Question

ee. You are considering two independent projects with cashflow information below. Both have been assigned a discount rate of 8%. Based on the profitability index, what is your recommendation concerning these projects? Year Project A Project B 0 -$39,500 -$42,000 1 20,000 10,000 2 24,000 35,000

A You should accept both projects since both of their PIs are positive

B You should accept both projects since both of their PIs are greater than 1

C You should only accept project B since it has the largest PI and the PI exceeds 1

D Neither project is acceptable

E You should accept project A since it has the higher PI

Answer 1

Year	Project A ($)	Project B ($)
0	-39,500	-42,000
1	20,000	10,000
2	24,000	35,000

Profitability index (PI) is variant of NPV technique. It is calculated by dividing present value of all cash inflows to present value of cash outflows.

Decision rule is - " Accept the project if PI is more than 1 and reject if it is less than 1."

PI = Present value of cash inflows / Present value of cash outflows.

At year 0, Initial investment (cash outflow ) for Project A = $ 39,500

At year 0, Initial investment (cash outflow ) for Project B = $ 42,000

For Project A

Using above formula, present value of cash inflow is calculated at 8 % discount rate.

For example for year 1 -

PV = 20000 / ( 1+ 0.08)¹ = 18518.51852 $

year	cash inflow	present value of cash inflow
1	20000	18518.51852
2	24000	20576.13169

The total present value of cash inflow for project A = 39094.65 $ (approx)

Present value of cash outflows for project A =  $ 39,500

PI = Present value of cash inflows / Present value of cash outflows.

= 39094.65 / 39,500 = 0.99 (approx)

For Project B

Using above formula, present value of cash inflow is calculated at 8 % discount rate.

year	cash inflow	present value of cash inflow
1	10000	9259.259259
2	35000	30006.85871

The total present value of cash inflow for project A = 39266.12 $ (approx)

Present value of cash outflows for project A =  $ 42,000

PI = Present value of cash inflows / Present value of cash outflows.

= 39266.12 / 42,000

= 0.93 (approx)

As the PI for both the projects is less than 1, both the projects should be rejected.

Correct answer is - D Neither project is acceptable

Hope it helps !