Question

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$239,642 –$15,729 1 25,700 5,431 2 58,000 8,261 3 52,000 13,648 4 395,000 8,205 Whichever project you choose, if any, you require a 6 percent return on your investment.

a. What is the payback period for Project A? b. What is the payback period for Project B? c. What is the discounted payback period for Project A? d. What is the discounted payback period for Project B? e. What is the NPV for Project A? f. What is the NPV for Project B ? g. What is the IRR for Project A? h. What is the IRR for Project B? i. What is the profitability index for Project A? j. What is the profitability index for Project B?

Answer 1

Payback period is the period in which Initial Investment is recivered.

Project A:

Year	Opening Bal	CF	Closing Bal
1	$ 2,39,642.00	$     25,700.00	$ 2,13,942.00
2	$ 2,13,942.00	$   58,000.00	$ 1,55,942.00
3	$ 1,55,942.00	$   52,000.00	$ 1,03,942.00
4	$ 1,03,942.00	$3,95,000.00	$ -2,91,058.00

Payback Period = Year in which least +ve CB + [ CB in That year / CF in next year ]

= 3 + [ 103942 / 395000 ]

= 3 + 0.26

= 3.26 Years

Project B:

Year	Opening Bal	CF	Closing Bal
1	$    15,729.00	$     5,431.00	$      10,298.00
2	$    10,298.00	$     8,261.00	$        2,037.00
3	$      2,037.00	$   13,648.00	$    -11,611.00
4	$ -11,611.00	$     8,205.00	$    -19,816.00

Payback Period = Year in which least +ve CB + [ CB in That year / CF in next year ]

= 2 + [ 2037 / 13648 ]

= 2 + 0.15

= 2.15 Years

Disc PBP is similar to PBP, here we consider time value of money.

Project A:

Year	Opening Bal	CF	PVF @6%	Disc CF	Closing Bal
1	$ 2,39,642.00	$     25,700.00	0.9434	$     24,245.28	$ 2,15,396.72
2	$ 2,15,396.72	$   58,000.00	0.8900	$     51,619.79	$ 1,63,776.92
3	$ 1,63,776.92	$   52,000.00	0.8396	$     43,660.20	$ 1,20,116.72
4	$ 1,20,116.72	$3,95,000.00	0.7921	$ 3,12,877.00	$ -1,92,760.28

Disc Payback Period = Year in which least +ve CB + [ CB in That year / CF in next year ]

= 3 + [ 120116.72 / 312877 ]

= 3 + 0.38

= 3.38 Years

Project B:

Year	Opening Bal	CF	PVF @6%	Disc CF	Closing Bal
1	$    15,729.00	$     5,431.00	0.9434	$       5,123.58	$      10,605.42
2	$    10,605.42	$     8,261.00	0.8900	$       7,352.26	$        3,253.15
3	$      3,253.15	$   13,648.00	0.8396	$     11,459.12	$      -8,205.97
4	$     -8,205.97	$     8,205.00	0.7921	$       6,499.13	$    -14,705.10

Disc Payback Period = Year in which least +ve CB + [ CB in That year / CF in next year ]

= 2 + [ 3253.15 / 11459.12 ]

= 2 + 0.28

= 2.28 Years

NPV = PV of Cash Inflows - PV of Cash Outflows

Project A:

Year	CF	PVF @6%	Disc CF
0	$ -2,39,642.00	1.0000	$ -2,39,642.00
1	$      25,700.00	0.9434	$      24,245.28
2	$    58,000.00	0.8900	$      51,619.79
3	$    52,000.00	0.8396	$      43,660.20
4	$ 3,95,000.00	0.7921	$ 3,12,877.00
NPV	$ 1,92,760.28

Project B:

Year	CF	PVF @6%	Disc CF
0	$    -15,729.00	1.0000	$    -15,729.00
1	$      5,431.00	0.9434	$        5,123.58
2	$      8,261.00	0.8900	$        7,352.26
3	$    13,648.00	0.8396	$      11,459.12
4	$      8,205.00	0.7921	$        6,499.13
NPV	$     14,705.10

PI = PV of Cash Inflows / PV of Cash Outflows

ProjectA:

Year	CF	PVF @6%	Disc CF
1	$    25,700.00	0.9434	$    24,245.28
2	$    58,000.00	0.8900	$    51,619.79
3	$    52,000.00	0.8396	$    43,660.20
4	$ 3,95,000.00	0.7921	$ 3,12,877.00
PV of Cash Inflows	$ 4,32,402.28
PV of Cash Outflows	$ 2,39,642.00
PI	$              1.80

ProjectB:

Year	CF	PVF @6%	Disc CF
1	$    5,431.00	0.9434	$      5,123.58
2	$    8,261.00	0.8900	$      7,352.26
3	$ 13,648.00	0.8396	$    11,459.12
4	$    8,205.00	0.7921	$      6,499.13
PV of Cash Inflows	$    30,434.10
PV of Cash Outflows	$    15,729.00
PI	$              1.93

IRR is the Rate at which PV of Cash Inflwos are equal to PV of Cash outflows

Project A:

Year	CF	PVF @26%	Disc CF
0	$ -2,39,642.00	1.0000	$ -2,39,642.00
1	$      25,700.00	0.7937	$      20,396.83
2	$    58,000.00	0.6299	$      36,533.13
3	$    52,000.00	0.4999	$      25,995.11
4	$ 3,95,000.00	0.3968	$ 1,56,716.57
NPV	$              -0.36

Hence IRR is 26%

Project B:

Year	CF	PVF @38%	Disc CF
0	$    -15,729.00	1.0000	$    -15,729.00
1	$      5,431.00	0.7246	$        3,935.51
2	$      8,261.00	0.5251	$        4,337.85
3	$    13,648.00	0.3805	$        5,193.16
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