Inflation and Forest Investment Analysis

What’s real?

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%

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

Terminology• Price with inflation included

– Nominal– Current dollar– Inflated– Actual

• Price with inflation not included– Real– Constant dollar– Deflated– Relative

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

Producer Price Index for Finished Goods

0

20

40

60

80

100

120

140

160

180

Year

1982

$'s

15.0

154

32.5

155.4

PPI 3.3%

Trend line 5.0%

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

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

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

Indiana Average Stand, Average Log Price

57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 01 03 05 07 09 110

100

200

300

400

500

600

700

Year

$'s p

er M

BFe

Nominal Price

Real Price, 1982 $'s

Trend Line, 1.11%

57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 01 03 05 07 09 110

100

200

300

400

500

600

700

Indiana Quality Stand Average Log Price

Year

$'s p

er M

BF

Nominal Price

Real Price, 1982 $'s

Trend Line, 1.12%

5859606162636465666768697071727374757677787980818283848586878889909192939495969798990001020304050607080910

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

Year

Annu

al R

ate

of R

etur

n (Y

ear-

over

-Yea

r)

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 = $104To get 5% return need to multiply $104 by (1+r)n, $104 (1.05)1 = $109.20

Nominal and Real ROR’sCombining 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

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 + i1 + r = (1 + i) / (1 + f) r = [(1 + i) / (1 + f)] - 1

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

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

Warning

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

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

Income tax on gain from disposal of assets

C = basis of asset In = nominal value in year nTi = tax rate (5% or 15%)

Tax due = Ti (In – C)

ExampleGeorge 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 = $16,000I80 = $50,000Ti = 15%Tax due = 0.15 ($50,000 - $16,000)

= 0.15 * $34,000 = $5,100

After-tax gain = $50,000 - $5,100 = $44,900

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)

After-Tax NPV

Vn – Ti [Vn – C/(1+f)n]NPV =

(1+r)n

Vn – Ti Vn+ Ti [C/(1+f)n]NPV =

(1+r)n

$2,000

$4,000

$6,000

$8,000

Basis = $2,000 nominal

Vn = $4,000

In = $8,000

Years 8

Capital gain = $6,000

Real gain = $2,000

Nominal and real gain

4

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 = 0.05Ti = 0.30I8 = $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

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

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.