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**Inflation and Forest Investment Analysis**

What’s real?

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What’s 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 =1.107 – 1 = 10.7%

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**Causes of Inflation Demand-pull inflation Cost-push 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

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143 2003 32.5 1957

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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 = (143/32.5)1/46 – 1 = – 1 = – 1 = 3.27% per annum

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

Vn = In/(1+f)n Example – Timberland is purchased for $500 per acre in In 2004 it’s sold for $3,500 per acre. If average annual inflation over this period is 3.27%, what is the sale price of the land in terms of 1957 values? V1957 = $3,500/ = $796 What is the real rate of return on the land? r = ($796/$500)1/46 – 1 = 0.01

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Nominal and Real ROR’s 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 (1+f)n = 100 (1.04)1 = $104 To get 5% return need to multiply $104 by (1+r)n, $104 (1.05)1 = $109.20

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**Nominal and Real ROR’s Combining the steps, In = V0 (1+r)n (1+f)n**

= V0 (1+ r + f + rf)n = V0 (1+i)n, therefore, i = r + f + rf = *0.04 = = 0.092, or, i = (1 + r) (1 + f) -1

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Nominal and Real ROR’s 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 PV’s**

PV = In/(1+i)n = [Vn (1+f)n] / (1+r+f+rf)n = [Vn(1+f)n]/[(1+r)n(1+f)n] = Vn/(1+r)n

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**Calculating Inflation Adjusted PV’s**

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 It’s 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 don’t 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**

How’s 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/(1+f)n] NPV = (1+r)n**

Vn – Ti Vn+ Ti (C/(1+f)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 = , r = 0.05 Ti = 0.15 I8 = $4,000/ = $8,000 $4,000 – 0.15[4,000 – 2,000/( )] 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 4 8 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, $2, = $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.

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