Question

John Claire, the CFO of Projection Investment Ltd, is considering two
mutually exclusive projects.

Year	Cash Flow (X) $’000	Cash Flow (Y) $’000
0	-40,000	-40,000
1	19,000	4,000
2	15,200	12,600
3	12,400	14,900
4	6,000	28,000

In each case, show your calculation clearly.
a If he applies the payback criterion, which project will he choose?

b If he applies the IRR criterion, which project will he choose?

c If he applies the NPV criterion with a required return of 9%, which project will he choose?

d At which discount rate (correct to 1 decimal place of a percentage) would he be indifferent between these two projects?

Answer 1

a. Payback Period Criterion:

X = 2.47 years

Y = 3.30 years

PROJECT X (in '000)
Particulars			Initial Outlay	Year 1	Year 2	Year 3	Year 4
Undiscounted Net Cash Flow			$ (40,000)	$ 19,000	$ 15,200	$ 12,400	$ 6,000
Cumulative Net Cash Flow				(21,000)	(5,800)	6,600	12,600
Completed Years			2
Uncompleted Years			0.47	=-5800/(-5800+6600)
Payback period			2.47 years

PROJECT Y (in '000)
Particulars			Initial Outlay	Year 1	Year 2	Year 3	Year 4
Undiscounted Net Cash Flow			$ (40,000)	$ 4,000	$ 12,600	$ 14,900	$ 28,000
Cumulative Net Cash Flow				(36,000)	(23,400)	(8,500)	19,500
Completed Years			3
Uncompleted Years			0.30	=8500/(8500+19500)
Payback period			3.30 years

Project X is better since the payback period is less.

b. IRR Criterion:

The project with higher IRR is chosen, hence Project X will be chosen.

c. NPV Criterion:

Project X- (Fig. in '000)

Years	Cash Flows	PV factor	PV
0	-40,000	1	-40,000.00
1	19,000	0.91743	17,431.19
2	15,200	0.84168	12,793.54
3	12,400	0.77218	9,575.08
4	6,000	0.70843	4,250.55
	NPV		4,050.35

Project Y- (Fig. in '000)

Years	Cash Flows	PV factor	PV
0	-40,000	1	-40,000.00
1	4,000	0.91743	3,669.72
2	12,600	0.84168	10,605.17
3	14,900	0.77218	11,505.53
4	28,000	0.70843	19,835.91
	NPV		5,616.33

Project Y is better since NPV is more.

d. The rate at which project will be indifferent: