Question

A company is considering two short-term projects. Based on the undiscounted payback period, which project is preferred? (Time 0 shows the investment amount, and upcoming years show expected benefit from each project)

Month	A	B
0	-$250	-$250
1	$40	$70
2	$50	$60
3	$60	$60
4	$40	$50
5	$80	$50
6	$50	$40

Please solve by hand, I am not allowed to use excel

Answer 1

Payback period (PBP) is time by when a project's cumulative cash flows equal zero.

For Project A,

Cumulative cash flow in year 4 ($) = - 250 + 40 + 50 + 60 + 40 = - 60

Cumulative cash flow in year 5 ($) = - 250 + 40 + 50 + 60 + 40 + 80 = 20

Therefore, PBP lies between years 4 and 5.

PBP (years) = 4 + (Absolute value of cumulative cash flow in year 4 / Cash flow in year 5)

= 4 + (60/80) = 4 + 0.75 = 4.75

For Project B,

Cumulative cash flow in year 4 ($) = - 250 + 70 + 60 + 60 + 50 = - 10

Cumulative cash flow in year 5 ($) = - 250 + 70 + 60 + 60 + 50 + 50 = 40

Therefore, PBP lies between years 4 and 5.

PBP (years) = 4 + (Absolute value of cumulative cash flow in year 4 / Cash flow in year 5)

= 4 + (10/50) = 4 + 0.2 = 4.2

Since Project B has lower PBP, project B should be chosen.