Your division is considering two investment projects, each of which requires an
ID: 2445158 • 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
1 520
2 10 10
3 15 8
4 20 6
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?
Explanation / Answer
computation of Payback period
Years Project A Cumulative cash flows Project B Cumulative cash flows
1 5 5 20 20
2 10 15 10 30
3 15 30 8 38
4 20 50 6 44
project A : payback perid = 2 + 10 / 15
= 2 + 0.67 = 2.67
Project B : payback period = 1+ 5 /10 = 1.5
b. Computation of Discounted payback period
Years Project A discount @10% PVCF Cummulative CF Project B PVCF Cumulative CF
1 5 0.909 4.55 4.55 20 18.18 18.18
2 10 0.826 8.26 12.81 10 8.26 26.44
3 15 0.751 11.27 24.08 8 6.01 32.45
4 20 0.683 13.66 37.74 6 4.09 36.54
Discounted pay back period:
Project A = 3 + (0.92 / 13.66) = 3.07
project B = 1 + (6.82 / 8.26) = 1.83
c. Computation of Net present value
Years Project A Discount@10% Present value cash flows Project B Present value of cash flows
1 5 0.909 4.55 20 18.18
2 10 0.826 8.26 10 8.26
3 15 0.751 11.27 8 6.01
4 20 0.683 13.66 6 4.09
Total cash inflows 37.74 36.54
less : initial investment (25) (25)
NPV 12.74 11.54
Project A is better NPV . so you can choose Poject A
d. Computation of NPV
Years Project A Discount@5% PVCF Project B PVCF
1 5 0.952 4.76 20 19.04
2 10 0.907 9.07 10 9.07
3 15 0.864 12.96 8 6.91
4 20 0.823 16.46 6 4.94
total cash inflows 43.25 39.96
less : initial investment (25) (25)
Npv 18.25 14.96
Project A i s better NPV . So you can choose Project A.
e. Computation of NPV
Years Project A Discount@15% PVCF Project B PVCF
1 5 0.869 4.35 20 17.38
2 10 0.756 7.56 10 7.56
3 15 0.658 9.87 8 5.26
4 20 0.572 11.44 6 3.43
Total cash inflows 33.22 33.63
less: initial invetment (25) (25)
NPV 8.22 8.63
Project B has more NPV than compare to the Project A . S you can choose anyone.
g. Based upon above table like c. and d. compute IRR
IRR = lower rate + ( lower rate NPV / lower rate NPV - higher rate NPV) * difference factor
project A :
IRR = 5+ (18.25 / 18.25 - 12.74) * 5 = 22%
Project B :
IRR = 5 + (14.96 / 14.96 - 11.54) * 5 = 27%.
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