86
.
(10.4) Crossover ratenonalgorithmic
Answer: d
MEDIUM
Find the differential cash flows by subtracting B’s cash flows from A’s cash flows for each year.
CF
0
=
2,000
CF
1
=
6,000
CF
2
=
1,000
CF
3
=
5,000
CF
4
=
5,000
Enter these cash flows and solve for the IRR/YR = crossover rate =
13.03%
.
87
.
(10.4) Crossover ratenonalgorithmic
Answer: c
MEDIUM
The crossover rate is the point where the two projects will have the same NPV.
To find the crossover rate,
subtract CF
B
from CF
A
:
$100,000 – $100,000 = 0.
$40,000 – $30,000 = $10,000.
$25,000 – $15,000 = $10,000.
$70,000 – $80,000 = $10,000.
$40,000 – $55,000 = $15,000.
Enter these into your CF register and solve for IRR/YR =
11.21%
.
88
.
(10.4) Crossover ratenonalgorithmic
Answer: d
MEDIUM
Find the differential cash flows to compute the crossover rate.
Subtracting Project A cash flows from Project
B cash flows, we obtain the following differential cash flows:
Year
B – A
Cash Flow
0$10017024032040520
Input the cash flows into your calculator‘s cash flow register and solve for IRR/YR to obtain the crossover rate
of
9.32%
.
89
.
(10.6) MIRR (constant cash flows; 3 years)
Answer: e
MEDIUM
WACC:
10.00%
Year:
0
1
2
3
Cash flows:
$800
$350
$350
$350
TV = Sum of compounded inflows:
Compounded values, FVs:
$423.50
$385.00
$350.00
$1,158.50
MIRR =
13.14%
Found as discount rate that equates PV of TV to cost, discounted back 3 years @ 10%
MIRR =
13.14%
Alternative calculation, using Excel's MIRR function
90
.
(10.6) MIRR (uneven cash flows; 4 years)
Answer: b
MEDIUM
WACC:
10.00%
Year:
0
1
2
3
4
Cash flows:
$900
$300
$320
$340
$360
TV = Sum of comp’ed inflows:
Compounded values:
$399.30
$387.20
$374.00
$360.00
$1,520.50
MIRR =
14.01%
Found as discount rate that equates PV of TV to cost, discounted back 4 years @ 10%
MIRR =
14.01%
Alternative calculation, using Excel's MIRR function
91
.
(10.8) Payback (uneven cash flows; 5 years)
Answer: e
MEDIUM
Year:
0
1
2
3
4
5
Cash flows:
$1,000
$300
$310
$320
$330
$340
Cumulative CF
$1,000
$700
$390
$70
$260
$600
Payback =
3.21
—
—
—
—
3.21
—
92
.
(10.8) Discounted payback (constant CFs; 3 years)
Answer: b
MEDIUM
WACC:
10.00%
Year:
0
1
2
3
Cash flows:
$1,000
$500
$500
$500
PV of CFs
$1,000
$455
$413
$376
Cumulative CF
$1,000
$545
$132
$243
Payback =
2.35
—
—
—
2.35
93
.
(10.8) Discounted payback (uneven CFs, 4 years)
Answer: d
MEDIUM
WACC:
10.00%
Year:
0
1
2
3
4
Cash flows:
$1,000
$525
$485
$445
$405
PV of CFs
$1,000
$477
$401
$334
$277
Cumulative CF
$1,000
$523
$122
$212
$489
Payback =
2.36
—
—
—
2.36
—
94
.
(10.11) Replacement chainnonalgorithmic
Answer: c
MEDIUM
To find the NPV of the systems we must use the replacement chain approach.
TimeSystem ASystem B
0$100,000$100,000160,00048,000260,000 – 100,000 = 40,00048,000360,00048,000 –
110,000 = 62,000460,000 – 100,000 = 40,00052,800560,00052,800660,00052,800
Use the CF key to enter the cash flows for each period.
I/YR = 11.
This should give the following NPVs:
NPV
A
= $6,796.93
NPV
B
=
$31,211.52
Computer B adds the most value, so the correct answer is c.
95
.
(10.11) Replacement chainnonalgorithmic
Answer: e
MEDIUM
The CFs and NPVs (calculated with I/YR = 10.5%) are as follows:
TimeProject AProject B
0$100,000$50,000140,00030,000240,00030,000340,00030,000 – 55,000 =
25,000440,00032,000540,00032,000640,00032,000NPV$71,687.18
≈
$71,687$41,655.58
≈
$41,656
96
.
(10.11) Replacement chainnonalgorithmic
Answer: d
MEDIUM
Machine A (Time Line in thousands):
0
r = 12%
1
5
6
10





1,000
350
350
375
375
1,200
850
With a financial calculator input the following:
CF
0
= 1,000,000
CF
14
= 350,000
CF
5
= 850,000
CF
610
= 375,000
I/YR = 12%
Solve for NPV
A
= $347,802.00.
Machine B (Time Line in thousands):
0
r = 12%
1
9
10




1,500
400
400
400
100
500
CF
0
= 1,500,000
CF
19
= 400,000
CF
10
= 500,000
I/YR = 12%
Solve for NPV
B
=
$792,286.54
.
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