Consider two mutually exclusive Projects A (3-year life) & B (4-year life), with
ID: 1172049 • Letter: C
Question
Consider two mutually exclusive Projects A (3-year life) & B (4-year life), with the following cash flows. The discount rate is 10%. Which statement is correct?project A
Year: cash flow
t=0: -$14,000
t=1: $7,000
t=2: $8,000
t=3: $9,000
project B
Year: cash flow
t=0: -$20,000
t=1: $ 8,000
t=2: $7,000
t=3: $7,000
t=4: $12,000 A. A is chosen because it has a higher NPV. B. B is chosen because it has a higher NPV. C. A is chosen because it has a shorter Pay Back Period. D. B is chosen because it has a shorter Pay Back Period. E. None of the above is correct. Consider two mutually exclusive Projects A (3-year life) & B (4-year life), with the following cash flows. The discount rate is 10%. Which statement is correct?
project A
Year: cash flow
t=0: -$14,000
t=1: $7,000
t=2: $8,000
t=3: $9,000
project B
Year: cash flow
t=0: -$20,000
t=1: $ 8,000
t=2: $7,000
t=3: $7,000
t=4: $12,000 A. A is chosen because it has a higher NPV. B. B is chosen because it has a higher NPV. C. A is chosen because it has a shorter Pay Back Period. D. B is chosen because it has a shorter Pay Back Period. E. None of the above is correct.
Explanation / Answer
To answer this question let us first compute the NPV of both these projects:
As we can see that "B" has a higher NPV. But one has to keep in mind the fact that A and B have unequal lives.
Payback period will not be applicable as it is used to compare project with equal lives.
As such both the NPV and payback method is not suitable for projects with different lives.
To evaluate project with unequal lives we consider annual net present value method (or the equivalent annual annuity approach). Annual net present value = NPV/Annuity discount factor for the project life
Hence the answer is option "e" - none of the above is correct.
Project A A B C = A*B Year Cash Flow 1+r PVIF PV 0 -14,000 1.10 1.0000 -14,000.00 1 7,000 0.9091 6,363.64 2 8,000 0.8264 6,611.57 3 9,000 0.7513 6,761.83 NPV 5,737.04 Project B A B C = A*B Year Cash Flow 1+r PVIF PV 0 -20,000.0 1.10 1.0000 -20,000.00 1 8,000.0 0.9091 7,272.73 2 7,000.0 0.8264 5,785.12 3 7,000.0 0.7513 5,259.20 4 12,000.0 0.6830 8,196.16 NPV 6,513.22