Your division is considering two investment projects, each of which requires an
ID: 2744844 • Letter: Y
Question
Your division is considering two investment projects, each of which requires an up-front expenditure of $25 million. You estimate that the cost of capital is 10% and that the investments will produce the following after-tax cash flows (in millions of dollars):
Year
Project A
Project B
1
$5 mil.
$20 mil.
2
$10 mil.
$10 mil.
3
$15 mil.
$8 mil.
4
$20 mil.
$6 mil.
a. What is the regular payback period for each of the projects?
b. What is the discounted payback period for each of the projects?
c. If the two projects are independent and the cost of capital is 10%, which project or projects should the firm undertake?
d. If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?
e. If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?
f. What is the crossover rate?
g. If the cost of capital is 10%, what is the modified IRR (MIRR) of each project?
Please show formulas!!! If you use a calc. then please list the values entered.. n=, i=, pv= , etc Thanks!
Year
Project A
Project B
1
$5 mil.
$20 mil.
2
$10 mil.
$10 mil.
3
$15 mil.
$8 mil.
4
$20 mil.
$6 mil.
Explanation / Answer
Part A:
To compute payback period, we need to prepare cumulative cash flow table
Year
CF A
CF B
CCF A
CCF B
0
-25
-25
-25
-25
1
5
20
-20
-5
2
10
10
-10
5
3
15
8
5
13
4
20
6
25
19
Payback period = last year of negative CCF + Last negative CCF/ CF in the first positive CCF year
Project A = 2+ 10/15
= 2.67 years
Project B = 1+ 5/20
= 1.25 years
Part B
To compute discounted PBP, we need to prepare cumulative present value table:
Year
CF A
CF B
Pv factor 10%
PV A
PV B
CPV A
CPV B
0
-25
-25
1.00000
-25.00
-25.00
-25.00
-25.00
1
5
20
0.90909
4.55
18.18
-20.45
-6.82
2
10
10
0.82645
8.26
8.26
-12.19
1.45
3
15
8
0.75131
11.27
6.01
-0.92
7.46
4
20
6
0.68301
13.66
4.10
12.74
11.55
Discounted Payback period = last year of negative CPV + Last negative CPV/ PV in the first positive CPV year
Project A = 3 + 0.92/13.66
= 3.07 years
Project B = 1+6.82/8.26
= 1.83 years
Part C
NPV = last year of CPV
Project A = 12.74
Project B = 11.55
Since both the projects have positive NPV, both the projects should be selected.
Part C
Here we need to compute NpV of the projects. NPV is the sum of present values.
Year
CF A
CF B
Pv factor 5%
PV A
PV B
0
-25
-25
1.00000
-25.00
-25.00
1
5
20
0.95238
4.76
19.05
2
10
10
0.90703
9.07
9.07
3
15
8
0.86384
12.96
6.91
4
20
6
0.82270
16.45
4.94
NPV
18.24
14.96
Since both the projects are mutually exclusive, we will select only one project. Since project A has higher NPV, project A should be selected.
Year
CF A
CF B
CCF A
CCF B
0
-25
-25
-25
-25
1
5
20
-20
-5
2
10
10
-10
5
3
15
8
5
13
4
20
6
25
19
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