# Consider a project with cash flows: Year 0 1 2 3 4 5 P -$19$10 $5$3 $5$10 Compute the...

## Question:

Consider a project with cash flows:

Year 0 1 2 3 4 5
P -$19$10 $5$3 $5$10

Compute the profitability index based on a 10% cost of capital and compute the payback time.

## Cost of Capital:

The cost of capital is the cost that needs to be paid to acquire the capital from the market. The capital can be the debt capital or equity capital. It is based on financial planning performed by the management.

The profitability index based on a 10% cost of capital:

Year Cash Flow PV factor @10% PV x Cash flow
0 -19 1 /(1.10)^0 =1 -19
1 10 1/(1.1)^1=>0.90909 9.0909
2 5 1/(1.1)^2=>0.82645 4.13225
3 3 1/(1.1)^3=>0.75131 2.25393
4 5 1/(1.1)^4=>0.68301 3.41505
5 10 1/(1.1)^5=>0.62092 6.2092
NPV 6.10133

Year Cash Flow Cumulative Cash Flow
1 10 10
2 5 10 + 5 = 15
3 3 15 + 3 = 18
4 5 18 + 5 = 23
5 10 23 + 10 = 33
As initial cash flow that needs to be recovered is $19. Therefore on the 4th year$19 can be recovered.
Hence, Payback period is 4 years. 