Question

Suppose your firm is considering investing in Project W with the cash flows shown in the table, that the required rate of return on projects of this risk class is 10 percent, and that the maximum allowable payback and discounted payback statistics for the project are 3.5 and 4.5 years, respectively. Use the PI decision to evaluate this project; should it be accepted or rejected?

A. PI = 1.04; reject the project

B. PI = 1.04; accept the project

C. PI = 0.04; reject the project

D. PI = 0.96; reject the project

E. PI = 0.96; accept the project

Project W Time Cash Flow 0 – $85,000 1 $12,000 2 $11,000 3 $13,000 4 $21,000 5 $31,000 6 $32,000

Answer 1

PI is Profitability index i.e. Present value of cash inflows divided by present value of cash out flows.

PI should be more than 1 in order to be financially viable.

Calculation of present value of cash inflows:

Year	Cash inflows	Present value interest factor @ 10%	Present values
1	12000	0.9091	10909.09
2	11000	0.8264	9090.91
3	13000	0.7513	9767.09
4	21000	0.6830	14343.28
5	31000	0.6209	19248.56
6	32000	0.5645	18063.17

Total present value of cash inflows = 81422.1

PI = Present value of inflows/ Outflow = 81422.1/85000 = 0.96

Payback period & Discounted payback period:

Payback period = First 4 years + Proportionate figure to recover up to 85,000

Payback period = (12000+11000+13000+21000) + [(85000-57000)/(88000-57000)] = 4.74 years

Discounted payback period = As the entire period of 6 years could not recover the initial investment so discounted payback period is above 6 years

Therefore,

PI = 0.96 and reject the project as the payback and discounted payback period are above maximum allowable period.