lev and the forest value lecture 5 (04/13/2015). the financially optimal rotation age

LEV and the Forest Value

Lecture 5 (04/13/2015)

The Financially Optimal Rotation Age

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Rotation Age (years)

Yie

ld (

mb

f/a

c)

0

50

100

150

200

250

300

350

400

LE

V (

$/a

c)

Yield LEV

LEV and MAI

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161

Rotation Age (years)

MA

I (m

bf/

ac/y

r)

0

50

100

150

200

250

300

350

400

LE

V (

$/ac

)

MAI LEV

CMAI

Marginal Analysis of the Rotation Decision

• The marginal benefits:

• The marginal costs:

1 (1 )a a incMB P Y t Price of wood Income tax rate

Growth of wood b/w age a and a+1

(1 )a inc

annual management costs

MC A t

(1 )prop inc

property taxes

t t

*

land rent

r LEV

(1 )a inc

inventory cost

r P Y t

Marginal Costs and Revenues and the LEV

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Rotation Age (years)

Ma

rgin

al C

os

ts a

nd

Be

ne

fits

($

/ac

/yr)

LEV MBa MCa

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Rotation Age (years)

Ma

rgin

al C

os

ts a

nd

Be

ne

fits

($

/ac

/yr)

LEV MBa MCa

Establishment Cost (E ) 200Price of Wood(P) 600Property Tax (tinc) 2Annual Management Costs (A) 1Income Tax (tinc) 0.22Interest Rate r 0.03

1 (1 )a a incMB P Y t

*

(1 ) (1 )

(1 )

a inc prop inc

a inc

MC A t t t

r LEV r P Y t

An increase inthe Interest Rate

Establishment Cost (E ) 200Price of Wood(P) 600Property Tax (tinc) 2Annual Management Costs (A) 1Income Tax (tinc) 0.22Interest Rate r 0.04

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Rotation Age (years)

Mar

gin

al C

ost

s an

d B

enef

its ($

/ac/

yr)

LEV MBa MCa

1 (1 )a a incMB P Y t

*

(1 ) (1 )

(1 )

a inc prop inc

a inc

MC A t t t

r LEV r P Y t

An increase inStumpage Price

Establishment Cost (E ) 200Price of Wood(P) 800Property Tax (tinc) 2Annual Management Costs (A) 1Income Tax (tinc) 0.22Interest Rate r 0.04

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Rotation Age (years)

Mar

gin

al C

ost

s an

d B

enef

its ($

/ac/

yr)

LEV MBa MCa

• In increase in establishment costs?

• In increase in annual management costs and property taxes?

• In increase in severance tax?

• In increase in income tax?

An increase in…Financially Optimal

Rotation Age (R*)

LEV

r Real rate Negative Negative

P Price of wood E=0

0

E>0

Neg.Positive

E Establishment Cost Positive Negative

A Annual man. costs 0 Negative

tprop Property tax 0 Negative

tinc Income tax 0 Negative

tsever Severance tax E=0

0

E>0

Pos.Negative

The impact of changes in economic variables on the financially optimal rotation

age and LEV

Forest Value

• Land Expectation Value: present value of costs and revenues from an infinite series of identical even-aged forest rotations starting from bare land;

• Forest Value (a generalization of LEV): the present value of a property with an existing stand of trees + the present value of a LEV for all future rotations of timber that will be grown on the property after harvesting the current stand.

The Forest Value allows us:

• To determine when a given stand should be cut;

• To separate the management of the current stand from that of future stands;

• To account for price changes that might occur during the life of the current stand;

Note: We will still assume that the rotations and prices associated with the future stands (i.e., the stands that are established after the current stand is cut) will be the same.

Time (years)

0 1 2 3 29 30 31 59 60

$5/acProperty tax

$84/acStand impro-vement cut

$5,948/acCut currentstand now

$4,400/acCut future

stand

…

Time (years)

$84/acStand impro-vement cut

$4,400/acCut future

stand

…0 1 2 3 9 10 11 39 40 41 69 70

$7,884/acCut after10 yrs

When to cut the stand?

