Cori's Dog House is considering the installation of a new computerized pressure cooker for hot dogs. The cooker will increase sales by $8,100 per year and will cut annual operating costs by $12,600. The system will cost $44,100 to purchase and install. This system is expected to have a 4-year life and will be depreciated to zero using straight-line depreciation and have no salvage value. The tax rate is 21 percent and the required return is 10.1 percent. What is the NPV of purchasing the pressure cooker?

Question

BlackTom AI · Accepted Answer

We start by identifying the incremental cash flows from the project and the appropriate tax treatment.

First, calculate annual operating increments: the cooker increases sales by 8,100 and reduces operating costs by 12,600, for a total annual incremental cash flow before tax of 8,100 + 12,600 = 20,700.

Next, determine depreciation: the initial cost is 44,100 and the asset is depreciated straight-line to zero over 4 years, so annual depreciation = 44,100 / 4 = 11,025.

Taxable income (taxable cash flow before tax minus depreciation) = 20,700 − 11,025 = 9,675.
Taxes = 0.21 × 9,675 = 2,031.75.
Net income = 9,675 − 2,031.75 = 7,643.25.

Add back non-cash depreciation to get after-tax cash flow (ATCF) each year: ATCF = Net income + Depreciation = 7,643.25 + 11,025 = 18,668.25.

Thus, the project yields an annual after-tax cash flow of approximately 18,668.25 for each of the 4 years.

Initial outlay is 44,100 (a cash outflow at time 0). There is no salvage value at year 4, so the flow in year 4 is purely the ATCF.

Now discount these cash flows at the required return of 10.1% to compute NPV. The present value factor for an annuity of 4 years at i = 10.1% is
PV factor = (1 − (1 + i)^(−n)) / i ≈ (1 − (1.101)^(−4)) / 0.101 ≈ 0.3195 / 0.101 ≈ 3.164.

PV of the four annual after-tax cash flows ≈ 18,668.25 × 3.164 ≈ 59,073 (approximately).

NPV = PV of inflows − initial outlay ≈ 59,073 − 44,100 ≈ 14,973.

We compare this to the given answer choices. The closest value to the computed NPV is around 14,948, which aligns with the second option in the list.

Now, evaluate the other options to see why they are not correct:

- −$8,979: This would imply the project has a large negative present value, which contradicts the positive after-tax cash flows and the sizable discount factor; there is no evidence of such a large outflow beyond the initial 44,100.

- $14,948: This is a positive NPV and matches the approximate calculation using the given numbers and discount rate, accounting for depreciation tax shield and operating savings.

- $21,125: This overstates the PV of the cash inflows relative to the initial outlay when applying the 10.1% discount rate; it suggests a higher annuity value than the ATCFs justify.

- $1,483: This would occur if the cash flows were significantly smaller or if the discount rate were much higher; it is far from the calculated level given the sizable annual ATCF.

- −$22,643: This would require a large net outflow after discounting all inflows, which is inconsistent with positive annual after-tax cash flows and the initial cost being the only initial outlay.

Putting the pieces together, the combination of annual after-tax cash flow and the 4-year discounting at 10.1% yields a positive NPV in the mid-teens, aligning with the option that reflects a positive value around 14,948.

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