Calculations concerning the profitability of forest fertilization.

ODC 651.7

237.4

FOLIA FORESTALIA _<4

METSÄNTUTKIMUSLAITOS

^• INSTITUTUM FORESTALE FENNIAE • HELSINKI 1970

KARI KEIPI JA ^OTTOKEKKONEN

CALCULATIONS CONCERNING THE PROFIT ABILITY OF FOREST FERTILIZATION

LASKELMIA METSÄN LANNOITUKSEN EDULLISUUDESTA

N:ot I—lB on lueteltu Folia Forestalia-sarjan julkaisuissa I—4l.

Nrs. I—lB arelisted in thepublications ^{I—4l of the FoliaForestalia series.}

1966 No 19 Paavo Tiihonen: Puutavaralajitaulukot. 1. Maan

eteläpuoliskon

mänty ja kuusi. 2,^— No20 Seppo Grönlund ja JuhaniKurikka: Markkinapuun alueittaiset hankintamäärätvuosina

1962 ja 1964.

Lopulliset

^tulokset.

RemovalsofcommercialroundwoodinFinlandby^districts in 1962and 1964. Finalresults. 4, No 21 KullervoKuusela: Alands skogar 1963—64. 2,^—

No22 Eero Paavilainen: Havaintoja kasvuturpeen käytöstä ^männyn istutuksessa.

Observations ontheuseof gardenpeat in Scotspine

planting.

1,^—

No23 Veikko O. Mäkinen: Metsikön runkoluku keskiläpimitan funktiona

pohjapinta-alan yksikköä

^kohti.

Numberof _stems in a stand _as functionof the meanbreast height ^diameter_perunity^of basal area. 1,^—

No24 Pentti Koivisto: Itä- ja Pohjois-Hämeen koivuvarat.

Birch resources in the

Forestry

^{Board Districts of Itä-Häme}and Pohjois-Häme. 1,^— No25 Seppo Ervasti —Terho Huttunen: Suomenpuunkäyttö vuonna 1964 ja vuoden 1965

ennakkotiedot.

Wood utilization in Finland in 1964 and preliminary ^{data for the} year 1965. 3,^— No26 Sampsa ^Sivonen ja ^{Matti Uusitalo:} Puunkasvatuksen kulut hakkuuvuonna 1965/66.

Expenses of timberproduction inFinland in the cutting ^season1965/66.2,^— No27 Kullervo Kuusela: Helsingin, Lounais-Suomen, Satakunnan, Uudenmaan-Hämeen,Pohjois-

Hämeen ja ^Itä-Hämeenmetsävarat vuosina 1964—65.

Forest resources in the Forestry Board Districts of Helsinki,

Lounais-Suomi,

^Satakunta, Uusimaa-Häme, Pohjois-Häme and Itä-Häme in 1964—65.3,—

1967 No28 Eero Reinius: ValtakunnanmetsienV inventoinnin tuloksianeljänEtelä-Suomenmetsän hoitolautakunnansoista ja metsäojitusalueista.

Results of the fifthnationalforestinventory concerning ^theswamps and forestdrainage

areasof four Forestry ^{Board Districts in southern Finland.} 3,^—

No29

Seppo

Ervasti, Esko Salo ja PekkaTiililä:Kiinteistöjen raakapuun

käytön

^{tutkimus vuo} sina 1964—66.

Real _{estates raw} woodutilization_survey in Finland in 1964—66. 2,^— No30 Sulo Väänänen: Yksityismetsien kantohinnathakkuuvuonna 1965/66.

Stumpage prices in private forests during thecutting ^season1965/66. 1,^— No31 Eero Paavilainen:Lannoituksen vaikutusrämemännikönjuurisuhteisiin.

Theeffectof fertilizationonthe _root systems of _swamp pine ^stands. 2,^— No 32 Metsätilastoa. I Metsävaranto.

