Question

Consider the following two mutually exclusive projects: year,0,1,2,3,4,cash flow,-304,700,26,400,54,000,51,000,412,000,cash flow,-15,729,5,212,8,998,13,146,9,060. Whichever project you choose, if any, you require a six 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 discount 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:

Payback period is the period in which initial investment is recovered.

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
If Actual PBP > Expected PBP - Project will be rejected
Actual PBP </= Expected PBP - Project will be accepted

Project A:

Year	Opening Balance	Cash Flow	Closing Balance
1	$       3,04,700.00	$     26,400.00	$    2,78,300.00
2	$       2,78,300.00	$     54,000.00	$    2,24,300.00
3	$       2,24,300.00	$     51,000.00	$    1,73,300.00
4	$       1,73,300.00	$ 4,12,000.00	$   -2,38,700.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 3 Years + [ $ 173300 / $ 412000 ]
= 3 Years + 0.42 Years
= 3.42 Years
Payback Period is 3.42 Years
PBP Refers Payback Period

Project B:

Year	Opening Balance	Cash Flow	Closing Balance
1	$          15,729.00	$       5,212.00	$       10,517.00
2	$          10,517.00	$       8,998.00	$          1,519.00
3	$            1,519.00	$     13,146.00	$      -11,627.00
4	$        -11,627.00	$       9,060.00	$      -20,687.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 2 Years + [ $ 1519 / $ 13146 ]
= 2 Years + 0.12 Years
= 2.12 Years
Payback Period is 2.12 Years
PBP Refers Payback Period

Discounted Payback period:
Discounted Payback period is the period in which initial investment is recovered after considering the time value of money.

Discounted PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Discounted Cash flow in Next Year ]
If Actual disc PBP > Expected disc PBP - Project will be rejected
Actual disc PBP </= Expected disc PBP - Project will be accepted

Project A:

Year	Opening Balance	Cash Flow	PVF @6 %	Disc CF	Closing Balance
1	$       3,04,700.00	$     26,400.00	0.9434	$     24,905.66	$    2,79,794.34
2	$       2,79,794.34	$     54,000.00	0.8900	$     48,059.81	$    2,31,734.53
3	$       2,31,734.53	$     51,000.00	0.8396	$     42,820.58	$    1,88,913.95
4	$       1,88,913.95	$ 4,12,000.00	0.7921	$ 3,26,342.59	$   -1,37,428.64

Disc PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 3 Years + [ $ 188913.95 / $ 326342.59 ]
= 3 Years + 0.58 Years
= 3.58 Years
Payback Period is 3.58 Years
PBP Refer Payback Period

Project B:

Year	Opening Balance	Cash Flow	PVF @6 %	Disc CF	Closing Balance
1	$          15,729.00	$       5,212.00	0.9434	$       4,916.98	$       10,812.02
2	$          10,812.02	$       8,998.00	0.8900	$       8,008.19	$          2,803.83
3	$            2,803.83	$     13,146.00	0.8396	$     11,037.64	$        -8,233.80
4	$           -8,233.80	$       9,060.00	0.7921	$       7,176.37	$      -15,410.17

Disc PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 2 Years + [ $ 2803.83 / $ 11037.64 ]
= 2 Years + 0.25 Years
= 2.25 Years
Payback Period is 2.25 Years
PBP Refer Payback Period

NPV :
NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.

Project A:

Year	CF	PVF @0.06	Disc CF
0	$ 3,04,700.00	1.0000	$ 3,04,700.00
1	$    26,400.00	0.9434	$    24,905.66
2	$    54,000.00	0.8900	$    48,059.81
3	$    51,000.00	0.8396	$    42,820.58
4	$ 4,12,000.00	0.7921	$ 3,26,342.59
NPV			$ 7,46,828.64

Project B:

Year	CF	PVF @0.06	Disc CF
0	$    15,729.00	1.0000	$    15,729.00
1	$      5,212.00	0.9434	$       4,916.98
2	$      8,998.00	0.8900	$       8,008.19
3	$    13,146.00	0.8396	$    11,037.64
4	$      9,060.00	0.7921	$       7,176.37
NPV			$    46,868.17

Profitability Index:

PI = PV of Cash inflows / PV of Cash Outflows
If PI > 1, Project will be accepted,
PI = 1, Indifference point. Project will be accepted/ Rejected.
PI < 1, Project will be rejected.

Project A:

Year	CF	PVF @0.06	Disc CF
1	$    26,400.00	0.9434	$    24,905.66
2	$    54,000.00	0.8900	$    48,059.81
3	$    51,000.00	0.8396	$    42,820.58
4	$ 4,12,000.00	0.7921	$ 3,26,342.59
PV of cash Inflows			$ 4,42,128.64
PV of cash Outflows			$ 3,04,700.00
Profitability Index:			1.45

Project B:

Year	CF	PVF @0.06	Disc CF
1	$    5,212.00	0.9434	$    4,916.98
2	$    8,998.00	0.8900	$    8,008.19
3	$ 13,146.00	0.8396	$ 11,037.64
4	$    9,060.00	0.7921	$    7,176.37
PV of cash Inflows			$ 31,139.17
PV of cash Outflows			$ 15,729.00
Profitability Index:			1.98

IRR :
IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows.

IRR = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in disc rate ] * 1%

If IRR > Cost of Capital - Project can be accepted
IRR = Cost of Capital - Indifferebce Point - Project will be accepted / Rejected
IRR < Cost of Capital - Project will be erejected

Project A:

Year	CF	PVF @18%	Disc CF
0	$ -3,04,700.00	1.0000	$ -3,04,700.00
1	$      26,400.00	0.8475	$      22,372.88
2	$      54,000.00	0.7182	$      38,781.96
3	$      51,000.00	0.6086	$      31,040.17
4	$ 4,12,000.00	0.5158	$ 2,12,505.02
NPV			$                    -

Hence IRR is 18%

Project B:

Year	CF	PVF @39%	Disc CF
0	$    -15,729.00	1.0000	$    -15,729.00
1	$        5,212.00	0.7194	$        3,749.64
2	$        8,998.00	0.5176	$        4,657.11
3	$      13,146.00	0.3724	$        4,894.96
4	$        9,060.00	0.2679	$        2,427.00
NPV			$                    -

Thus IRR is 39%

Pls do rate, if the answer is correct and comment, if any further assistance is required.