## Question

###### Calculating Profitability Index What is the profitability index for the following set of cash flows if...

Calculating Profitability Index What is the profitability index for the following set of cash flows if the relevant discount rate is 10 percent? What if the discount rate is 15 percent? If it is 22 percent? Year Cash Flow -$29,500 16,900 13,600 8,300

## Answers

To calculate the PI, we need to calculate the NPV:

When discount rate = 10%

Year CF Discount Factor Discounted CF 0 $ -29,500.00 1/(1+0.1)^0= 1 1*-29500= $ -29,500.00 1 $ 16,900.00 1/(1+0.1)^1= 0.909090909 0.909090909090909*16900= $ 15,363.64 2 $ 13,600.00 1/(1+0.1)^2= 0.826446281 0.826446280991735*13600= $ 11,239.67 3 $ 8,300.00 1/(1+0.1)^3= 0.751314801 0.751314800901578*8300= $ 6,235.91 NPV = Sum of all Discounted CF $ 3,339.22 Profitability Index1.11

When discount rate = 15%

Year CF Discount Factor Discounted CF 0 $ -29,500.00 1/(1+0.15)^0= 1 1*-29500= $ -29,500.00 1 $ 16,900.00 1/(1+0.15)^1= 0.869565217 0.869565217391304*16900= $ 14,695.65 2 $ 13,600.00 1/(1+0.15)^2= 0.756143667 0.756143667296787*13600= $ 10,283.55 3 $ 8,300.00 1/(1+0.15)^3= 0.657516232 0.657516232431988*8300= $ 5,457.38 NPV = Sum of all Discounted CF $ 936.59 Profitability Index1.03

When discount rate = 22%

Year CF Discount Factor Discounted CF 0 $ -29,500.00 1/(1+0.22)^0= 1 1*-29500= $ -29,500.00 1 $ 16,900.00 1/(1+0.22)^1= 0.819672131 0.819672131147541*16900= $ 13,852.46 2 $ 13,600.00 1/(1+0.22)^2= 0.671862403 0.671862402579952*13600= $ 9,137.33 3 $ 8,300.00 1/(1+0.22)^3= 0.550706887 0.550706887360616*8300= $ 4,570.87 NPV = Sum of all Discounted CF $ -1,939.35 Profitability Index0.93 NPV Profitability Inder =1+ Initial investment 3339.22 Profitability Inder =1+ 29500 Profitability Index = 1.11NPV Profitability Inder =1+ Initial investment 963.59 Profitability Index =1+ 29500 Profitability Inder = 1.03NPV Profitability Inder =1+ Initial investment 1939.35 Profitability Index =1+ 29500 Profitability Inder = 0.93

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