Question

1. The following cash flows are given for the Project Z

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            C0            C1            C2            C3            C4               C5

         -$7000    +$3,000   +$4,000   +$6,000     +$2,500      +$2,000

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Calculate the following:     (a) NPV (Net Present Value) at 12% discount rate  
                                             (b) IRR (Internal Rate of Return)  

                                             (c) The payback period for Project (Z)

Answer 1

a) Net Present Value (NPV) : NPV is the sum of present value of all Cash inflows and Casho outflows of a project.

Compuation Net Present Value for Project Z

Year	Cash Flows	Present Value Factor @12%	Present Value of Cash Flows
0	$(7,000)	1	$(7,000)
1	$3,000	0.8929	$2,678.7
2	$4,000	0.7972	$3,188.8
3	$6,000	0.7118	$4,270.8
4	$2,500	0.6335	$1,583.75
5	$2,000	0.5674	$1,134.8
NPV	$5,856.8

Ans : NPV of the Project is $5856.8

b) Internal Rate of Return (IRR) is the rate at which Present Value of Cash Inflows is equal to Present Value of Cash Flows i.e. NPV is 0.

IRR is calculated by trial and error method

Assumed Discount Rate at 43 %

Year	Cash Flows	Present Value Factor @43%	Present Value of Cash Flows
0	$(7,000)	1	$(7,000)
1	$3,000	0.6993	$2097.9
2	$4,000	0.4890	$1956
3	$6,000	0.3420	$2052
4	$2,500	0.2391	$597.75
5	$2,000	0.1672	$334.4
NPV	38.05

Assumed Discount Rate at 44 %

Year	Cash Flows	Present Value Factor @43%	Present Value of Cash Flows
0	$(7,000)	1	$(7,000)
1	$3,000	0.6944	$2083.2
2	$4,000	0.4823	$1929.2
3	$6,000	0.3349	$2009.4
4	$2,500	0.2326	$581.5
5	$2,000	0.1615	$323
NPV	(73.7)

IRR rate is between 43% and 44%.

IRR Rate = 43% + 38.05 / 111.73
= 43 + 0.34
=~43.34%

Ans : IRR of the project is ~43.34%

c) Payback Period

Yr	Cash Flows	Cumulative Cash Flows
0	$(7,000)	$(7,000)
1	$3,000	$(4,000)
2	$4,000	0
3	$6,000	$6,000
4	$2,500	$2,500
5	$2,000	$2,000

Payback Period = 2 years i.e. in 2 year entire intial investment is recovered.

Discounted Payback Period using 12% discount rate

Yr	Cash Flows	Present Value Factor @ 12%	Present Value of Cash Flows	Cumulative Present Value of Cash Flows
0	$(7,000)	1	$(7,000)	$(7,000)
1	$3,000	0.8929	$2,678.7	$(4321.3)
2	$4,000	0.7972	$3,188.8	$(1132.5)
3	$6,000	0.7118	$4,270.8	$3138.3
4	$2,500	0.6335	$1,583.75	$4722.05
5	$2,000	0.5674	$1,134.8	$5856.85

Discounted PBP = T + CPVCF / PVCF

where,

T = time period where cumulative present value of cash flows was last negative
CPVCF = Cumulative Present Value Cash Flow of Period T
PVCF = Present Value of Cash Flow of the period following the period t

Discounted PBP = Year 2 + $1132.5 / $4270.8
= 2 + 0.265
= 2.265 = ~2.27 years