Michigan Mattress Company is considering the purchase of land and the construction of a new plant.The land, which be bought immediately (at t = 0), has a cost of $100,000 and the building, which would be erected at the end of the fir = 1), would cost $500,000.It is estimated that the firm's after-tax cash flow will be increased by $100,000 starting at of the second year, and that this incremental flow would increase at a 10 percent rate annually over the next 10 year the approximate payback period?
A)2 years
B)4 years
C)6 years
D)8 years
E)10 years

Question

Quizplus · Accepted Answer

The initial investment is $100,000 + $500,000 = $600,000.
The annual incremental cash flow starts at the end of the first year, so the payback period will be longer than 1 year.
To calculate the payback period, we need to find out in which year the cumulative cash flow equals the initial investment of $600,000.
Year 1: No incremental cash flow. Cumulative cash flow = -$600,000
Year 2: Incremental cash flow = $100,000. Cumulative cash flow = -$500,000
Year 3: Incremental cash flow = $110,000. Cumulative cash flow = -$390,000
Year 4: Incremental cash flow = $121,000. Cumulative cash flow = -$269,000
Year 5: Incremental cash flow = $133,100. Cumulative cash flow = -$135,900
Year 6: Incremental cash flow = $146,410. Cumulative cash flow = $10,510
The cumulative cash flow becomes positive in the sixth year, so the payback period is between 5 and 6 years. To estimate the payback period, we can use linear interpolation:
Payback period = Year 5 + (Cumulative cash flow at the end of Year 5 / Incremental cash flow in Year 6) = 5 + ($135,900 / $146,410) = 5.93 years.
Therefore, the best choice is C, 6 years.

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