Question

Year 0 Cash Flow −$7,400

Year 1 Cash Flow $2,700

Year 2 Cash Flow $5,400

Year 3 Cash Flow $5,000

a. What is the profitability index for the cash flows if the relevant discount rate is 10 percent?

b. What is the profitability index for the cash flows if the relevant discount rate is 17 percent?

c. What is the profitability index for the cash flows if the relevant discount rate is 22 percent?

Answer 1

Solution

Profitability indenx=Present value of future cashflows/Initial investment

a. Present value of a cashflow=Cashflow/(1+r)^n

where

r-intrest rate or discount rate per period-10%

n-number of discounting periods

Thus

Total present value of future cashflows=2700/(1+.1)^1+5400/(1+.1)^2+5000/(1+.1)^3

Solving

Total present value of future cashflows=10673.929

Thus profitability index=10673.929/7400

Thus profitability index=1.442

b

Present value of a cashflow=Cashflow/(1+r)^n

where

r-intrest rate or discount rate per period-17%

n-number of discounting periods

Thus

Total present value of future cashflows=2700/(1+.17)^1+5400/(1+.17)^2+5000/(1+.17)^3

Solving

Total present value of future cashflows=9374.318

Thus profitability index=9374.318/7400

Thus profitability index=1.267

c.

Present value of a cashflow=Cashflow/(1+r)^n

where

r-intrest rate or discount rate per period-22%

n-number of discounting periods

Thus

Total present value of future cashflows=2700/(1+.22)^1+5400/(1+.22)^2+5000/(1+.22)^3

Solving

Total present value of future cashflows=8594.706

Thus profitability index=8594.706/7400

Thus profitability index=1.161