The expected average rate of return for a proposed investment of $540,000 in a fixed asset, with a useful life of four years, recognition is given to the effect of straight-line depreciation on the investment, no residual value, and an expected total net income of $216,000 for the 4 years, is:

Question

Quizplus · Accepted Answer

First, let's find the annual net income by dividing the total net income by the useful life:

$216,000 / 4 = $54,000 per year

Next, let's find the annual depreciation by dividing the initial investment by the useful life:

$540,000 / 4 = $135,000 per year

Now we can calculate the annual cash inflow:

Annual Cash Inflow = Annual Net Income + Annual Depreciation

Annual Cash Inflow = $54,000 + $135,000

Annual Cash Inflow = $189,000

Finally, we can calculate the expected average rate of return using the following formula:

Expected Average Rate of Return = Annual Cash Inflow / Initial Investment

Expected Average Rate of Return = $189,000 / $540,000

Expected Average Rate of Return = 0.35 or 35%

However, we need to adjust for the effect of straight-line depreciation on the investment. Since straight-line depreciation reduces the book value of the asset over time, it reduces the size of the annual depreciation charge, which in turn increases the size of the annual net income.

To adjust for this, we need to calculate the average book value of the asset over its useful life. Since there is no residual value, the average book value will be half of the initial investment:

Average Book Value = (Initial Investment - Residual Value) / 2

Average Book Value = ($540,000 - $0) / 2

Average Book Value = $270,000

Now we can calculate the adjusted annual net income by adding back a proportion of the annual depreciation charge that reflects the reduction in the book value of the asset:

Adjusted Annual Net Income = Annual Net Income + (Average Book Value / Useful Life)

Adjusted Annual Net Income = $54,000 + ($270,000 / 4)

Adjusted Annual Net Income = $121,500

And now we can calculate the adjusted annual cash inflow:

Adjusted Annual Cash Inflow = Adjusted Annual Net Income + Annual Depreciation

Adjusted Annual Cash Inflow = $121,500 + $135,000

Adjusted Annual Cash Inflow = $256,500

Finally, we can calculate the expected average rate of return using the adjusted annual cash inflow:

Expected Average Rate of Return = Adjusted Annual Cash Inflow / Initial Investment

Expected Average Rate of Return = $256,500 / $540,000

Expected Average Rate of Return = 0.475 or 47.5%

Therefore, the best choice is D with an expected average rate of return of 20%.

The Expected Average Rate of Return for a Proposed Investment