Question

P10–4 Long-term investment decision, payback method Bill Williams has the opportunity
to invest in project A that costs $9,000 today and promises to pay annual end-ofyear
payments of $2,200, $2,500, $2,500, $2,000, and $1,800 over the next 5 years.
Or, Bill can invest $9,000 in project B that promises to pay annual end-of-year payments
of $1,500, $1,500, $1,500, $3,500, and $4,000 over the next 5 years.
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?

please show excel formulas  Thanks!

Answer 1

a. The payback period of project A is calculated as follows:

Payback period = A + (B/C)

= 3 Years + (1,800 / 2.000)

= 3 years + 0.90 years

= 3.90 years

Where,

A = Last period number with negative cumulative cash flow

B = Cumulative cash flow at the end of the period A

C = Cash inflow after the period A

The excel formula to calculate cumulative cash flow is as follows:

The result of the above excel is as follows:

Year	Annual cash flow ($)	Cumulative cash flow ($)
0	-9000	-9000
1	2200	-6800
2	2500	-4300
3	2500	-1800
4	2000	200
5	1800	2000

b. The payback period of project A is calculated as follows:

Payback period = A + (B/C)

= 4 Years + (1,000 / 4.000)

= 4 years + 0.25 years

= 4.25 years

Where,

Year	Annual cash flow ($)	Cumulative cash flow ($)
0	-9000	-9000
1	1500	-7500
2	1500	-6000
3	1500	-4500
4	3500	-1000
5	4000	3000

c. Under the payback period method for decision making purpose the project with a shorter payback period is acceptable.

Payback period of project A = 3.90 years

payback period of project B = 4.25 years

From the above, we can easily conclude that project A should be accepted.

d. Yes, there is a problem in selecting the project because of the major drawback of payback period i.e. it avoids the time value of money. This is the reason the net present value method is the most acceptable method of capital budgeting.

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