Question

Payback Period, Net Present Value, and Internal Rate of Return

An organization’s initial outlay for a proposed project is $2,000,000. Use the table below to calculate the payback period, net present value, and internal rate of return for the project.

Free Cash Flows
Year	Amount		Year	Amount
1	$0.00		6	$0.00
2	$0.00		7	$0.00
3	$1,000,000.00		8	$500,000.00
4	$50.00		9	$500,000.00
5	$750,000.00		10	$500,000.00

As the CEO of the organization, if the firm’s cost of capital is 10%, your organizational goal for payback period is 9 years, taking into account the internal rate of return, would you allow this project to move forward? Why or why not?

Answer 1

Payback Period for the Project

Year	Cash Flows ($)	Cumulative net Cash flow ($)
0	-20,00,000.00	-20,00,000.00
1	-	-20,00,000.00
2	-	-20,00,000.00
3	10,00,000.00	-10,00,000.00
4	50.00	-9,99,950.00
5	7,50,000.00	-2,49,950.00
6	-	-2,49,950.00
7	-	-2,49,950.00
8	5,00,000.00	2,50,050.00
9	5,00,000.00	7,50,050.00
10	5,00,000.00	12,50,050.00

Payback Period = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 7 Year + ($249,950 / $500,000)

= 7 Year + 0.50 years

= 7.50 Years

“The Payback Period for the Project = 7.50 Years”

Net Present Value (NPV)

Year	Annual Cash Inflow ($)	Present Value Factor at 10%	Present Value of Annual Cash Inflow ($)
1	0	0.90909	0
2	0	0.82645	0
3	10,00,000.00	0.75131	7,51,314.80
4	50.00	0.68301	34.15
5	7,50,000.00	0.62092	4,65,690.99
6	0	0.56447	0
7	0	0.51316	0
8	5,00,000.00	0.46651	2,33,253.69
9	5,00,000.00	0.42410	2,12,048.81
10	5,00,000.00	0.38554	1,92,771.64
TOTAL			18,55,114.09

Net Present Value = Present Value of annual cash inflows – Initial Investment

= $18,55,114.09 - $20,00,000

= -$1,44,885.91 (Negative NPV)

Internal Rate of Return

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 7%

Year	Annual Cash Inflow ($)	Present Value Factor at 7%	Present Value of Annual Cash Inflow ($)
1	0	0.93458	0
2	0	0.87344	0
3	10,00,000.00	0.81630	8,16,297.88
4	50.00	0.76290	38.14
5	7,50,000.00	0.71299	5,34,739.63
6	0	0.66634	0
7	0	0.62275	0
8	5,00,000.00	0.58201	2,91,004.55
9	5,00,000.00	0.54393	2,71,966.87
10	5,00,000.00	0.50835	2,54,174.65
TOTAL			21,68,221.73

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $21,68,221.73 - $20,00,000

= $ 1,68,221.73

Step – 2, NPV at 7% is positive, Calculate the NPV again at a higher discount rate, Say 9%

Year	Annual Cash Inflow ($)	Present Value Factor at 9%	Present Value of Annual Cash Inflow ($)
1	0	0.91743	0
2	0	0.84168	0
3	10,00,000.00	0.77218	7,72,183.48
4	50.00	0.70843	35.42
5	7,50,000.00	0.64993	4,87,448.54
6	0	0.59627	0
7	0	0.54703	0
8	5,00,000.00	0.50187	2,50,933.14
9	5,00,000.00	0.46043	2,30,213.89
10	5,00,000.00	0.42241	2,11,205.40
TOTAL			19,52,019.87

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $19,52,019.87 - $20,00,000

= -$47,980.13 (Negative)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.07 + [$1,68,221.73 x (0.09 – 0.07)]

              $ 1,68,221.73 – (-$47,980.13)

= 0.07 + 0.0154

= 0.0854

= 8.54%

"Internal Rate of Return (IRR) = 8.54%"