Question

Please show work step by step, no excel. Thank you!

The three alternative projects shown below have the expected cash flows that are given, and the cost of capital is 10%.

1. Calculate the paybacks for all three projects. Rank the projects from best to worst based on their paybacks.
2. Calculate the NPVs for all three projects. Rank the projects from best to worst based on their NPVs.
3. Why are these two sets of rankings different?

year	0	1	2	3	4	5
Project A	-10	4	3	2	1	5
Project B	-10	1	2	3	4	5
Project C	-10	4	3	2	1	10

Answer 1

(a)

year	Project A	Cumulative CF		Project B	Cumulative CF		Project C	Cumulative CF
0	-10	-10		-10	-10		-10	-10
1	4	-6		1	-9		4	-6
2	3	-3		2	-7		3	-3
3	2	-1		3	-4		2	-1
4	1	0		4	0		1	0
5	5	5		5	5		10	10

Therefore payback period of project A = 4 years (since entire initial investment is collected till the end of year 4)

Payback period of project B = 4 years (since entire initial investment is collected till the end of year 4)

Payback period of project B = 4 years (since entire initial investment is collected till the end of year 4)

Therefore, ranking of all the projects will be same based on payback period

(b)

year	PVF @ 10%	Project A	PV		Project B	PV		Project C	PV
0	1.000	-10	-10.000		-10	-10.000		-10	-10.000
1	0.909	4	3.636		1	0.909		4	3.636
2	0.826	3	2.479		2	1.653		3	2.479
3	0.751	2	1.503		3	2.254		2	1.503
4	0.683	1	0.683		4	2.732		1	0.683
5	0.621	5	3.105		5	3.105		10	6.209
	NPV		1.406			0.653			4.511
	Ranking based on NPV		2			1			3

(c)

	Project A	Project B	Project C
Ranking based on Payback period	1	1	1
Ranking based on NPV	2	1	3

Payback period is simply the time required to recover the initial investment amount

While NPV, is PV of cash inflows - PV of cash outflows.

Difference in ranking based on Payback period and NPV is due to following reasons:

Payback period simply ignores the cash flows after the initial investment is recovered

Payback period does not consider time value of money.

NPV is more scientific since it takes into consideration all the cash flows from projects based on there Present value.