Question

​Long-term investment​ decision, payback method Personal Finance Problem   Bill Williams has the opportunity to invest in project A that costs

$ 6 comma 600$6,600

today and promises to pay

$ 2 comma 200$2,200​,

$ 2 comma 500$2,500​,

$ 2 comma 500$2,500​,

$ 2 comma 000$2,000

and

$ 1 comma 700$1,700

over the next 5 years. ​ Or, Bill can invest

$ 6 comma 600$6,600

in project B that promises to pay

$ 1 comma 300$1,300​,

$ 1 comma 300$1,300​,

$ 1 comma 300$1,300​,

$ 3 comma 400$3,400

and

$ 4 comma 100$4,100

over the next 5 years.  

​(​Hint:

For mixed stream cash​ inflows, calculate cumulative cash inflows on a​ year-to-year basis until the initial investment is

recovered.​)

a.  How long will it take for Bill to recoup his initial investment in project​ A?

b.  How long will it take for Bill to recoup his initial investment in project​ B?

c.  Using the payback​ period, which project should Bill​ choose?

d.  Do you see any problems with his​ choice?

Answer 1

(a): Project A:

Year	Cash flow	Cumulative cash flow
0	-          6,600	-                                   6,600
1	2,200	-                                   4,400
2	2,500	-                                   1,900
3	2,500	600
4	2,000
5	1,700

Thus initial investment is being recouped in 3rd year when cumulative cash flows becomes positive. Exact time = 2 + (1900/2500) = 2.76 years

(b): Project B:

Year	Cash flow	Cumulative cash flow
0	-          6,600	-                                   6,600
1	1,300	-                                   5,300
2	1,300	-                                   4,000
3	1,300	-                                   2,700
4	3,400	700
5	4,100

Thus initial investment is being recouped in 4th year when cumulative cash flows becomes positive. Exact time = 3 + (2700/3400) = 3.79 years

(c): Using payback period method Bill should select project A as its payback period is lower than B. In other words for A the initial investment is recouped and recovered faster and earlier.

(d): Yes, there is a problem with his choice as the payback period fails to consider the cash flows after the payback period. In case of B cash flow amount increases during later years and so the higher amounts of $3,400 and $4,100 in 4th and 5th years are ignored. Use of NPV method would have given a better result for Bill.