Inflation and Forest Investment Analysis

1
Inflation and Forest Investment Analysis

• Whats real?

2
Whats Inflation

• An increase in prices that makes a market
  basket of goods and services more expensive over
  time.
• Basket costs 1,400 in 2003 and 1,550 in 2004, a
  one year period.
• Increase in cost is 150
• increase, the annual rate of inflation, is
• 150/1,400 10.7, or
• (1,550/1,400)1/1 1 1.107 1 10.7

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Causes of Inflation

• Demand-pull inflation
• Too many people chasing too few goods and
  services
• Cost-push inflation
• Costs of factors of production rise, pushing up
  prices of goods and services
• Monetary inflation
• Government prints more money, leading to demand
  pull inflation

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Terminology

• Price with inflation included
• Nominal
• Current dollar
• Inflated
• Actual
• Price with inflation not included
• Real
• Constant dollar
• Deflated
• Relative

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Nomenclature

• f annual inflation rate
• r real interest rate
• i inflated or nominal interest rate
• i (r f rf)
• In inflated or nominal dollar value in year n
• Vn future value in year n, in constant dollars
  of year 0

6
154
155.4
Nominal PPI 3.3
Trend line 5.0
32.5
15.0
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Average Annual Rate of Inflation

• Rate of inflation between two points in time more
  than one year apart.
• Calculate as,
• f (Vn/V0)1/n -1
• (155.4/32.5)1/48 1
• 4.780.02083 1
• 1.0331 1
• 3.31 per annum

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Converting the value of an asset from its nominal
to its real value

• Vn In/(1f)n
• Example Timberland is purchased for 500 per
  acre in 1957. In 2005 its sold for 3,500 per
  acre. If average annual inflation over this
  period is 3.31, what is the sale price of the
  land in terms of 1982 values?
• V2005 3,500/1.033148 733.22
• What is the real rate of return on the land?
• r (733.22/500)1/48 1 0.008

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Indiana Forest Products Price Report and Trend
Analysis

• See FNR-177-W 2006, Table 8
• PPI for finished goods
• Avg. Stand
• Nominal
• Index number
• Real price
• Quality Stand
• Nominal
• Index number
• Real price

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Average Stand of Indiana Timber
Nominal Price Series
Trend Line 1.1 per annum
Real Price Series, 1982 s
11
High Quality Stand of Indiana Timber
Nominal Price Series
Trend Line 1.4 per annum
Real Price Series, 1982 s
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Nominal and Real RORs

• Loan 100 now to be returned in one year. You
  want a 5 real rate of return, r, i.e. 5 more
  than inflation. If inflation will be 4 over the
  year you need 104 back just to keep same
  purchasing power of 100.
• 100 (1f)n 100 (1.04)1 104
• To get 5 return need to multiply 104 by
  (1r)n,
• 104 (1.05)1 109.20

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Nominal and Real RORs

• Combining the steps,
• Calculate current or inflated value is,
• In V0 (1r)n (1f)n
• V0 (1 r f rf)n V0 (1i)n,
• therefore,
• i r f rf
• 0.05 0.04 0.050.04
• 0.09 0.002 0.092,
• or,
• i (1 r) (1 f) -1

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Nominal and Real RORs

• If you know the nominal rate of return and
  inflation rate, solve for the real rate of
  return,
• (1 r) (1 f) 1 i
• 1 r (1 i) / (1 f)
• r (1 i) / (1 f) - 1

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Calculating Inflation Adjusted PVs

• PV0 In/(1i)n
• Vn (1f)n / (1rfrf)n
• Vn(1f)n/(1r)n(1f)n
• Vn(1f)n/(1r)n(1f)n
• Vn/(1r)n

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Calculating Inflation Adjusted PVs

• Guidelines for computing net present value (NPV)
• If future cash flows are in constant dollars
  compute NPV with a real interest rate, r
• If future cash flows are in current dollars
  compute NPV with a nominal interest rate. Use
  same inflation rate in the cash flows and nominal
  interest rate

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Warning

• Never mix real dollars and nominal dollars in the
  same equation

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Recommendation

• Its usually easier to work in real terms, that
  is adjust all cash flows to real values, and
  discount with real interest rate, r
• However, have to use nominal values for after-tax
  calculations,
• Tax laws generally dont adjust rates for
  inflation, and never adjust basis of assets for
  inflation

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Income tax on gain from disposal of assets

• C basis of asset
• In nominal value in year n
• Ti tax rate (5 or 15)
• Tax due Ti (In C)

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Example

• George buys timberland in 1975 for 120,000 of
  which 80,000 is attributable to merchantable
  timber. In 1980 he sells 20 of the merchant-able
  timber for 50,000. What is the tax on the sale?
• C 0.2 80,000 16,000
• I80 50,000
• Ti 15
• Tax due 0.15 (50,000 - 16,000)
• 0.15 34,000
• 5,100
• After-tax gain 50,000 - 5,100 44,900

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Tax Basis

• Used to determine gain or loss on the disposal
  of an asset
• Hows basis determined?
• Purchased assets acquisition cost
• Gift basis of donor used by donee (carryover
  basis)
• Inheritance fair market value on deceased date
  of death (stepped-up basis)

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After-Tax NPV

• Vn Ti Vn C/(1f)n
• NPV
• (1r)n
• Vn Ti Vn Ti (C/(1f)n
• NPV
• (1r)n

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After-Tax NPV, Example

• Buy an asset for 2,000 and sell it 8 years for
  8,000. Annual inflation rate is 9.05.
• f 0.0905, r 0.05
• Ti 0.15
• I8 4,000/1.09058 8,000
• 4,000 0.154,000 2,000/(1.09058)
• NPV
• (1.05)8
• 2,402.78

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Nominal and real gain
In 8,000
8,000
6,000
Capital gain 6,000
Vn 4,000
4,000
Real gain 2,000
2,000
Basis 2,000 nominal
8
4
Years
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After-Tax NPV With No Inflation

• 4,000 0.15 (4,000 2,000)
• NPV
• (1.05)8
• 2,504.31
• Decrease in after-tax NPV due to inflation is,
• 2,504.31 - 2,402.78 101.52

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Affect of Inflation on Series Payment Formulas
annual and periodic

• Basic formulas assume fixed payments
• If payments are fixed in nominal terms must use
  nominal interest rate, i, in series payment
  formulas.
• If nominal payments rise at exactly the inflation
  rate, they are fixed in real terms and must use
  real interest rate in formulas.