Question

You are analyzing two projects with the cash flows shown below.

Year:                        0                     1                  2                 3               4                    5           

Project 1:     -$6,000       $1,000      $1,000    $1,500    $2,000    $4,000     

Project 2:     -$6,000       $2,500      $2,000    $1,500    $1,000    $1,500

Construct an NPV chart with discount rates from 1% - 25%.   On your NPV chart, please identify and label the following points:

a) The IRR of project 1 (calculate the value and label the value on the chart)

b) The IRR of project 2 (calculate the value and label the value on the chart)

c) The discount rate at which the NPV of the two projects is equal (i.e., the incremental IRR). (calculate the value and label the value on the chart)

d) What is the simple payback period for each project?

e) If you can only do one of the two projects, which project will you do if your firm’s cost of capital is 6%? Why?

f) If you had no capital constraints (i.e., if you had unlimited funds), which projects would you do if your firm’s cost of capital was 12%?

g) If you could only do one project, which project would you do if your firm’s cost of capital was 12%? Why?

h) Which projects would you do if your firm’s cost of capital was 16%? Why?

Answer 1

IRR :
IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows or Rate of growth is expected from project/ Investment. At IRR, NPV of Project/ Investment will be Zero. It assumes that intermediary Cfs are reinvested at IRR only.

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

NPV :
NPV is the difference between Present value of Cash Inflows and Present value of cash outflows.

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.

Part A:

Year	CF	PVF @13 %	Disc CF	PVF @14 %	Disc CF
0	$         (6,000.00)	1.0000	$         -6,000.00	1.0000	$         -6,000.00
1	$          1,000.00	0.8850	$             884.96	0.8772	$             877.19
2	$          1,000.00	0.7831	$             783.15	0.7695	$             769.47
3	$          1,500.00	0.6931	$          1,039.58	0.6750	$          1,012.46
4	$          2,000.00	0.6133	$          1,226.64	0.5921	$          1,184.16
5	$          4,000.00	0.5428	$          2,171.04	0.5194	$          2,077.47
NPV			$             105.35		$              -79.25

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 13 % + [ 105.35 / ( 105.35 - ( -79.25) ) ] * 1 %
= 13 % + [ 105.35 / ( 184.6) ] * 1 %
= 13 % + [ 0.57 ] * 1 %
= 13 % + 0.57 %
= 13.57 %

Part B:

Year	CF	PVF @14 %	Disc CF	PVF @15 %	Disc CF
0	$         (6,000.00)	1.0000	$         -6,000.00	1.0000	$         -6,000.00
1	$          2,500.00	0.8772	$          2,192.98	0.8696	$          2,173.91
2	$          2,000.00	0.7695	$          1,538.94	0.7561	$          1,512.29
3	$          1,500.00	0.6750	$          1,012.46	0.6575	$             986.27
4	$          1,000.00	0.5921	$             592.08	0.5718	$             571.75
5	$          1,500.00	0.5194	$             779.05	0.4972	$             745.77
NPV			$             115.51		$              -10.01

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 14 % + [ 115.51 / ( 115.51 - ( -10.01) ) ] * 1 %
= 14 % + [ 115.51 / ( 125.52) ] * 1 %
= 14 % + [ 0.92 ] * 1 %
= 14 % + 0.92 %
= 14.92 %
Part C:

Year	CF of Project 1	CF of Project 2	Diff CF	PVF @10 %	Disc CF	PVF @11 %	Disc CF
0	$ -60,000.00	$ -60,000.00	$                 -	1.0000	$                 -	1.0000	$                 -
1	$      1,000.00	$      2,500.00	$   -1,500.00	0.9091	$   -1,363.64	0.9009	$   -1,351.35
2	$      1,000.00	$      2,000.00	$   -1,000.00	0.8264	$      -826.45	0.8116	$      -811.62
3	$      1,500.00	$      1,500.00	$                 -	0.7513	$                 -	0.7312	$                 -
4	$      2,000.00	$      1,000.00	$    1,000.00	0.6830	$        683.01	0.6587	$        658.73
5	$      4,000.00	$      1,500.00	$    2,500.00	0.6209	$    1,552.30	0.5935	$    1,483.63
NPV	$          45.23		$        -20.61

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

= 10 % + [ $ 45.23 / $ 65.85 ] * 1%
= 10 % + [ 0.69 ] * 1%
= 10 % + [ 0.69 % ]
= 10.69 %

Till Cross over Rate (10.69 % ) we can consider the Project with Higher NPV at cost of capital i.e Project 1
After Cross over Rate (10.69 % ) we can consider the Project with Lower NPV at cost of capital i.e Project 2

Part D:

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 1:

Year	Opening Balance	Cash Flow	Closing Balance
1	$            6,000.00	$         1,000.00	$          5,000.00
2	$            5,000.00	$         1,000.00	$          4,000.00
3	$            4,000.00	$         1,500.00	$          2,500.00
4	$            2,500.00	$         2,000.00	$             500.00
5	$               500.00	$         4,000.00	$        -3,500.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 4 Years + [ $ 500 / $ 4000 ]
= 4 Years + 0.13 Years
= 4.13 Years

Payback Period is 4.13 Years

Project 2:

Year	Opening Balance	Cash Flow	Closing Balance
1	$            6,000.00	$         2,500.00	$          3,500.00
2	$            3,500.00	$         2,000.00	$          1,500.00
3	$            1,500.00	$         1,500.00	$                      -
4	$                        -	$         1,000.00	$        -1,000.00
5	$           -1,000.00	$         1,500.00	$        -2,500.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 3 Years + [ $ 0 / $ 1000 ]
= 3 Years + 0 Years
= 3 Years Payback Period is 3 Years

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