Introductory Corporate Finance: Cash Flow Estimation Inflation in Cash Flow Estimation Nominal vs Real Cash Flows and Discount Rates

What This Is

Inflation in cash flow estimation is a critical concept in corporate finance, as it affects the accuracy of financial projections and valuation models. When estimating cash flows, companies must distinguish between nominal and real cash flows, as well as the corresponding discount rates. For instance, consider a company projecting cash flows for the next 5 years, with expected inflation of 3% per annum. If the company uses a nominal discount rate of 10%, the present value of the cash flows will be overstated by approximately 15% due to inflation. To accurately estimate cash flows, companies must use real discount rates and adjust for inflation.

Key Formulas & Models

• PV = FV / (1 + r)^n – present value of a future cash flow; r is the discount rate, n is the number of periods.
  • FV: future value of the cash flow
  • r: discount rate (real or nominal)
  • n: number of periods
• PV = Σ (CFt / (1 + r)^t) – present value of a series of cash flows; CFt is the cash flow at time t.
  • CFt: cash flow at time t
  • r: discount rate (real or nominal)
  • t: time period
• r = rnom + π – real discount rate; rnom is the nominal discount rate, π is the inflation rate.
  • rnom: nominal discount rate
  • π: inflation rate
• CFnom = CFreal × (1 + π)^t – nominal cash flow; CFreal is the real cash flow, π is the inflation rate.
  • CFreal: real cash flow
  • π: inflation rate
  • t: time period
• rnom = rreal + π – nominal discount rate; rreal is the real discount rate, π is the inflation rate.
  • rreal: real discount rate
  • π: inflation rate
• PV = Σ (CFnomt / (1 + rnom)^t) – present value of a series of nominal cash flows.
  • CFnomt: nominal cash flow at time t
  • rnom: nominal discount rate
  • t: time period
• CFreal = CFnom / (1 + π)^t – real cash flow; CFnom is the nominal cash flow, π is the inflation rate.
  • CFnom: nominal cash flow
  • π: inflation rate
  • t: time period

Step-by-Step Calculation

1. Estimate the real cash flows using the expected inflation rate and the nominal cash flows.
2. Calculate the real discount rate using the nominal discount rate and the inflation rate.
3. Use the real discount rate to calculate the present value of the real cash flows.
4. Convert the present value of the real cash flows to nominal terms using the inflation rate.
5. Compare the present value of the nominal cash flows using the nominal discount rate and the present value of the real cash flows using the real discount rate.

Common Mistakes

• Mistake: Using the nominal discount rate to estimate the present value of real cash flows.
  • Correction: Use the real discount rate to estimate the present value of real cash flows.
• Mistake: Ignoring the impact of inflation on cash flows.
  • Correction: Adjust the cash flows for inflation using the real cash flow formula.
• Mistake: Using the nominal discount rate to calculate the present value of a series of nominal cash flows.
  • Correction: Use the real discount rate to calculate the present value of a series of real cash flows and then convert to nominal terms.

Exam / CFA Tips

• Be careful when using the real discount rate to estimate the present value of real cash flows, as it may not accurately reflect the company's cost of capital.
• When estimating cash flows, consider the impact of inflation on both the cash flows and the discount rate.
• Use the correct formula to convert between nominal and real cash flows and discount rates.

Quick Practice Problem

A company has EBIT of $10M, interest $2M, tax 25% – compute the debt-free leverage (DFL) using the following formula:

DFL = (EBIT - Interest) / (EBIT - Interest + Tax)

Answer: DFL = 0.75

Explanation: The company's DFL is 0.75, indicating that 75% of its EBIT is debt-free.

Last-Minute Cram Sheet

• ⚠️ In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield.
• PV = FV / (1 + r)^n
• r = rnom + π
• CFnom = CFreal × (1 + π)^t
• rnom = rreal + π
• PV = Σ (CFnomt / (1 + rnom)^t)
• CFreal = CFnom / (1 + π)^t
• DFL = (EBIT - Interest) / (EBIT - Interest + Tax)
• WACC = wd × rd(1-T) + wps × rps + we × re
• DOL = Q(P-V) / (Q(P-V)-F)