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Fact Pattern: Henderson, Inc., has purchased a new fleet of trucks to deliver its merchandise. The trucks have a useful life of 8 years and cost a total of $500,000. Henderson expects its net increase in after-tax cash flow to be $150,000 in Year 1, $175,000 in Year 2, $125,000 in Year 3, and $100,000 in each of the remaining years.What is the payback reciprocal for Henderson’s fleet of trucks?

Question

Fact Pattern: Henderson, Inc., has purchased a new fleet of trucks to deliver its merchandise. The trucks have a useful life of 8 years and cost a total of 500,000.Hendersonexpectsitsnetincreaseinaftertaxcashflowtobe500,000. Henderson expects its net increase in after-tax cash flow to be 150,000 in Year 1, 175,000inYear2,175,000 in Year 2, 125,000 in Year 3, and $100,000 in each of the remaining years.What is the payback reciprocal for Henderson’s fleet of trucks?

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Solution

The payback period is the time it takes for an investment to generate an amount of income or cash equal to the cost of the investment. The payback reciprocal is the inverse of the payback period, which is used to estimate the internal rate of return.

Step 1: Calculate the payback period

Year 1: 150,000Year2:150,000 Year 2: 175,000 Year 3: 125,000Year48:125,000 Year 4-8: 100,000 * 5 = $500,000

Total cash inflow over 8 years = 150,000+150,000 + 175,000 + 125,000+125,000 + 500,000 = $950,000

The cost of the trucks is $500,000. The payback period is the time it takes for the cash inflows to equal the cost of the trucks.

By adding the cash inflows, we find that the cost of the trucks is covered in Year 4 (150,000+150,000 + 175,000 + 125,000+125,000 + 50,000 = $500,000). So, the payback period is 4 years.

Step 2: Calculate the payback reciprocal

The payback reciprocal is the inverse of the payback period.

Payback reciprocal = 1 / Payback period = 1 / 4 = 0.25

So, the payback reciprocal for Henderson’s fleet of trucks is 0.25.

This problem has been solved

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