Robins Hardware is adding a new product line that will require an investment of $ 1 comma 418 comma 000. Managers estimate that this investment will have a 10-year life and generate net cash inflows of $ 300 comma 000 the first year, $ 270 comma 000 the second year, and $ 260 comma 000 each year thereafter for eight years. Assume the project has no residual value. Compute the ARR for the investment. Round to two places.
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To compute the Accounting Rate of Return (ARR), follow these steps:
1. Calculate the initial investment. The initial investment is given as $1,418,000.
2. Determine the average annual operating income. The operating income is the net cash inflows from the investment. However, since ARR is based on accounting concepts, we first need to calculate the depreciation expense.
The investment has a 10-year life and no residual value. This means the asset will be depreciated straight-line over its useful life. Thus, the annual depreciation expense is: Depreciation Expense = Initial Investment / Useful Life = $1,418,000 / 10 years = $141,800 per year
3. Subtract the annual depreciation from each year's net cash inflow to find the accounting net operating income (before taxes) for each year. For the first year, net operating income is
= $300,000 - $141,800
= $158,200.
For the second year,
net operating income is $270,000 - $141,800
net operating income = $128,200.
For each of the remaining eight years,
net operating income is $260,000 - $141,800
net operating income = $118,200.
4. Since ARR requires the average income, we sum up the operating incomes for all years and then divide by the number of years:
Average annual operating income = (Total net operating income across all years) / Number of years
So first, we add up all the net operating incomes:
Total net operating income = $158,200 (first year) + $128,200 (second year) + 8 * $118,200 (remaining years) = $158,200 + $128,200 + $945,600
(remaining years) = $1,232,000
5. Now, compute the average annual operating income:
Average annual operating income = $1,232,000 / 10
Average annual operating income = $123,200 per year
6. Finally, calculate the ARR using the formula:
ARR = Average Annual Operating Income / Initial Investment
ARR = $123,200 / $1,418,000
ARR = 0.086854 or 8.69% (rounded to two decimal places)
So the Accounting Rate of Return (ARR) for the investment is approximately 8.69%.