10-12 a. Purchase price $ 900,000
Installation 165,000
is positive and its IRR is greater than the firm’s cost of capital.
c. Environmental effects could be added by estimating penalties or any other cash
10-13 a.
r
NPVA
NPVB
0.0%
$1,288
$820
10.0
$479
$372
12.0
$366
$308
14.8
$228
$229
18.0
$94
$150
20.7
$0
$94
25.8
−$150
$0
30.0
−$245
−$62
Answers and Solutions: 10 – 12
choose Project B if r = 17%.
d. Here is the MIRR for Project A when r = 10%:
$1,340.47:
$1,340.47 = $3,545.30/(1 + MIRR)7
MIRRA = 14.91%.
Similarly, $650 = $1,992.31/(1 + MIRR)7
MIRRB = 17.35%.
e. To find the crossover rate, construct a Project ∆ which is the difference in the two
Answers and Solutions: 10 – 14
Inputs 19 -10250000 1750000 0
N
I/YR
FV
PMT
PV
website, in whole or in part.
10-15 a. Financial calculator solution:
Plan A
Inputs 20 10 8000000 0
Plan B
Inputs 20 10 3400000 0
Plan A
Inputs 20 -50000000 8000000 0
Output = 15.03
IRRA = 15.03%.
Plan B
Inputs 20 -15000000 3400000 0
N
I/YR
FV
PMT
PV
N
I/YR
FV
PMT
PV
N
I/YR
FV
PMT
PV
b. If the company takes Plan A rather than B, its cash flows will be (in millions of dollars):
Cash Flows Cash Flows Project ∆
Year from A from B Cash Flows
0 ($50) ($15.0) ($35.0)
1 8 3.4 4.6
2 8 3.4 4.6
– – – –
– – – –
– – – –
Output = -39,162,393
Output = 11.71
IRR = 11.71%.
N
I/YR
FV
PMT
PV
c.
N P V ( M i l l i o n s o f D o l l a r s )
C r o s s o v e r R a t e = 1 1 . 7 %
I R R A = 1 5 . 0 3 %
I R R B = 2 2 . 2 6 %
A
B
C o s t o f C a p i t a l ( % )
1 2 5
I R R = 1 1 . 7 %
10
1 0 0
75
15
50
20
25
25
– 2 5
30
– 5 0
5
10-16 Plane A: Expected life = 5 years; Cost = $100 million; NCF = $30 million;
COC = 12%.
Plane B: Expected life = 10 years; Cost = $132 million; NCF = $25 million;
-70
Enter these values into the cash flow register: CF0 = -100; CF1-4 = 30; CF5 = -70;
CF6-10 = 30. Then enter I/YR = 12, and press the NPV key to get NPVA = $12.764
Enter these cash flows into the cash flow register, along with the interest rate, and
press the NPV key to get NPVB = $9.256 million.
Project A is the better project and will increase the company’s value by $12.764
10-17 0 1 2 3 4 5 6 7 8
A: | | | | | | | | |
-10 4 4 4 4 4 4 4 4
–10
= 10, and press the NPV key to get Extended NPVA = $4.5096 ≈ $4.51 million.
0 1 2 3 4 5 6 7 8
B: | | | | | | | | |
million.
The EAA of Machine A is found by first finding the PV: N = 4, I/YR = 10, PMT
= 4, FV = 0; solve for PV = $12.679. The NPV is $12.679 − $10 = $2.679 million.
We convert this to an equivalent annual annuity by inputting: N = 4, I/YR = 10, PV
10%
10%
10-18 Cash flow time line for Machine 190-3:
0 1 2 3
| | | |
-190,000 87,000 87,000 87,000
EAA190-3: Using a financial calculator, input the following data:
N = 3; I/YR = 14; PV = -11982; and FV = 0. Solve for PMT = EAA =
$5,161.
I/YR = 14; and solve for NPV360-6 = $22,256 (for 6 years).
EAA360-6: Using a financial calculator, input the following data:
N = 6; I/YR = 14; PV = -22256; and FV = 0. Solve for PMT = EAA =
10-19 a. The project’s expected cash flows are as follows (in millions of dollars):
2 (25.0)
14%