Capital Budgeting with Leverage

Three equivalent methods for valuing a levered project — WACC, Adjusted Present Value (APV), and Flow to Equity (FTE). When each is most convenient.

Three valuation methods, one answer

When a project is financed with both debt and equity, you have three internally consistent ways to compute its value. All three give the same number when applied correctly. They differ in which inputs you need and how natural the calculation feels.

Method	Discount rate	Cash flow	When to use
WACC	After-tax WACC	FCF (project)	Stable capital structure
APV	Unlevered cost of capital	FCF + separately, tax shield	Changing capital structure
FTE	Cost of equity	FCF to equity	Want equity value directly

Method 1: WACC

Discount the project’s free cash flow at the firm’s WACC:

V = \sum_{t=1}^{\infty} \frac{FCF_t}{(1 + \text{WACC})^t}.

The tax shield is implicitly captured in the $(1-t)$ adjustment on the cost of debt within WACC.

When it works: projects that maintain a constant $D/V$ ratio, like the firm overall. Most M&A deals and most public-firm valuations use WACC as the default.

When it breaks: projects with debt that’s scheduled to pay down rapidly, or LBOs with high initial leverage that declines. The WACC changes year by year if the capital structure does, and mechanically applying a single average rate misvalues the project.

Method 2: Adjusted Present Value (APV)

Two steps:

Value the project as if it were all-equity financed: discount FCF at the unlevered cost of capital $r_U$ : $V_U = \sum_t \frac{FCF_t}{(1+r_U)^t}$
Separately compute the PV of the interest tax shield: $PV(\text{TS}) = \sum_t \frac{t \cdot r_D \cdot D_t}{(1+r_D)^t}$
Sum: $V = V_U + PV(TS)$ .

When it works: LBOs and project finance with debt schedules that are known in advance. You can model each year’s specific debt balance and tax shield without averaging.

Why some practitioners prefer it: APV separates the operating value from the financing value. Useful for understanding where value comes from.

Method 3: Flow to Equity (FTE)

Discount free cash flow to equity (FCFE — covered in Unit 3) at the cost of equity $r_E$ :

\text{Equity value} = \sum_t \frac{FCFE_t}{(1 + r_E)^t}.

FCFE = FCF + (net debt taken on - debt repaid - interest after tax).

When it works: when you want equity value directly (e.g., buying out an equity stake) and the cost of equity is the most defensible input.

Why some practitioners avoid it: FCFE is more sensitive to financing assumptions than FCF, so small errors in modeling debt amplify into the valuation. Easier to make mistakes than with WACC or APV.

When they disagree (you’ve made an error)

In a frictionless setting all three give identical valuations. If your three numbers diverge, one of three things is wrong:

Inconsistent inputs. Cost of equity not properly levered for the assumed $D/E$ . Or vice versa.
Wrong cash-flow definitions. FCF vs FCFE mixed up. Tax- shield treatment inconsistent.
Changing capital structure not reflected. WACC implicitly assumes constant $D/V$ . If you’re modeling a debt pay-down, use APV or year-varying WACC.

A worked comparison

Project with perpetual after-tax operating cash flow (FCF) of $10M per year, financed with $40M of debt at 5% (constant). Tax rate 25%. Unlevered cost of capital $r_U = 11\%$ .

WACC method:

$r_E$ (re-levered): $11 + (D/E)(1-t)(11-5) $. We need$ E$ first.
Iterate: $V = FCF / WACC$ . WACC depends on $E/V$ , which depends on $V$ .
Easier: use APV first.

APV method:

$V_U = 10 / 0.11 = \$ 90.9M$.
$PV(TS) = 0.25 \times 40 = \$ 10M$.
$V = 90.9 + 10 = \$ 100.9M$.
Equity value $E = V - D = 100.9 - 40 = \$ 60.9M$.
$D/E = 40/60.9 = 0.657$ .

WACC re-check:

$r_E = 0.11 + 0.657 \times (1 - 0.25) \times (0.11 - 0.05) = 0.11 + 0.0296 = 13.96\%$ .
$WACC = (60.9/100.9)(0.1396) + (40/100.9)(0.05)(0.75) = 0.0843 + 0.0149 = 9.92\%$ .
$V_{WACC} = 10 / 0.0992 = \$ 100.8M$ ✓ (matches APV within rounding).

FTE method:

After-tax interest = $40 × 0.05 × 0.75 = $1.5M$.
$FCFE = FCF - \text{interest after tax} = 10 - 1.5 = \$ 8.5M$ (perpetual debt, no net borrowing/repayment).
$\text{Equity} = 8.5 / 0.1396 = \$ 60.9M$ ✓.

All three methods agree at $100.9M total firm value and $60.9M equity value.

Practical guidance

For most undergraduate problem sets and most stable public-firm valuations: WACC. Simplest, single discount rate.
For LBOs, project finance, or anything with a known debt schedule: APV. Most transparent about what’s coming from operations vs financing.
When you want equity value directly and the capital structure is stable: FTE. Less common in practice; equivalent to others when done right.

The error to avoid: applying the firm’s WACC to a project whose capital structure (or risk) differs from the firm overall. We flagged this in Unit 4 (cost of capital) and it returns here. The discount rate must match the cash flow’s risk and financing.

Where this ends Unit 5

We’ve now built the full machinery for valuing real projects with realistic capital structures. Unit 6 covers special topics — real options, M&A, risk management — that build on this foundation.