Question

A company is considering a project that has an up-front cost paid today at t = 0. The project will generate positive cash flows of $59,529 a year at the end of each for the next 6 years. The project’s NPV is $89,007 and the company’s return on the project is 9.3 percent. What is the project’s payback?

Answer 1

As return on project given in question means it's project IRR, So first we calculate the cost of project by reverse calculation and then calculate project's payback.

In IRR, cost of project equal to PV of all cash inflow @ IRR i.e. 9.30% as NPV is zero in IRR.

So Cost of Project = C x PVIFA(i,t)

Where C = Cash Inflow

PVIFA = Present Value Interest Factor of Annuity @ i (Interest) for t (time)

= $59,529 x PVIFA(9.30% , 6)

= $59,529 x 4.4461

= $264,683.79 or say $264,680 (we received $264,683.79 we taken $264,680 for calculation)

or

Assume cash out flow A and calculate using table.

Year	Cash Flow	IRR @ 9.30%	PV
0	A	1	A
1	$ 59,529.00	0.9149	$         54,463.08
2	$ 59,529.00	0.8371	$         49,831.73
3	$ 59,529.00	0.7659	$         45,593.26
4	$ 59,529.00	0.7007	$         41,711.97
5	$ 59,529.00	0.6411	$         38,164.04
6	$ 59,529.00	0.5866	$         34,919.71
Net Present Value	A + $ 264,683.79

As we know in IRR calculation NPV '0' (ZERO)

so,

NPV = A + $ 264,683.79

0 = A + $264,683.79

A or Cost of project = $264,683.79 we take $264,680 for calculation it's not affect our calculation.

Calculation of Payback Period
Year	Cash Flow	Cummulative Cash Flow
0	$ (264,680.00)	$           (264,680)
1	$      59,529.00	$           (205,151)
2	$      59,529.00	$           (145,622)
3	$      59,529.00	$             (86,093)
4	$      59,529.00	$             (26,564)
5	$      59,529.00	$                32,965
6	$      59,529.00	$                92,494

Payback Period =	A +	B
C

Where,
A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A; and
C is the total cash inflow during the period following period A

Cumulative net cash flow is the sum of inflows to date, minus the initial outflow.

Payback Period = 4 + ($26,564/ $ 59,529*)

= 4 + 0.4462

= 4.4462 Years or Round off 4.45 Years

* Total Cash inflow in that year i.e. Negative cash flow cover and other positive = $26,564+$32,965 =$59,529

or

Here Annual cash flow is same so we can calculate Payback period via below formula

Payback Period =Initial Investment / Net Cash Flow per Period

= $264,680 / $59,529

=4.4462 Years or Round off 4.45 Years

For understaning calculate in both way otherwise it can calculate without table as calculate in above for fast answer in exam and homework, It shows smarter presentation.