Question

King, Inc. has the following mutually exclusive projects available. The company has historically used a 4-year cut-off for projects. The required return is 11 percent.

Year	Cash Flow (Project X)	Cash Flow (Project Y)
0	-$82,000	-$125,000
1	15,700	38,600
2	18,300	33,400
3	23,900	31,200
4	26,200	27,500
5	32,100	24,000

(a)	Calculate the Payback period of both projects.
(b)	State two advantages and two disadvantages of Payback period rule?
(c)	Calculate the IRR of both projects.
(d)	Under what circumstances IRR may generate wrong decision? Why?
(e)	Calculate the NPV of both projects.
(f)	Which project should you accept and what is the best reason for that decision?

Answer 1

Answer to a):

Project X:

	Project X	Initial Investment= $82000
Year	Cash Inflow($)	Cumulative Cash Inflows
1	15700	15700
2	18300	34000
3	23900	57900
4	26200	84100
5	32100	116200

For payback, the cash inflows arising from the investment should be $82,000. During the first 3 years, the project will pay $57,900. Remaining $24,100 ($82000-$57900) will be recovered in a part of Year 4 as full year will pay $26,200.

Hence Payback Period = 3 + (24,100/26200)

=3.92 years

Project Y:

	Project Y	Initial Investmen= $125000
Year	Cash Inflow($)	Cumulative Cash Inflows
1	38600	38600
2	33400	72000
3	31200	103200
4	27500	130700
5	24000	154700

For payback, the cash inflows arising from the investment should be $1,25,000. During the first 3 years, the project will pay $ 1,03,200. Remaining $21,8000 ($1,25,000-$1,03,200) will be recovered in a part of Year 4 as full year will pay $27,500

Hence Payback Period = 3 + (21,800/27,500)

=3.79 years

Project Y should be selected based on Payback Period as it has shorter Payback Period than Project X.

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Answer to b):-

The 2 advantages of Payback rule is -

i) Payback rule is simplistic in nature and can be calculated on the basis of simple cash flow or discounted cash flow

ii) It is a time saving technique

The 2 disadvantages of Payback rule is -

i) It does not consider post payback period profitability

ii) It ignores time value of money

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Answer to c):

Project

At IRR,

Cash Outflow = Cash Inflow

Cash Outflow = $82,000

	Project X
Year	Cash Inflow($)	Df@11%	PV	Df@12%	PV
1	15700	0.9	14130	0.893	14020.1
2	18300	0.811	14841.3	0.797	14585.1
3	23900	0.731	17470.9	0.711	16992.9
4	26200	0.658	17239.6	0.635	16637
5	32100	0.593	19035.3	0.567	18200.7
	Total		82717		80436
	Less: Initial Investment		(82,000)		(82,000)
	Net Present Value		717		-1564

IRR = Lower rate + Lower rate NPV/(Lower rate NPV-Higher rate NPV) * Differences in rates

= 11 + 717/(717-(-1564)*1

= 11 + 717/2281

= 11.32%

	Project Y
Year	Cash Inflow($)	Df@11%		Df@8%	PV
1	38600	0.9	34740	0.925	35705
2	33400	0.811	27087.4	0.857	28623.8
3	31200	0.731	22807.2	0.793	24741.6
4	27500	0.658	18095	0.735	20212.5
5	24000	0.593	14232	0.681	16344
	Total		116962		125627
	Less: Initial Investment		(125,000)		(125,000)
	Net Present Value		(8,038)		627

IRR = Lower rate + Lower rate NPV/(Lower rate NPV-Higher rate NPV) * Differences in rates

= 8 + 627/(627-(-8028) * 3

= 8+ (627/8655)*3

= 8+ .217

= 8.217%

IRR of Project X is higher than Project Y.

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Answer to (d):

IRR may generate wrong decision under the following circumstances:-

a) Discrete Cash Flows giving rises to multiple rate of IRR instead of a single rate of IRR.

b) Att times, IRR may be in negative values indicating erosion of Investment which is not true in reality

Answer to e):

	Project X
Year	Cash Inflow($)	Df@11%
1	15700	0.9	14130
2	18300	0.811	14841.3
3	23900	0.731	17470.9
4	26200	0.658	17239.6
5	32100	0.593	19035.3
	Total		82717
	Less: Initial Investment		(82,000)
	Net Present Value		717
	Project Y
Year	Cash Inflow($)	Df@11%
1	38600	0.9	34740
2	33400	0.811	27087.4
3	31200	0.731	22807.2
4	27500	0.658	18095
5	24000	0.593	14232
	Total		116962
	Less: Initial Investment		(125,000)
	Net Present Value		(8,038)

Based on Net Present Value, Project X should be selected as NPV of Project X is positive and higher than Project Y.

Answer to f):

Particulars	Project X	Project Y	Decision
Payback Period	3.92	3.79	Y
IRR	11.32%	8.217%	X
NPV	717	(8038)	X

As Payback Period does not consider time value of Money, it is better to accept Project X due to its better IRR and NPV as compared to Project Y