Question

1)you've estimated the following cash flows (in$) for a project

A. B

year. cash flow

0 -5,300

1 1,325

2 2,148

3 2,209

what is the IRE for the project

2)you've estimated the following cash flows (in$) for 2 projects:

A. B. C.   

year. ProjectA. ProjectB

0. -78 -261

1 15 50

2 21 73

3 29 82

4 35 127

the required return is 7% for both projects

What is the IRR for project B?

What is the NVP of project B?

If the projects are mutually exclusive which project you choose? project B, based on the IRR; project A, based on IRR; project A, based on IRR; project B based on NVP?

3) wh smith company is evaluating three projects: A,B,C with cash flows as given in the table. each project requires an initial investment of $97,000 and has requirement return of 7%

year. A. B. C

1 50,000 0 20,000

2 40,000 50,000 40,000

3 20,000 50,000 40,000

4 10,000 40,000 40,000

What is the payback period for a project A(in years)?

Answer 1

(1) IRR calculation-

Year	Cash flow
0	-5300
1	1325
2	2148
3	2209
Total	382

at IRR the NPV of the project will be zero. Current Value of the project without discounting = $382 in 3 years ($127.33) per year

Hence Dummy IRR = $127.33/$5300*100 =2.40%

Lets take IRR between 3% to 4%

Year	Cash flow	PVF@3%	PV of cash flow	PVF@4%	PV of cash flow
0	-5300	1	-5300	1	-5300
1	1325	0.97087	1286	0.96154	1274
2	2148	0.94260	2025	0.92456	1986
3	2209	0.91514	2022	0.88900	1964
NPV			32.65		-76.22

NPV at IRR 3% = $32.65

NPV at IRR 4% =$-76.22

Applying Interpolation IRR= 3% +[1%/(32.65-(-76.22)]*32.65 = 3.296%

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(2)

Year	Project-A	Project-B
0	-78	-261
1	15	50
2	21	73
3	29	82
4	35	127

# Requirement -1(IRR of project-B)-

Lets take IRR between 8-9% for project B

Year	Project-B CASH FLOW	pvf@8%	PV of cash flows	PVF@9%	PV of the cash flow
0	-261	1	-261	1	-261
1	50	0.9259	46.30	0.917	45.87
2	73	0.8573	62.59	0.842	61.44
3	82	0.7938	65.09	0.772	63.32
4	127	0.7350	93.35	0.708	89.97
	NPV		6.33		-0.40

By applying Interpolation IRR of project -B = 8%+[1%/(6.33-(-0.40)]*6.33 = 8.940%

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#Requirement-2(NPV of project-B)

Year	Project-B CASH FLOW	pvf@7%	PV of cash flows
0	-261	1	-261
1	50	0.9346	46.73
2	73	0.8734	63.76
3	82	0.8163	66.94
4	127	0.7629	96.89
	NPV		13.31

NPV of the project B = $13.31

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#Requirement-3(Which project to be shown)

Year	Project-A	pvf@7%	PV of cash flows
0	-78	1	-78
1	15	0.9346	14.02
2	21	0.8734	18.34
3	29	0.8163	23.67
4	35	0.7629	26.70
	NPV		4.73

NPV of the project A =$4.73

NPV of Project B = $13.31

If projects are mutually exclusive then the project having highest NPV should be choosen.

Hence project B should be choosen based on NPV

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(3)

(i)Normal pay back period-

Normal pay back period = A +(B/C)

Where,
A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A; and
C is the total cash inflow during the period following period A

Year	Cash Inflows(project -A)	Cumulative
0	-97000	-97000
1	50000	-47000
2(A)	40000	-7000(B)
3	20000(C)	13000
4	10000	23000

Hence normal pay back period = 2 + (7000/20000) = 2.35 years

(ii) Discounted pay back period-

Discounted pay back period = A +(B/C)

Where,
A = Last period with a negative discounted cumulative cash flow;
B = Absolute value of discounted cumulative cash flow at the end of the period A; and
C = Discounted cash flow during the period after A.

Year	Cash Inflows(project -A)	PVF@7%	PV of cash flow	Cumulative
0	-97000	1	-97000	-97000
1	50000	0.93458	46729	-50271
2(A)	40000	0.87344	34938	-15333(B)
3	20000	0.81630	16326(C)	992
4	10000	0.76290	7629	8621

Discounted pay back period = 2 + (15333/16326) = 2.94 years.