Question

Year 0 = Cash Flow -$16,700 Year 1 = Cash Flow $9,700 Year 2 = Cash Flow $7,800 Year 3 = Cash Flow $4,400

What is the profitability index for the set of cash flows if the relevant discount rate is 10 percent? What is the profitability index for the set of cash flows if the relevant discount rate is 15 percent? What is the profitability index for the set of cash flows if the relevant discount rate is 22 percent?

Answer 1

Calculate the NPV when the discount rate is 10%

NPV = Sum of present value of cash flows - Year 0 Cash flow

NPV = 9700 / (1 + 10%) + 7800 / (1 + 10%)^2 + 4400 / (1 + 10%)^3 - 16700

= 1870.25

Profitability Index = (NPV + Year 0 Cash flow) / Year 0 Cash flow

= (1870.25 + 16700) / 16700

= 1.11

Calculate the NPV when the discount rate is 15%

NPV = Sum of present value of cash flows - Year 0 Cash flow

NPV = 9700 / (1 + 15%) + 7800 / (1 + 15%)^2 + 4400 / (1 + 15%)^3 - 16700

= 525.77

Profitability Index = (NPV + Year 0 Cash flow) / Year 0 Cash flow

= (525.77 + 16700) / 16700

= 1.03

Calculate the NPV when the discount rate is 22%

NPV = Sum of present value of cash flows - Year 0 Cash flow

NPV = 9700 / (1 + 22%) + 7800 / (1 + 22%)^2 + 4400 / (1 + 22%)^3 - 16700

= (1085.54)

Profitability Index = (NPV + Year 0 Cash flow) / Year 0 Cash flow

= (-1085.54 + 16700) / 16700

= 0.94