NPV and inflation

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NPV and inflation
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Objective

• Understand how to account for the effect of
  inflation, especially for longer-lived projects

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Inflation

• Erosion of the purchasing power of money
• Slow Subdued (creeping) inflation
• or
• Rapid Rampant (hyperinflation)

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Problems with inflation

• Inflation renders time comparisons very
  difficult.
• 100 in 2001 is a different amount than 100 in
  1996.

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Exemplification

• A Toyota Corolla was selling at an average price
  of 15,000 in 1996, today it sells at an average
  price of 18,000.
• How much more expensive is it?
• It is hard to tell because the purchasing power
  of 1 has changed since 1996.
• The average annual income has changed as well.

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Solution

• Bring both prices to a common denominator.
• Price the 2001 Toyota using 1996 dollars.

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The Fisher Effect

• Reference point 1996 dollars (real dollars)
• Real dollars Current dollars/(1 infl)t
• X 18,000/(1.03)5
• X 15,527
• In real terms, the Toyota Corolla increased in
  price by 3.5 since 1996, that is, at an average
  of per year

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The Fisher Effect

• (1 r) (1 infl)(1 r)
• r nominal rate of return (nominal discount
  rate) - the rate required as a compensation for
  risk, time preference, and inflation.
• r real rate of return (real discount rate) -
  the rate required as a compensation for risk and
  time preference.

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NPV analysis and inflation Recommended approach

• Discount real dollars cash flow at the real
  discount rate
• Discount nominal dollars cash flow at the nominal
  discount rate

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Exemplification 1 NPV calculation

• ATNOR projection for project ABC (nominal
  dollars)
• Year 1 23 m
• Year 2 21 m
• Year 3 15 m
• Initial cost 47 m
• No depreciation, no change in NWC, no debt
  financing
• Real discount rate 10
• Expected inflation 4

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NPV calculation (a)

• Discount nominal dollars cash flow at the nominal
  discount rate
• Nominal discount rate (1.1)(1.04) - 1 14.4
• NPV 23/(1.144) 21/(1.144)2 15/ (1.144)3
  - 47
• NPV 20.1 16.04 10.02 - 47 - 0.84 m

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NPV calculation (b)

• Discount real dollars cash flow at the real
  discount rate
• Real cash flow
• Year 1 23/(1.04) 22.12 m
• Year 2 21/(1.04)2 19.42 m
• Year 3 15/(1.04)3 13.34 m
• NPV 22.12/(1.1) 19.42/(1.1)2 13.34/
  (1.1)3 - 47
• NPV 20.1 16.04 10.02 - 47 - 0.84 m

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Exemplification 2

• XYZ's new project will incur the following
  nominal cash flow at the end of next year
• Revenues 150,000 - expected to increase at 5
  in real terms
• Labor costs 80,000 - expected to increase at 3
  in real terms
• Other costs 40,000 - expected to decrease at 1
  in real terms
• The company will lease machinery for
  20,000/year. The lease payments start at the end
  of year 1 and are fixed in nominal terms.
• The rate of inflation is expected to be 6/year.
  The real required rate of return is 10. The
  lease payments have to be discounted at a real
  rate of 7. There are no taxes. All cash flow
  occur at the end of the year.
• Calculate the NPV of the project.

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NPV Calculation

• NPV PV(revenue) -PV(labor costs) - PV(other
  costs) - PV(lease costs)
• Use real dollars and the real discount rate

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Revenue

• Deflate next years revenues and apply the
  dividend growth model to calculate PV
• Deflating Calculating the real dollar
  equivalent
• PV(revenue) 150,000/(1.06)/(0.1 - 0.05)
  2,830,189

16
Labor Costs

• Deflate next years labor costs and apply the
  dividend growth model to calculate PV
• PV (labor costs) 80,000/(1.06)/(0.1 - 0.03)
  1,078,167

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Other costs

• Deflate next years other costs and apply the
  dividend growth model to calculate PV
• PV (other costs) 40,000/(1.06)/(0.1 0.01)
  343,053

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Leasing costs

• Deflate next years lease costs and apply the
  dividend growth model to calculate PV
• Lease payments in real terms
• 18,86817,800.16,792..etc.
• Note that real-dollar lease payments decline at
  5.66/year
• PV(lease payments) 18,868/(0.07 0.0566)
  149,036
• Remember that the real discount rate for lease
  payments is 7

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Putting it together

• NPV PV(revenue) -PV(labor costs) - PV(other
  costs) - PV(lease costs)
• PV 2,830,189 - 1,078,167 - 343,053 -
  149,036 1,259,938

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Summary

• Discount real dollars cash flow at the real
  discount rate
• Discount nominal dollars cash flow at the nominal
  discount rate