84.15= 0.528 of thestock price. PVGO thus represents a fraction of 0.472 of the stock price.2. (a) (4 points) The current value of D&R’s debt is D = 150, and the current value of its equityis E = 10 × 15 = 150. The total current value of the firm is therefore VL= D + E = 300.(b) (4 points) The weighted average cost of capital isWACC = (1 − tc) rDDVL+ rEEVL= (1 − 0.40)(0.08)150300+ (0.16)150300= 10.4%.UGBA 103 Final – Solutions 2(c) (4 points) We haveVL=X(1 − tc)WACC⇔ 300 =X(1 − 0.40)0.104⇒ X = 52.(d) (4 points) We know that VL= VU+ tcD, so thatVU= VL− tcD = 300 − (0.4)(150) = 240.(e) (4 points) We haveVU=X(1 − tc)r⇔ 240 =52(1 − 0.40)r⇒ r = 13%.(f) (3 points) The net present value of the project isNPV = −75 +19.5(1 − 0.40)0.13= 15.(g) (5 points) The adjusted net present value APV of the project consists of the net presentvalue under an “all-equity financing” policy and the present value of the future taxshields resulting from the additional debt issued as a result of this new project:APV = NPV +tcrDL (75 + APV )rD= NPV + tcL (75 + APV )= 15 + (0.40)(0.25)(75 + APV ).We can solve for APV in this last equation to obtain APV = 25.(h) (5 points) The adjusted rate of return is given by the Modigliani-Miller formula:r∗= r(1 − tCL) = 0.13h1 − (0.40)(0.25)i= 11.7%.The adjusted net present value of the project is simplyAPV = −75 +19.5(1 − 0.40)0.117= 25.(i) (4 points) The additional debt that will be issued is∆D = L(75 + APV ) = (0.25)(75 + 25) = 25.The equity of the firm will be increased by∆E = (1 − L)(75 + APV ) = (1 − 0.25)(75 + 25) = 75.(j) (5 points) The total value of the firm’s debt is nowD0= D + ∆D = 150 + 25 = 175,and that of the equity isE0= E + ∆E = 150 + 75 = 225.UGBA 103 Final – Solutions 3The total value of the firm is thereforeV0L= D0+ E0= 175 + 225 = 400.Also, the firm will now generate annual pre-tax earnings ofX0= X + 19.5 = 52 + 19.5 = 71.5.The new weighted average cost of capital WACC0must therefore satisfyV0L=X0(1 − tc)WACC0⇔ 400 =71.5(1 − 0.40)WACC0⇒ WACC0= 10.725%.(k) (8 points) We need to figure out the interest payment on the debt each year. This isdone in the following table.End of Year1 2 3 4 5Debt outstanding 4,000 3,000 2,000 1,000 0Principal paid 1,000 1,000 1,000 1,000 1,000Interest paid 412.5 330 247.5 165 82.5Interest tax shield 165 132 99 66 33The present value of the tax shield is thereforePV (tax shields) =1651.0825+132(1.0825)2+99(1.0825)3+66(1.0825)4+33(1.0825)5= $409,