Transcript Inflation and Forest Investment Analysis

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
180
160
154
140
155.4
PPI 3.3%
100
Trend line 5.0%
80
60
40
20
32.5
15.0
Year
10
5
10
2
99
96
93
90
87
84
81
78
75
72
69
66
63
60
0
57
1982 $'s
120
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
700
600
Nominal Price
$'s per MBFe
500
400
Real Price, 1982 $'s
300
Trend Line, 1.11%
200
100
0
57
60
63
66
69
72
75
78
81
84
Year
87
90
93
96
99
02
05
08
11
Indiana Quality Stand Average Log Price
700
600
Nominal Price
500
Real Price, 1982 $'s
$'s per MBF
400
300
200
Trend Line, 1.12%
100
0
57
60
63
66
69
72
75
78
81
84
Year
87
90
93
96
99
02
05
08
11
20.00
15.00
Annual Rate of Return (Year-over-Year)
10.00
5.00
0.00
58
61
64
67
70
73
76
79
82
85
-5.00
-10.00
-15.00
-20.00
Year
88
91
94
97
00
03
06
09
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,
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 + i
1 + 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 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 = 0.30
I8 = $4,000*1.09058 = $8,000
$4,000 – 0.30[4,000 – 2,000/(1.09058)]
NPV =
(1.05)8
= $2,098
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 – 0.30 ($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.