Forest statistics of Finland. I Forest _resources. 3,^—

No33 Seppo ^Ervasti ja ^{Esko Salo:} Kiinteistöillälämmön kehittämiseen käytetyt polttoaineet

v. 1965.

Fuels used by real estates for the generation of heatin 1965. 2,^— No34 VeikkoO. Mäkinen: Viljelykuusikoiden^kasvu- jarakennetunnuksia.

Growth and structure characteristisc of cultivated spruce stands. 2,^—

No35 Seppo Ervasti—Terho Huttunen: Suomen puunkäyttö ^vuonna1965 ja ennakkotietoja vuodelta 1966.

Wood utilizationinFinland in 1965 and

preliminary

^{data for the} year 1966.4,^— No36 Eero Paavilainen— Kyösti Virrankoski: Tutkimuksia veden kapillaarisesta noususta tur

peessa.

Studies onthe capillary ^{rise of} water in

peat. 1,50

No37 MattiHeikinheimo—Heikki Veijalainen: Kiinteistöjen polttoainevarastot ^talvella 1965/66.

Fuel stocks of real estates in Finland in winter

1965/66.

2,—

1968 No38 L. Runeberg: Förhällandet mellan driftsöverskott och beskattad inkomst vid skogs beskattningen ^{i Finland.}

Therelationshipbetween surplus and taxable incomein forest taxationinFinland.2,^— No39 MattiUusitalo: Puun kasvatuksen kuluthakkuuvuonna 1966/67.

Costs of timberproduction ^{in Finland} during ^thecutting season 1966/67.2, ^— No40 Jorma Sainio—Pentti Sorrola: Eri polttoaineet teollisuuden lämmön ja ^{voiman sekä}

kiinteistöjen ^lämmönkehittämisessävuonna 1965.

Differentfuels in the generation^{of industrialheat and} power and inthe generationof heat by real estates in 1965. 2,^—

No41 Pentti Rikkonen: Havupaperipuidenkuorimishäviö VK-16 koneella kuorittaessa.

Thebarking ^{loss of coniferous} pulpwood barked with VK-16 machines. 2,—

No42KullervoKuusela ja ^{Alli Salovaara:} Etelä-Savon,Etelä-Karjalan,Itä-Savon, Pohjois-Karja lan, Pohjois-Savon ja Keski-Suomen metsävarat vuosina 1966—67.

Forest_resources in theForestry BoardDistricts ofE-Sa,E-Ka, I-Sa,P-Ka, ^{P-Saand K-S} in 1966—67. 3,—

No43 Eero Paavilainen:Vanhojenrämemäntyjen ^kasvun elpyminen lannoituksen vaikutuksesta.

On the _response tofertilizationof old pine trees growing^on pine swamps. 2,—

N0 44 Lalli Laine: Kuplamörsky, (Rhizina undulataFr.), uusi metsän tuhosieni maassamme.

Rhizina undulata Fr., ^anewforest disease in Finland. 1,^—

Luettelo jatkuu ^3. kansisivulla

FOLIA FORESTALIA 84

Metsäntutkimuslaitos.InstitutumForestaliaFenniae.Helsinki1970

Kari

Keipi

^{& Otto}

Kekkonen

CALCULATIONS CONCERNING ^THE PROFITABILITY OF

FOREST FERTILIZATION

PREFACE

The present

study

^{has been made in the} Finnish Forest Research Institute,

Department

ofForest Economics. Itwasinitiated

by

^OTTO KEKKONEN,M.F., ^who collected ^the

material,

and _wrote the first draft of the

manuscript.

KARIKEIPI,M.F.,

completed

^the

work,

^amend

ing

^the calculationsand

revising

^the

manuscript.

In the course of

study

^{the authors have}

received valuable assistance and advice from several

people;

^itis

appropriate

^thatthe

Depart

ment of Forest Economics and the authors

hereby formally

express their

appreciation

^to these

people.

