Question

Marge Simpson Inc. has following business opportunities with following cash flow information. Assume Marge’s opportunity cost of capital is 12%.

Year	Project A	Project B
0	−$20,000	−$20,000
1	15,000	2,000
2	15,000	2,500
3	13,000	3,000
4	3,000	50,000

Calculate profitability index for both projects.

Answer 1

Given about a two projects,

Calculating PI for Project A first,

initial cost C0 = $20000

cash flow over the next 4 years are

CF1 = $15000

CF2 = $15000

CF3 = $13000

CF4 = $3000

Cost of capital d = 12%

Profitability index of a project B= PV of future cash flows/initial investment

So, PV of future cash flows = CF1/(1+d) + CF2/(1+d)^2 + CF3/(1+d)^3 + CF4/(1+d)^4

=> PV of future cash flows = 15000/1.12 + 15000/1.12^2 + 13000/1.12^3 + 3000/1.12^4 = $36510.46

So, profitability index PI of project B = 36510.46/20000 = 1.826

Now Calculating PI for Project B,

initial cost C0 = $20000

cash flow over the next 4 years are

CF1 = $2000

CF2 = $2500

CF3 = $3000

CF4 = $50000

Cost of capital d = 12%

Profitability index of a project B = PV of future cash flows/initial investment

So, PV of future cash flows = CF1/(1+d) + CF2/(1+d)^2 + CF3/(1+d)^3 + CF4/(1+d)^4

=> PV of future cash flows = 2000/1.12 + 2500/1.12^2 + 3000/1.12^3 + 50000/1.12^4 = $37689.94

So, profitability index PI of project B = 37689.94/20000 = 1.884