Question

# Year Cash Flow 0 −\$9,700           1 3,800           2 4,600           3 5,000      &nb

 Year Cash Flow 0 −\$9,700 1 3,800 2 4,600 3 5,000

 Required :
 (a) What is the profitability index for the cashflows if the relevant discount rate is 11 percent?

 (b) What is the profitability index for the cashflows if the relevant discount rate is 16 percent?

 (c) What is the profitability index for the cashflows if the relevant discount rate is 21 percent?

The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows.

(a) The equation for the profitability index at a required return of 11 percent is:

PI = (\$3,800 / 1.11 + \$4,600 / 1.112 + \$5,000 / 1.113) / \$9,700 = 1.115

(b) The equation for the profitability index at a required return of 16 percent is:

PI = (\$3,800 / 1.16 + \$4,600 / 1.162 + \$5,000 / 1.163) / \$9,700 = 1.020

(c) The equation for the profitability index at a required return of 21 percent is:

PI = (\$3,800 / 1.21 + \$4,600 / 1.212 + \$5,000 / 1.213) / \$9,700 = 0.939