Skip to content
DP
Required Returnsadvanced

Cash-Flow and Discount-Rate Consistency

A valuation is only coherent when the cash flow and the discount rate describe the same claim. The three matching rules are strict. Discount free cash flow to the firm (FCFF), a pre-financing cash flow to all investors, at the WACC. Discount free cash flow to equity (FCFE), the cash left after creditors are paid, at the cost of equity. And keep nominal cash flows with nominal rates, real with real. Mixing a cash flow with the wrong rate is one of the most common and damaging valuation errors.

Why it matters

Every discount rate is the required return of a particular group of capital providers, so it must be paired with the cash flow that actually belongs to that group. WACC blends the returns of all investors, so it discounts the cash flow available to all of them, FCFF. The cost of equity is the shareholders’ required return alone, so it discounts what shareholders actually receive, FCFE, which is derived by subtracting creditor cash flows from project cash flow in the flow-through-to-equity model. The same logic governs inflation. A rate that includes expected inflation must meet a cash flow that also includes it, or the two double-count or cancel inconsistently.

Formulas

FCFF discounted at the WACC
Vfirm=∑t=1nFCFFt(1+WACC)tV_{firm} = \sum_{t=1}^{n} \dfrac{FCFF_t}{(1 + WACC)^t}
FCFF is the cash available to all capital providers before financing flows. It pairs with the WACC, which blends the required returns of debt and equity. This values the whole firm.
FCFE discounted at the cost of equity
Vequity=∑t=1nFCFEt(1+ke)tV_{equity} = \sum_{t=1}^{n} \dfrac{FCFE_t}{(1 + k_e)^t}
FCFE is what remains after creditor cash flows, namely after-tax interest and net principal. It pairs with the cost of equity kek_e, the shareholders’ required return. This is the flow-through-to-equity model.
Real and nominal consistency (Fisher)
1+rnominal=(1+rreal)(1+π)1 + r_{nominal} = (1 + r_{real})(1 + \pi)
Match nominal cash flows with nominal rates and real cash flows with real rates. The Fisher relation links the two through expected inflation π\pi. Never discount a nominal cash flow at a real rate or the reverse.

Worked examples

Scenario

A project generates FCFF of US$6 million a year and, after paying after-tax interest and principal, leaves FCFE of US$4 million a year. The WACC is 10 percent and the cost of equity is 14 percent. Show the correct pairings and one wrong pairing, treating each as a level perpetuity for illustration.

Solution

Correct firm value discounts FCFF at the WACC, so US$6 million divided by 0.10 gives an enterprise value of US$60 million. Correct equity value discounts FCFE at the cost of equity, so US$4 million divided by 0.14 gives about US$28.6 million. A common error is to discount the equity cash flow FCFE at the WACC, US$4 million over 0.10, which gives US$40 million and overstates equity value badly, because the WACC is too low a rate for the riskier residual equity claim. Match each cash flow to the rate that belongs to it.

Common mistakes

  • ✗FCFF and FCFE can be discounted at the same rate. They belong to different claimants. FCFF pairs with the WACC, FCFE with the higher cost of equity, since equity is the riskier residual claim.
  • ✗You can discount FCFE at the WACC to value equity. That mismatches the cash flow and rate and overstates equity value, because the WACC understates the return equity holders require.
  • ✗Inflation can be ignored as long as you are consistent within the cash flows. The rate must match too. A nominal rate needs nominal cash flows and a real rate needs real cash flows, linked by the Fisher relation.
  • ✗Adding expected inflation to a real cash flow but keeping a real rate is harmless. It double-counts growth from inflation against a rate that excludes it, distorting the present value.

Revision bullets

  • •Match the cash flow to the discount rate of the same claimants
  • •FCFF, a cash flow to all investors, is discounted at the WACC
  • •FCFE, the cash left after creditors, is discounted at the cost of equity
  • •FCFE at the cost of equity is the flow-through-to-equity model
  • •Keep nominal cash flows with nominal rates and real with real
  • •The Fisher relation links real and nominal rates through inflation

Quick check

To value the whole firm, free cash flow to the firm (FCFF) should be discounted at the

An analyst discounts free cash flow to equity (FCFE) at the WACC rather than the cost of equity. The likely effect is to

Connected topics

Free Cash FlowWACCCost of Equity (CAPM)Project vs Firm RateEnterprise DCF

Sources

  1. Titman & Martin, Ch. 5
    Titman, S. & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
    Chapter on required returns and the flow-through-to-equity model. Matching FCFF to the WACC and FCFE to the cost of equity follows this text.
  2. Fisher (1930)
    Fisher, I. The Theory of Interest. Macmillan, 1930.
    Original statement of the relation linking nominal interest rates, real rates and expected inflation, the basis for nominal-real consistency.
How to cite this page
Dr. Phil's Quant Lab. (2026). Cash-Flow and Discount-Rate Consistency. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-cashflow-rate-consistency
← Back to the atlasSee in the network →