^{The authors wouldalso like to} thankall thosewho

gaveassistancein

preparing

thispaperfor

publication.

April,

¹⁹⁷⁰ Helsinki

Lauri Heikinheimo

10324—70/80

CONTENTS

PREFACE ₁

1. INTRODUCTION 3

2. FACTORS AFFECTING THE PROFITABILITY OF FERTILIZATION 3

21. Costsandreturns 3

22.Period ofinvestment 4

23. Calculative_rate ofinterest 4

3. INVESTMENTCALCULATIONS.Thepresent

value,

^{the internalrate ofreturnandthe}

pay-back period,

5

4. MEASURING THE RETURNS PRODUCED BY FERTILIZATION 6

41.Short-termfertilization ₅ 411.The

felling

^valuemethod 6

412.Themethodbasedonshortenedrotation g

42.

Long-term

fertilization

g 5. CALCULATIONS CONCERNING THE PROFITABILITY OF A SINGLE FERTILI

ZATION IN STANDS OVER60 YEARS OLD

9 51. Sourcematerialsandframeworkofthecalculations

9

511. Growthand

yield

^tables 9

512.Fertilizationtrialmaterialandthe increaseinincrementobtained 9

513. Costoffertilization 11

514.

Stumpage prices

^and

regeneration

^{costs 11} 52.Resultsbased_onthe

felling

^valuemethod 12 53. Results ^obtained with the method ^basedonshortenedrotation 14 6. RELIABILITY OF THE RESULTS ,16

7. CONCLUSIONS 16

BIBLIOGRAPHY 18

SUOMENKIELINEN SELOSTUS 20

APPENDICES 21-23

3 1. INTRODUCTION

Fertilization is

gaining ground

^{in forest} management. ^In

Finland,

^{where the}

shortage

of roundwoodis

perhaps

^the greatest ^obstacle

to the

expansion

^{of forest}

industry,

^forest fertilization is

likely

^{to be increased}

greatly

inthe next few _years.

Forestfertilizationcanbeviewedfromseveral

angles:

^the

government's,

^{theindustrial} compa

ny's

^orthe

private

^{forestowner's.The decision}

making authority

^{inthegovernment}

integrates

the treatment of forests in the total national economy.

Wood-using industry

^sees fertilization

asameansof

securing

^its

supply

^{ofrawmaterial.}

Fortheforest_owner, fertilization ispart ofhis management

practice.

The present

study

^{will review forest fertili} zation from the

point

^{of view ofa}

private

forest owner. Tostart

with,

^the factors to be taken ^into account inthe ^economic

planning

of fertilization will be discussed. The factors

affecting

^the

profitability

^of fertilization will be

analyzed

^and a few methodsof

calculating

the

profitability

^{willbe discussed. Thesecalcu} lationmethods will be

applied

^tothe

practical

situationof

determining

^the

profits

^obtainable from a

single

fertilization of Scots

pine

^and

Norway

sprucestands atfinal

cutting

age.

They

are based _on increment increases recorded on

the fertilization

sample plots

^{of the Finnish} Forest Research Institute and on

growth

^and

yield

^{tables worked} out for

pine

^and spruce

standstreatedwith

repeated thinnings.

The

object

^{of the} present

study

^{is not so} much _to

investigate

^{the absolute financial}

profits accruing

^from fertilization _astoobserve the

development

^{of the}

advantages

^{of fertili} zationinmaturestandswith

increasing growing

stock d.b.h. Thepart

played by

^thestumpage

price

^levelinthe

profits

^{obtainablefromfertili} zationwill alsobe

analyzed.

The _purpose of this

preliminary study

^is

to ascertainthe ^economic

advantages

^{of fertili} zation in certain individual _cases and aboveall to discover theoverall

possibilities

^ofstudiesof this kind in Finnish conditions. It was deemed necessary ^to find out whether sufficientinfor mation existed _on the

development

^{of the} value of trees as a result of diameter increase.

