Course 2, #4

[sum guy]

Question 4 seems pretty poor to me. First off, I don’t see anywhere where they specify how the debt is to be repaid– at the end of the year, as a perpetuity of interest payments, or whatever– and that decision affects the value of the tax shield. But more importantly, it looks like they disregarded the tax payment due on the profit earned by the project.

Here’s how I would get the answer they got:

First, assume debt is fully repaid at the end of year, so there’s only one interest payment:
PV (Tax Shield) = PV(Interest payments * tax rate)
= PV(54,000 * 0.08 * 0.35)
= PV(1512)
= 1400 <- use interest rate on debt (8%) for PV

Now, treat the project as fully equity financed
PV (Future inflows) = 120,000/1.2
= 100,000

PV (Payments) = 100,000

So APV = 1400 + 100,000 – 100,000 = 1400 (C)


But what they’ve done is ignored that you need to use AFTER-TAX returns on the investment in calculating APV. When you count the tax that they'll pay on their $20,000 in profits, this looks like a negative APV project to me. (I suppose that when they said "the expected inflow is $120,000 at the end of the year" they meant net of taxes, but it sure don't read that way to me!)

(But I hope they don't throw this out, 'cause I put C.)