Question

Assume a \(90,000 investment and the following cash flows for two alternatives:

Year	Investment A	Investment B
1	\)25,000	\(40,000
2	30,000	40,000
3	25,000	28,000
4	19,000	--
5	25,000	--

a. Calculate the payback for investments A and B.

b. If the inflow in the fifth year for Investment A was \)25,000,000 instead of $25,000, would your answer change under the payback method?

Short answer

Answer

1. Project B has a lower payback period; therefore, it must be selected.

Cash inflow of the 5th year will not affect the answer under the payback method.

Step-by-step solution

Definition of Payback Period

Payback period is the matric used by the company under the capital budgeting methods which help them to selects the investment based on the time taken by the investment to cover the amount of potential investment through cash inflows.

Calculation of payback period for A and B investment

Investment A:

$$\begin{gathered} Paybackperiod=Periodbeforefullrecovery+\frac{Amountrecoveredinlastperiod}{Cashflowinperiod} \\ =3+\frac{\$10,000}{\$19,000} \\ =3+0.5 \\ =3.5years \end{gathered}$$

Investment B:

$$\begin{gathered} Paybackperiod=Periodbeforefullrecovery+\frac{Amountrecoveredinlastperiod}{Cashflowinperiod} \\ =2+\frac{\$10,000}{\$28,000} \\ =2+0.4 \\ =2.4years \end{gathered}$$

The business entity must select project B.

Working note:

Year	Cash inflow Investment A	Accumulated cash inflow for investment A	Cash inflow for Investment B	Accumulated cash inflow for investment B
1	$25,000	$25,000	$40,000	$40,000
2	30,000	$55,000	40,000	$80,000
3	25,000	$80,000	28,000
4	19,000		--
5	25,000		--

Change in cash inflow

The answer would not change under the payback method if the cash inflow in the 5th year were $25,000,000 instead of $25,000 because the initial investment cost will be covered in 3.5 years. Therefore, a change in the cash inflow of the 5th year would not affect the answer.