Another

objective

^{is to determine whether} calculations of this type could be carried_out within the framework of

presently

^available

growth

^and

yield

^tables.

2. FACTORS AFFECTING THE PROFITABILITY OF FERTILIZATION

21. Costs and returns

Costs referto the

compensation

^theowners of the

capital

^and

production

^{factors used}

by

an

enterprise

^{must obtain inordertomakethe}

capital

^and

production

^factors

continuously

available to that

enterprise (DUE

^{& CLOWER}

1966,

p.

116).

The costs can be divided^into

payable,

^i.e.,

explicit,

or

non-payable,

i.e.,

implicit

^costs.

Explicit

^{costs arisewhenthe}

production

^factors

are owned

by

someoneother thantheenter

prise

^{or the} entrepreneur. If the entrepreneur himself _owns the

production

^{factors the cost}

arising

^{from their use is}

implicit (DUE

^&

CLOWER 1966,_p.

117).

Forest fertilization

usually

^{involves both}

explicit

^and

implicit

^costs.

Payable

^{costs arise} from the

purchase

^{of fertilizerand}

usually

^also from

transporting

^ittothe fertilization site. If the forest _owner himself

spreads

^the

fertilizer,

the

arising

^{cost is}

implicit

^{and its amount is} determined

by

^the

profit

^{obtained from the} alternative _useofhired _manpower.In

addition,

fertilization entails the cost of interest onthe

capital,

^either

explicit

^of

implicit.

^{In this} con

text

explicit

^and

implicit

^costsarenot

separated.

The fertilization cost proper ^can

usually

^be estimatedwith afair

degree

^ofaccuracy. The determinationof interest on

capital

^{is more}

complicated

^{and will be discussed}

separately

later.

Only

^thedifferencesbetweenalternativesare

of

importance

^ininvestmentcalculations

(DEAN 1960,

p.

562;

^HONKO

1966,

p.

42;

^VIRKKU NEN

1965,

p.

67).

^Investmentinfertilization is

considered,

^inthe present

study,

^{toaffect the}

returns and _costsofthe ^standwhichis

fertilized,

whereas it is _not considered _to affect the

returns and costs of the other stands of the forest

enterprise.

^Studies

will, therefore,

^con

cern individual stands. However the financial situation of the forest

enterprise

^{affects the}

cost of

financing,

^{andwhen the financial}

plan

is drafted the status ofthewholeforest _enter

prise

^{must be takeninto}consideration

(TANT

TU 1941,_pp.

259-261)

Returns refer to the _gross incomerealized from increment increase

produced by

^fertili zation.The returns

produced by

^a

single

^fertili zation of ^{short-term effect} canbe

assumed,

in

principle,

^{to arise intwodifferent}ways. First,

astandwitha

given

^rotationmaybe considered.

The returns in this _case arise from the in creased

quantity

^of

large

^-dia

meter wood obtained

during

^the

giver

rotation than would have ^{beenobtainedwithout} fertilization. The value of _returns is obtained

by measuring

^{the increase}

produced

^{in the}

cutting

^{value of the stand from the date} of fertilization to the end of the

period

^of rotation.

Second,

^a

given

^{volumeofwoodtobe} grown may be considered.Thereturns arisein this _case from theinterest saved due to the shortened

period

^{of rota} tion. It is then assumed that the stand's

maturity

age is determined

by

^{the sizeof the}

trees and thatafterthefertilizationis_no

longer

effective ^thestandcontinuesits

development

ⁱⁿ the same way ^{as an}unfertilized standof the

same size. Thismethodwas

proposed by

^CAR BONNIER

(1962).

In the_eventthat the fertilizationhasa

long

term effect orseveral consecutive fertilizations

are carried _{out to} the ^end of the rotation, neither ofthe above

assumptions

^{is sufficient} alone. The _returns from fertilization _may be taken_toarisefromanartificial

improvement

^of site

quality.

