Inflation and Forest Investment Analysis

1. Inflation and Forest Investment Analysis What’s real?

2. 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 – 1 =1.107 – 1 = 10.7%

3. 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

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

5. 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 PPI 3.3% Trend line 5.0% 32.5 15.0

7. 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

8. 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 1957. In 2005 it’s 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

9. Indiana Forest Products Price Report and Trend Analysis • See FNR-177-W, Table 8 • PPI for finished goods • Avg. Stand • Nominal • Index number • Real price • Quality Stand • Nominal • Index number • Real price

10. Indiana Average Stand, Average Log Price

13. 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

14. Nominal and Real ROR’s Combining the steps, Calculate current or inflated value is, In = V0 (1+r)n (1+f)n = V0 (1+ r + f + rf)n = V0 (1+i)n, therefore, i = r + f + rf = 0.05 + 0.04 + 0.05*0.04 = 0.09 + 0.002 = 0.092, or, i = (1 + r) (1 + f) -1

15. 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

16. Calculating Inflation Adjusted PV’s PV0 = 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+f)n]/[(1+r)n(1+f)n] = Vn/(1+r)n

17. 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

18. Warning • Never mix real dollars and nominal dollars in the same equation

19. 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

20. 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)

21. 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

22. 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)

23. After-Tax NPV Vn – Ti [Vn – C/(1+f)n] NPV = (1+r)n Vn – TiVn+ Ti[C/(1+f)n] NPV = (1+r)n

24. 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

25. 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 = 0.30 I8 = $4,000*1.09058= $8,000 Vn = $2,000 * 1.058 = $4,000 $4,000 – 0.30[4,000 – 2,000/(1.09058)] NPV = (1.05)8 = $2,098

26. After-Tax NPV With No Inflation $4,000 – 0.30 ($4,000 – $2,000) NPV = (1.05)8 = $2,301 Decrease in after-tax NPV due to inflation is, $2,301 - $2,098 = $203

27. 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.