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Werkcollege 1 Problem 1a E(CF)t=1 = 0.5 * $141.494 + 0.5 * $182.105 = $161.799,5 $161.799,5 NPV = 1.20 − $100.368 = $34.464,92 Problem 1b E(CF)t=1 = $161.799,5 and cost of capital = 0.2, incoming cashflows on t=1 $161.799,5 discounted : = $134.832,92. 1.2 Problem 1c 100% debt, so cost of capital = 5%. The cash flows of debt are independent of the “project outcome” so $100.368*1,05 (rate) = $105.386,4 MM1: A (assets) = U (unlevered equity) = E (levered equity) + D (debt) D (debt) E (levered equity) U (unlevered) $100.368 $34464,92 $134.832,92 $105.386,4 (p 0.5) $36.107,6 $141.494 $105.386,4 (p 0.5) $76.718,6 $182.105 Initial value MM1 levered equity is $34464,92 Problem 3a E(CF)t=1 = 0.8* $50 mln + 0.2* $20 mln = $44 mln $44 mln PV = 1.10 = $40 mln, ‘current market value of the unlevered equity’ = $40mln Problem 3b $20 mln PV(debt)t=0 = 1.05 (ππ) = $19,0476 mln MM1: A (assets) = U (unlevered equity) = E (levered equity) + D (debt) D (debt) E (levered equity) U (unlevered) $19,05 mln $20,95 mln $40 mln $20 mln $30 mln $50 mln (p 0.8) $20 mln $0 $20 mln (p 0.2) Levered equity market value = $20,95 mln MM1: PV(unlevered) = PV (levered equity) + PV(debt) Problem 3c Expected returns without leverage: PV = $40 mln, dus 0.8* 0.25 (50-40/40) + 0.2*-0.5 (20-40/40) = 0.1 (10% = rentevoet) Expected return with leverage PV = $20,95 mln, dus 0.8*0.43 (30-20,95/20,95) + 0.2*-1 = 0.1456 (14,56%) Problem 3c With leverage: -0.5 (-50%) met kans 0.2 Without leverage: -1 (-100%) met kans 0.2 Problem 13 No debt, so all-equity and rU = 9.2% πΈ π· MM2: πΈ+π· ππΈ(πΏ) + πΈ+π· ππ· = ππ met rU = market value of unlevered equity geeft: ππΈ(πΏ) = ππ + π· πΈ (ππ − ππ· ) π· .15 ππ (πππ¦πππ) = 9.2% en πΈ = .85 - rE (levered) = 9,76% Problem 10 πΈ π· MM2: πΈ+π· ππΈ(πΏ) + πΈ+π· ππ· = ππ . De rE (cost of capital of equity) (“In fact, risk-free leverage raises it the most (because it does not share any of the risk”), Problem 19 πΈ π· βπΈ(πΏ) + β = βπ πΈ+π· πΈ+π· π· D+E= V= 170 mln, β = 1.80 Risk-free debt: βπ· = 0 Start Activa = $170 mln EV = $170 mln Issuing debt Activa = $170 mln Geld van lening = $35.96 mln EV = $170 mln Debt = $35.96 mln Repurchase stock Activa = $157 mln EV = $121.04 mln Debt = $35.96 mln Ch15 – Problem 3a πΈ π· MM2 met taxes: : πΈ+π· ππΈ(πΏππ£ππππ) + πΈ+π· ππ· ∗ (1 − πc) = ππ€πππ Without interest: $2500*0.6 = $1500 PV = $1500/0,04 (“each year” -> perpetuity, dus 0,04 ipv 1,04) = $37.500 PV (Interest Tax Shield (ITS)) = πc * D Interest Tax shield = Interest * Tax Rate Net Income = EBIT – Interest Exp. - Taxes Problem 3b With interest (deductable): EBIT $2500 Interest (deduct) Income before tax Net income (after tax) $1600 $900 $540 So: $540 + $1600 = $2140 Problem 3c $2140 (with leverage) - $1500 (without leverage) = $640 Problem 3d Yes, $1600*40% = $640 Problem 5 Borrowing amount (/pending principle) Interest ITS (Interest Tax Shield) ITS t=1 $75 mln over t=2 $50 mln over t=3 $25 mln over t=4 $0 over 0.10*100 = $10 mln 0.25 (πc) *$10 mln = $2,5 mln 2.5 0.10*75 = $7,5 mln 0.25 (πc) *$7,5 mln = $1,875 ml 1.875 0.10*50 = $5 mln 0.25 (πc) *$5 mln = $1,25 ml 1.25 0.10*25 = $2,5 mln 0.25 (πc) *$2,5 mln = $0,625 ml 0.625 PV = 2.5/1.10 + 1.875/1.10^2 + 1.25/1.10^3 + 0.625/1.10^4 = $5.188 mln