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?
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A. B. C. D. E.Explanation
Payback = 5 + 135.9/146.41 = 5.928 years = 6 years.
To calculate the payback period, we need to determine the time it takes for the initial investment to be recovered through the incremental after-tax cash flows. Let's break down the information given:
To calculate the payback period, we need to determine when the cumulative incremental after-tax cash flows equal or exceed the initial investment. Let's calculate the cumulative incremental cash flows for each year:
Year 2: $100,000 (initial incremental after-tax cash flow) Year 3: $100,000 + 10% * $100,000 = $110,000 Year 4: $110,000 + 10% * $110,000 = $121,000 Year 5: $121,000 + 10% * $121,000 = $133,100 Year 6: $133,100 + 10% * $133,100 = $146,410 Year 7: $146,410 + 10% * $146,410 = $161,051 Year 8: $161,051 + 10% * $161,051 = $177,156.10 Year 9: $177,156.10 + 10% * $177,156.10 = $194,871.71 Year 10: $194,871.71 + 10% * $194,871.71 = $214,358.88 Year 11: $214,358.88 + 10% * $214,358.88 = $235,794.77
From the calculations, we can see that at the end of Year 8, the cumulative incremental after-tax cash flows exceed the initial investment of $600,000 ($100,000 for land + $500,000 for building). Therefore, the payback period is approximately 8 years.
The answer choice that matches the approximate payback period is: E. 8 years