A fast-food company invests $2.2 million to buy machines for making slurpees. These can be depreciated using the MACRS schedule shown above. If the cost of capital is 10%, what is the increase in the net present value (NPV) of the product gained by using MACRS depreciation over straight-line depreciation for three years?

Question

BlackTom AI · Accepted Answer

First, I restate the information provided in the problem to be sure we’re aligned: a fast-food company spends 2.2 million on machines for making slurpees. The depreciation method MACRS is given (with rates shown as Year 0: 33.33%, Year 1: 44.45%, Year 2: 14.81%, Year 3: 7.41%), and the cost of capital is 10%. The question asks for the increase in the net present value (NPV) of the product gained by using MACRS depreciation over straight-line depreciation for three years.

Next, I identify the missing elements necessary to compute the NPV difference. To calculate the incremental NPV from using MACRS versus straight-line, we need to know:
- The corporate tax rate applied to earnings (to determine the tax shield from depreciation).
- The operating cash flows that depreciation affects (usually the pre-tax income or EBIT related to the project), or equivalently the assumption that depreciation interacts with a steady stream of cash flows such that tax shields can be computed from depreciation amounts alone.
- Whether there are any other differences in cash flows between the MACRS scenario and the straight-line scenario besides depreciation (e.g., salvage values, changes in working capital), though typically the depreciation tax shield is the main driver for this comparison.

Given only the cost of the asset (2.2 million), the MACRS percentages, and the cost of capital (10%), we do not have the tax rate or the baseline (pre-depreciation) earnings to apply the depreciation shields to. Without the tax rate, we cannot convert depreciation into a tax shield (tax shield = depreciation × tax rate), and without the baseline cash flows or EBIT, we cannot compute the actual after-tax cash flows that depreciation affects. Consequently, we cannot numerically determine the difference in NPV between MACRS and straight-line.

In summary, the calculation requires at least the tax rate (and ideally the project’s pre-tax earnings or EBIT or a stated corporate cash-flow pattern). Since these inputs are not provided, the result cannot be computed from the given information alone. If you provide the tax rate (and any assumed or given EBIT/pre-tax cash flows), I can complete the step-by-step calculation of the NPV increase and verify whether the correct answer is $190,321 or another value.

If we attempt to outline the approach once those inputs are known:
- Compute depreciation under MACRS for each year (given percentages times 2.2 million), and under straight-line (2.2 million / 3 years, or as specified for the asset class).
- For each year, determine the tax shield from depreciation (Depreciation × Tax Rate) and the resulting after-tax cash flow impact (assuming EBIT is constant or given).
- Determine the after-tax cash flow difference between MACRS and straight-line for each year.
- Discount those incremental cash flows at the cost of capital (10%) back to present value, and sum to get the incremental NPV.
- The final answer would be the sum of those discounted differentials across the three years (positive if MACRS provides a larger tax shield, hence higher NPV).

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