Michigan Mattress Company is considering the purchase of land and the construction of a new plant. The land, which would be bought immediately (at t = 0), has a cost of $100,000 and the building, which would be erected at the end of the first year (t = 1), would cost $500,000. It is estimated that the firm's after-tax cash flow will be increased by $100,000 starting at the end of the second year, and that this incremental flow would increase at a 10 percent rate annually over the next 10 years. What is the approximate payback period?

Question

Quizplus · Accepted Answer

The initial investment is $100,000 (for land) + $500,000 (for building) = $600,000.
The annual after-tax cash flow starts at $100,000 at the end of year 2 and increases at a rate of 10% annually for 10 years. We can calculate the incremental cash flows for each year using the formula:
Incremental cash flow = $100,000 x (1 + 10%)^n, where n = number of years since the end of year 2.
So the incremental cash flows are:
Year 3: $110,000
Year 4: $121,000
Year 5: $133,100
Year 6: $146,410
Year 7: $161,051
Year 8: $177,156
Year 9: $194,872
Year 10: $214,359
Year 11: $235,795
Year 12: $259,374
To calculate the payback period, we need to find the year when the cumulative incremental cash flows equal the initial investment of $600,000. We can use a table to keep track of the cumulative incremental cash flows:
Year | Incremental cash flow | Cumulative cash flow
2    | $100,000                           | $100,000
3    | $110,000                           | $210,000
4    | $121,000                           | $331,000
5    | $133,100                           | $464,100
6    | $146,410                           | $610,510
7    | $161,051                           | $771,561
8    | $177,156                           | $948,717
9    | $194,872                           | $1,143,589
10 | $214,359                           | $1,357,948
11 | $235,795                           | $1,593,743
12 | $259,374                           | $1,853,117
The payback period falls between year 6 and year 7, when the cumulative incremental cash flow reaches $771,561 (year 7). To approximate the payback period, we can use linear interpolation:
Payback period = 6 + (600,000 - 610,510) / 146,410
Payback period = 6.41 years
Therefore, the approximate payback period is 6 years.

Michigan Mattress Company Is Considering the Purchase of Land and the Construction