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 =1.107 – 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
160
143
2003
120
100
80
60
32.5
40
Year
99
10
2
96
93
90
87
84
81
78
75
72
69
66
63
1957
60
20
0
57
1987 base year
140
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
= 4.40.02174 – 1
= 1.0327 – 1
= 3.27% 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 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 = $3,500/1.032747 = $796
• What is the real rate of return on the land?
r = ($796/$500)1/46 – 1 = 0.01
Table 8. Weighted average actual price, price index, and deflated price for an average and quality stand
of timber in Indiana, 1957 to 2003.
Year
Producer
Price Index
(1)
(2)
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1
32.5
33.2
33.1
33.4
33.4
33.5
33.4
33.5
34.1
35.2
35.6
36.6
38.0
39.3
40.5
41.8
45.6
52.6
58.2
60.8
64.7
69.8
77.6
88.0
Average Stand
Nominal
Index
Price
Number
(3)
($/MBF)
55.6
53.7
54.8
57.5
58.9
59.6
59.3
60.1
63.6
68.8
70.1
74.7
77.7
83.1
85.9
90.2
112.6
135.3
125.1
133.6
143.6
181.7
201.5
207.8
(4)
100.0
96.6
98.5
103.5
105.9
107.3
106.7
108.1
114.3
123.7
126.0
134.2
139.7
149.4
154.4
162.2
202.5
243.3
225.0
240.2
258.1
326.1
362.3
373.6
Real
Price 1
(5)
($/MBF)
171.1
161.8
165.5
172.3
176.3
178.1
177.6
179.5
186.4
195.4
196.8
204.0
204.5
211.5
212.0
215.8
247.0
257.3
215.0
219.7
221.9
260.3
259.6
236.1
Nominal
Price
(6)
($/MBF)
66.6
64.0
67.5
68.7
70.0
72.3
74.5
74.4
78.5
86.0
87.2
92.7
98.6
103.9
107.4
112.2
139.0
170.2
166.3
172.7
188.0
234.9
260.7
309.3
Quality Stand
Index
Number
(7)
100.0
96.1
101.4
103.2
105.1
108.6
111.9
111.8
118.0
129.2
131.0
139.3
148.2
156.0
161.3
168.5
208.8
255.7
249.8
259.4
282.4
352.9
391.6
464.5
Real
Price 1
(8)
($/MBF)
204.9
192.8
204.0
205.7
209.5
215.8
223.1
222.2
230.3
244.3
245.0
253.4
259.6
264.3
265.2
268.4
304.9
323.7
285.8
284.1
290.6
336.6
336.0
351.5
Actual price deflated by Producer Price Index for Finished Goods, U.S. Dept. Commerce, 1982 base year.
Table 8. Weighted average actual price, price index, and deflated price for an average and quality stand
of timber in Indiana, 1957 to 2003.
Year
Producer
Price Index
(1)
(2)
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
1
96.1
100.0
101.6
103.7
104.7
103.2
105.4
108.0
113.6
119.2
121.7
123.2
124.7
125.5
127.9
131.3
131.8
130.7
133.0
138.0
140.7
138.9
142.5
Average Stand
Nominal
Index
Real
Price
Number
Price 1
(3)
(4)
(5)
($/MBF)
($/MBF)
206.7
371.7
215.1
196.8
353.8
196.8
207.6
373.3
204.3
235.8
424.0
227.4
210.5
378.5
201.0
223.6
402.0
216.6
257.3
462.7
244.2
262.1
471.3
242.7
285.9
514.0
251.6
288.3
518.3
241.8
268.1
482.1
220.3
293.4
527.6
238.2
355.2
638.8
284.9
364.8
655.9
290.6
354.0
636.4
276.7
337.7
607.1
257.2
357.5
642.7
271.2
391.1
703.3
299.3
389.2
699.8
292.6
426.5
766.9
309.1
389.7
700.8
277.0
410.7
738.4
295.7
433.7
779.7
304.3
Nominal
Price
(6)
($/MBF)
284.9
277.3
294.4
322.7
274.0
312.2
334.6
345.9
404.9
397.9
362.9
417.6
491.2
507.4
451.6
495.4
448.3
501.7
526.3
617.6
538.5
561.2
567.9
Quality Stand
Index
Number
(7)
427.8
416.5
442.2
484.6
411.5
468.9
502.6
519.6
608.1
597.6
545.1
627.1
737.8
762.1
678.3
744.0
673.3
753.5
790.5
927.5
808.8
842.9
852.9
Real
Price 1
(8)
($/MBF)
296.4
277.3
289.8
311.2
261.7
302.5
317.5
320.3
356.4
333.8
298.2
338.9
393.9
404.3
353.1
377.3
340.2
383.9
395.7
447.5
382.7
404.0
398.5
Actual price deflated by Producer Price Index for Finished Goods, U.S. Dept. Commerce, 1982 base year.
Figure 2. Average stand of timber, nominal, deflated, and trend line price series, 1957 to 2003.
500
450
350
Trend line
1.20% per year
Real price,
1982 $’s
300
250
200
150
Nominal
Price
100
50
Year
03
01
99
97
95
93
91
89
87
85
83
81
79
77
75
73
71
69
67
65
63
61
59
0
57
$ per MBF
400
Figure 3. Quality stand of timber, nominal, deflated, and trend line price series 1957 to 2003.
700.0
600.0
Trend line
1.52% per
year
Real price,
1982 $’s
400.0
300.0
200.0
Nominal
Price
100.0
Year
02
99
96
93
90
87
84
81
78
75
72
69
66
63
60
0.0
57
$ per MBF
500.0
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
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
= 0.05 + 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 + i
1 + r = (1 + i) / (1 + f)
r = [(1 + i) / (1 + f)] - 1
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+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 n
Ti = tax rate (5% or 15%)
Tax due = Ti (In – C)
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 merchantable 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
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
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 – 0.15[4,000 – 2,000/(1.09058)]
NPV =
(1.05)8
= $2,402.78
Nominal and real gain
In = $8,000
$8,000
$6,000
Vn = $4,000
$4,000
Capital
gain =
$6,000
Real
gain =
$2,000
$2,000
Basis = $2,000
nominal
Years
4
8
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
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.