Question

5) Assume that it costs $1,000 to start a project. If the project will give $400 profit in the first year, $500 in the second year and $300 in the third year. find the pay back period. Now assume that the interest rate is 10%, find the net present value (NPV) and the profitability index (PI) for this project

Answer 1

1)Payback period: The period by which we will recover the intial investment.

Year	Annual Cashflows	Cumulative Cashflows
0	($1000)	($1000)
1	$400	($600)
2	$500	($100)
3	$300	$200

When cashflow are not same , we have to calculate cumulative cashflows and use the below formula

Payback period = A + (B/C)

A = last period number with a negative cumulative cash flow = Year 2

B = absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A = $100

C = total cash inflow during the period following period A = $300

Solution:

Payback period = 2years + ($100/$300)years

Payback period = 2years + 0.33 years

Payback period = 2.33 years

2)Net Present Value (NPV)

Year	Cashflow	PVF	PV
0	($1000)	1	($1000)
1	$400	0.909	$363.6
2	$500	0.826	$413
3	$300	0.751	$225.3
		Total	$1.9

3) Profitability Index(PI) : Any PI which is higher than 1 is good.

Formula:PV of Future Cashflows / Initial Investment

PI = (363.6+413+225.3) / $1000

PI = $1001.9 / $1000

PI = 1.0019