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 (𝑟𝑓) = $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%
𝐸
𝐷
MM2: 𝐸+𝐷 𝑟𝐸(𝐿) + 𝐸+𝐷 𝑟𝐷 = 𝑟𝑈 met rU = market value of unlevered equity
geeft: 𝑟𝐸(𝐿) = 𝑟𝑈 +
𝐷
𝐸
(𝑟𝑈 − 𝑟𝐷 )
𝐷
.15
𝑟𝑈 (𝑃𝑎𝑦𝑃𝑎𝑙) = 9.2% en 𝐸 = .85
- rE (levered) = 9,76%
Problem 10
𝐸
𝐷
MM2: 𝐸+𝐷 𝑟𝐸(𝐿) + 𝐸+𝐷 𝑟𝐷 = 𝑟𝑈 . 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
𝐸
𝐷
β𝐸(𝐿) +
β = β𝑈
𝐸+𝐷
𝐸+𝐷 𝐷
D+E= V= 170 mln, β = 1.80
Risk-free debt: β𝐷 = 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
𝐸
𝐷
MM2 met taxes: : 𝐸+𝐷 𝑟𝐸(𝐿𝑒𝑣𝑒𝑟𝑒𝑑) + 𝐸+𝐷 𝑟𝐷 ∗ (1 − 𝜏c) = 𝑟𝑤𝑎𝑐𝑐
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)) = 𝜏c * 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 (𝜏c) *$10
mln = $2,5 mln
2.5
0.10*75 = $7,5
mln
0.25 (𝜏c) *$7,5
mln = $1,875 ml
1.875
0.10*50 = $5
mln
0.25 (𝜏c) *$5
mln = $1,25 ml
1.25
0.10*25 = $2,5
mln
0.25 (𝜏c) *$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