Question

Projects A B

Cost (initial investment) 40000 250000

Year Cash flows of A Cash flows of B

1 10000 40000

2 10000 120000

3 10000 200000

4 10000 200000

5 10000 200000

6 10000 200000

What are the Payback Periods of Projects A, and B? Assume all cash flows are evenly spread throughout the year and already discounted. If the cut-off period ( الفتره المقبوله) is three years, which projects do you accept?

Answer 1

Year	A	Cumulative Cashflow A	B	Cumulative Cashflow B
(Initial Investment)	-40000	-40000	-250000	-250000
1	10000	-30000	40000	-210000
2	10000	-20000	120000	-90000
3	10000	-10000	200000	110000
4	10000	0	200000	310000
5	10000	10000	200000	510000
6	10000	20000	200000	710000

Payback periods:

Payback period is the time when cumulative cashflow becomes zero. At this time the project has recovered all of its initial investment and starts generating profit.

Project A

As we can see in the table above, the cumulative cashflow of A becomes zero in year 4, so the payback period of A is 4 years

Project B

As we can see in the table above the cumulative cashflow becomes zero between year 2 and 3, so the payback period exists between 2 and 3. further we can calculate exact payback period by interpolation.

Interpolation formula:

Putting values in above formula

y-2=(3-2)/(110000-(-90000)) x (0-2)

y=2.45

so the payback period of project B is 2.45 years

if the cutoff period is 3 years then we would select project B as it has payback period of 2.45 years, that means it will have recovered its investment before cutoff period. similarly we will not choose project A as its payback period is 4 years, that means it will not have recovered its initial invesment till the cutoff period.