Continuing on from Question 1:

ABC is still considering investing in the project with the initial cost of $560,000 and that will earn unlevered free cash flows (FCFF) of $96,000 per year in perpetuity. The unlevered cost of capital is still 20% and the tax rate is 40%.

Assume instead of funding with 100% equity, ABC funds the project with $280,000 in perpetual debt (wtih an interest rate of 10%) and the remainder of funding will be with equity.

What is the NPV of the levered project using the APV method?

Question

Continuing on from Question 1:

ABC is still considering investing in the project with the initial cost of $560,000 and that will earn unlevered free cash flows (FCFF) of $96,000 per year in perpetuity. The unlevered cost of capital is still 20% and the tax rate is 40%.

Assume instead of funding with 100% equity, ABC funds the project with $280,000 in perpetual debt (wtih an interest rate of 10%) and the remainder of funding will be with equity.

What is the NPV of the levered project using the APV method?

BlackTom AI · Accepted Answer

We start by laying out what the APV framework requires for this problem.

First, calculate the value of the project as if it were financed entirely with equity (unlevered). The project generates unlevered free cash flows (FCFF) of $96,000 per year in perpetuity, and the unlevered cost of capital is 20%. The value of the project in an all-equity financing world is V_unlevered = FCFF / r_unlevered = 96,000 / 0.20 = 480,000. This is the baseline value before any debt is considered.

Next, determine the financing side under the new structure: $280,000 of debt is used, funded at a 10% interest rate, with the remaining amount funded by equity. The annual interest expense on this debt is Interest = 0.10 × 280,000 = 28,000. The tax rate is 40%, so the annual tax shield from the debt is Tax shield = Tax rate × Interest = 0.40 × 28,000 = 11,200 per year, perpetually (since the debt is perpetual).

In the APV framework, the present value of the tax shields from debt with perpetual debt equals the tax shield per year divided by the cost of debt, but there is a standard shortcut for perpetual debt with constant tax rate: PV of tax shields = Tax rate × D = 0.40 × 280,000 = 112,000. This reflects the perpetual stream of tax savings from the debt.

Now combine the components to get the levered value:
- V_levered = V_unlevered + PV(Tax shields) = 480,000 + 112,000 = 592,000.

Finally, compare this levered value to the initial investment outlay to get the APV (NPV of the levered project):
- NPV_APV = V_levered − Initial cost = 592,000 − 560,000 = 32,000.

Now evaluate the answer choices one by one to see which aligns with these calculations.

Option A: $368,000. This would imply a much smaller levered value or a larger outlay than the calculation supports, and it ignores the substantial but finite value of the tax shield (112k) and the unchanged unlevered project value of 480k. The math does not fit the APV framework here.

Option B: $592,000. This matches the levered value before subtracting the initial investment. It represents V_levered, not the NPV. If you were asked for the project value under levered financing, this would be the figure—but the question asks for NPV, which requires subtracting the initial cost.

Option C: $32,000. This is the NPV of the levered project after accounting for the initial outlay of $560,000, given V_levered = 592,000. It is consistent with the APV decomposition: 480,000 (unlevered value) + 112,000 (PV of tax shields) − 560,000 (initial cost) equals 32,000.

Option D: $512,000. This value could arise from miscounting components, such as using V_unlevered plus some but not all of the tax shield, or misplacing the initial investment, but it does not align with the full APV calculation described above.

In summary, when applying APV with perpetual debt of 280,000 at 10%, the unlevered project value is 480,000, the PV of tax shields is 112,000, yielding a levered value of 592,000. Subtracting the initial outlay of 560,000 gives an NPV of 32,000. The option that corresponds to this NPV is the one representing 32,000, while the other options either reflect partial calculations or misinterpret the levered value versus the net present value.

MGT232H5 S LEC0105 Quiz 4

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