$10.$ The payback period

The payback method helps firms establish and identify a maximum acceptable payback period that helps in their capital budgeting decisions.

Consider the case of Green Caterpillar Garden Supplies Inc.:

Green Caterpillar Garden Supplies Inc. is a small firm, and several of its managers are worried about how soon the firm will be able to recover its initial investment from Project Alpha$$s expected future cash flows. To answer this question, Green Caterpillar$$s CFO has asked that you compute the project$$s payback period using the following expected net cash flows and assuming that the cash flows are received evenly throughout each year.

Complete the following table and compute the project$$s conventional payback period. For full credit, complete the entire table. $($Note: Round the conventional payback period to the nearest two decimal places. If your answer is negative use a minus sign.$)$

Year $0$

Year $1$

Year $2$

Year $3$

Expected cash flow $-$$$4,500,000$ $$1,800,000$ $$3,825,000$ $$1,575,000$

Cumulative cash flow

Conventional payback period: years

The conventional payback period ignores the time value of money, and this concerns Green Caterpillar$$s CFO. He has now asked you to compute Alpha$$s discounted payback period, assuming the company has a $9\%$ cost of capital. Complete the following table and perform any necessary calculations. Round the discounted cash flow values to the nearest whole dollar, and the discounted payback period to the nearest two decimal places. For full credit, complete the entire table. $($Note: If your answer is negative use a minus sign.$)$

Year $0$

Year $1$

Year $2$

Year $3$

Cash flow $-$$$4,500,000$ $$1,800,000$ $$3,825,000$ $$1,575,000$

Discounted cash flow

Cumulative discounted cash flow

Discounted payback period: years

Which version of a project$$s payback period should the CFO use when evaluating Project Alpha, given its theoretical superiority?

The discounted payback period

The regular payback period

One theoretical disadvantage of both payback methods$$compared to the net present value method$$is that they fail to consider the value of the cash flows beyond the point in time equal to the payback period.

How much value does the discounted payback period method fail to recognize due to this theoretical deficiency?

$$4,435,615$

$$1,216,189$

$$1,586,991$

$$2,867,565$