• Cut it now:– Forest Value = Current Timber Value + LEV

1( )

,1 1

(1 ) (1 )

(1 ) 1

R nR R t

t p p R ht p

R

E r I r P Y CA

LEVr r

(60 30)

60

$84(1.05) $4,400 $5

(1.05) 1 0.05

$363.04316 $4,400$100 $169.42 /

17.67919ac

$5,948/ac

0 $5,948 / $169.42 / $6,117.42 /FV ac ac ac

When to cut the stand?

• Cut it 10 years from now:

– Forest Value = Present Value of Costs and Revenues for first 10 years + Present Value of

LEV

10

$169.42$104.01/

(1 0.05) 1.62889LEV

LEVPV ac

10

$7,884

(1.05)CurrentRotationPV

$4,840.09 $38.61 $4,801.48 / ac

10

10

$5(1.05 1)

0.05(1.05)

10 $4,905.49 /CurrentRotation LEVFV PV PV ac

Forest Value

• Assumptions:1. The current stand will be harvested;

2. A new stand will be established;

3. All future rotations of the new stand will be identical.

• Definition:– The Forest Value is the present value of the projected

costs and revenues from an existing forest tract, plus the present value of an infinite series of identical future forest rotations that starts after the current tract is harvested.

Calculating the Forest Value

• New notation:

• Forest Value formula:

0

0

p,T 0

Ch

the time when the currect stand is to be cut;

Y the expected yield of product p from the current stand at time T ; and

C the cost of selling the current stand of timber.

C

T

0 0

0 0

,1

of harvest revenues present value of annualfrom the current stand revenues up to when the current

stand is cut

[(1 ) 1]

(1 ) (1 ) (1

nC C

p p T h Tp

T T

Net present value Net

P Y CA r LEV

FVr r r r

0

LEV of future rotations

)T

Discounted

Land value and timber value

• Forest Value = Land Value + Timber Value– Land Value = LEV– Timber Value = Forest Value – LEV

0 0

0 0

,1 ( ) [(1 ) 1]

(1 ) (1 )

nAnnual Land CostC C

p p T h Tp

T T

P Y Cr LEV A r

Timber Valuer r r

What if real prices change?

• Assumption: the price changes will end by the end of the current rotation

0 0 0

0 0

, ,1 ( ) [(1 ) 1]

(1 ) (1 )

nAnnual Land CostC C

p T p T h Tp

T T

P Y Cr LEV A r

Timber Valuer r r

When calculating the LEV, use the new, steady state price: Pp,∞

An exampleItem Amount Assumptions for the Current and Future Stands Current sawtimber volume 18 mbf/ac Current pulpwood volume 14 cords/ac Current sawtimber price $325/mbf Current pulpwood price $7/cord Expected sawtimber volume in 10yrs 24 mbf/ac Expected pulpwood volume in 10yrs 12 cords/ac Expected real sawtimber price in 10yrs $450/mbf Expected real pulpwood price in 10yrs $15/cord Property tax $5 Real alternate rate of return 5% Assumptions for the Current and Future Stands Timber stand improvement cut (age 30 yrs) pulpwood harvest

12 cords/ac

Final (age 60) sawtimber harvest 13 mbf/ac Final (age 60) pulpwood harvest 25 cords/ac

2

,0 ,01

$325/ 18 $7/ 14 $5,948Cp p

p

Timber value P Y mbf mbf cd cd

Cut now:

301' 12 $15 (1.05) 13 $450 25 $15 $7,002.95RFV

160

' $7,002.95 $5$296.11

(1 ) 1 (1.05) 1 0.05RR

FV taxLEV

r r

$5,948 $296.11 $6,244.13CutNowForestValue

Cut in 10 yrs:

2

,10 ,101

$450/ 24 $15/ 12 $10,980Cp p

p

Timber value P Y mbf mbf cd cd

10

$10,980$38.61 $6,740.77 $38.61 $6,702.16

(1.05)timberPV

10

$296.11$181.79

(1.05)LEVPV

10 $6,702.16 $181.79 $6,883.95CutIn yrsForestValue