Adjusted Present Value

Standard DCF deals with debt in a slightly sneaky way. You discount the whole firm's cash flows at WACC, and WACC contains the term $r_d(1-t)$ — the after-tax cost of debt. Interest is tax-deductible, so borrowing is cheap, so the discount rate drops, so the value rises. The benefit of leverage is in there, but it is dissolved into the discount rate where you cannot see it or check it.

That dissolving trick has a price. A single WACC assumes the capital structure stays at one fixed ratio for the entire forecast and forever afterwards. Now think about a leveraged buyout: debt is 70% of the capital on day one and 25% by year five as cash sweeps pay it down. There is no single WACC that describes that. You would have to recompute the weights, re-lever the beta and rebuild the discount rate every single year — and each year's rate depends on that year's equity value, which is what you are trying to solve for.

Adjusted present value cuts the knot by refusing to mix the two effects at all.

The one line

$$\text{APV} = V_U + \text{PV(tax shields)} - \text{PV(distress costs)}.$$

$V_U$ is the unlevered value: the business valued as if it were funded entirely by equity, so you discount free cash flow to the firm at the unlevered cost of equity $r_U$ — the return shareholders would demand with no debt in the structure. Then you add the financing side effects back, one at a time, each with its own cash flows and its own discount rate. Operating value and financing value stay in separate boxes.

Worked example: it agrees with WACC when it should

A business generates free cash flow to the firm of $100m a year, flat, forever. Its unlevered cost of equity is 10%, so $V_U = 100 / 0.10 = 1000$. It carries $400m of permanent debt at 6%, and the marginal tax rate is 25%.

Each year the interest bill is $400 \times 0.06 = 24$, and deducting it saves $24 \times 0.25 = 6$ in tax. Because the debt is permanent and its size is contractually fixed, the shield is about as risky as the debt itself, so discount it at $r_d$:

$$\text{PV(shield)} = \frac{6}{0.06} = 100 = t \times D.$$

So $\text{APV} = 1000 + 100 = 1100$, and equity is worth $1100 - 400 = 700$.

Check it against WACC. Debt is $400/1100 = 36.36\%$ of value. Under Modigliani–Miller with taxes, $\text{WACC} = r_U(1 - t \cdot D/V) = 0.10 \times (1 - 0.25 \times 0.3636) = 9.091\%$, and $100 / 0.09091 = 1100$. Same answer, to the dollar. APV is not a different theory; it is the same arithmetic with the seams showing.

Worked example: where WACC gives up

Now the same firm is bought in an LBO. Debt is $400m at the start of year 1, swept down to $300m by year 2 and $200m by year 3. The ratio moves every year, so no fixed WACC applies. APV does not care — you just value the schedule:

Year	Debt	Interest at 6%	Tax shield at 25%	Discounted at 6%
1	400	24.0	6.0	5.66
2	300	18.0	4.5	4.01
3	200	12.0	3.0	2.52

The three-year shield is worth $5.66 + 4.01 + 2.52 = 12.18$, and you add the value of whatever shields survive past year 3 on top. This is why sponsors and restructuring desks reach for APV: the financing plan is the deal, and it deserves its own schedule rather than a smeared-out discount rate.

Which rate discounts the shield?

This is the live argument, and it turns on one question: is the debt a fixed dollar amount, or a fixed percentage of value?

• Fixed debt (Myers, 1974). The shield is as safe as the loan, so discount at $r_d$. The perpetuity collapses to $t \times D$.
• Rebalanced debt (Miles–Ezzell, Harris–Pringle). If the company keeps debt at a constant fraction of a value that moves with the business, then future shields inherit the business's risk, so discount them at $r_U$. In our example that gives $6 / 0.10 = 60$ instead of 100 — a 4% swing in total value from a modelling convention alone.

Investment-grade corporates with a target ratio look like the second case; a levered buyout with a fixed amortisation schedule looks like the first. Say which one you assumed.