^Asa

result,

^{the sitewill}

yield

more

timber ^than before ^while at the _same time the rotationis shortened.On thebasis of ^{the results,}of fertilization

experiments

^to datewecannotyet ^discribetheinfluenceofsev eralconsecutive fertilizationsonthe

productive capacity

^{ofthe soil. It is not known whether} there is

any ^sense in

expecting

^a

"permanent improvement

^{of the site" asaresultoffertili} zation. It is

believed,

^for

example,

^{that fertili} zationwith

nitrogen

^alonemaybefore

long

^lead

to a deficit ofother nutrients

(VIRO

^1967, p.

122).

22. Period of investment

The

period

^ofinvestment

equals

^theremain

ing length

^{of the rotation of the fertilized} stand. If

a

cutting

^{of the incrementincrease}

produced by

fertilization _is made

immediately

afterthedirectactionoffertilization_ceases,the result

maybe astandthatcontainslessthan^the

optimum density suggested by

^the

growth

^and

yield

^tables.

Rather,

^{it isoften}

suggested

^that fertilization makes

possible

anincrease inthis

optimum density (

e.g EINOLA 1964,p.

61).

Thebasis for

selecting

^{an investment alter} nativeis

always

^the

optimum period

^ofinvest

ment

(HONKO

^1966, p. 62;EINOLA 1960,_p.

81).

^{In this} case,

therefore,

^{the economic} rotationwillbe usedincalculations

concerning

the

stand,

^{as hasbeendone}

previously

^inforest value calculations

[e.g.,

^HEIKKILÄ 1930, _p.

815).

¹

Owing

^{to the} calculation methods

used, however,

^this can be

applied only

^toanunferti lized stand.

23. Calculative _rate of interest

A characteristic of forest

fertilization,

^and ofinvestmentin

general,

^{isthetimedimension.}

Consequently,

^the

expenditure required

^forand theincome

produced by

^{aninvestmentarenot}

1) Seefootnote2onpage7.

comparable,

^{but must be either}

compounded

or discounted to the same

point

^{in timewith} the aid ofa

given

calculative _rate of interest.

The lower limit of the rateof interest used in calculations _may ^be set at the cost of

financing

^the fertilization. This is

usually

^the

ratethe

capital

^{wouldearninan}alternativeuse.

According

^{to HONKO}

(1966,

p.

65), however,

the rate of interest tobe used in calculations

ultimately equals

^thereturn

expected

^fromthe investment.Hence therate

depends

^both onthe cost of

financing

^{and on the forest owner's} economic

objectives

^{and his}

subjective

^evalua tions

(HAHTOLA 1967,

p.

33).

^{The rate of} interest used in calculations _is therefore the link thatconnects anindividualinvestment with the overall

objectives

^{of the}

enterprise

^{and also} withtheworldoutsidethe

enterprise.

Several factors _must be taken intoaccount

when the rate of ^interest to be ^usedin calcula tions is

being

determined:thecostof

financing;

the relative

uncertainty

^ofthe investment; the

liquidity

^{of the}

investment;

^and

possibly

^also the effect of taxation _on the returns from different investments. The rate,

therefore, ultimately depends

^{ontheforestowner's}

judge

ment, ^on the ^basis of whichatarget ^{rate of}

return is defined in each _case before _aninvest-

ment is made

(JÖRGENSEN

1962; ^HONKO

1966;

^{DUE& CLOWER}

1966).

In young forests the

uncertainty

^associated withthefertilization

yield

^{isalso much}greater thanin old

Liquidity

^is poorerfor^the fertilization of _young stands than for mature

forests. Hence,^the rateofinterest

expected by

theforest_owneris

obviously higher

^the younger the forest to be fertilized. For

example,

^{in a} stand

approaching maturity

^the

expected

^rate

might

^{be5%, ina}

middle-aged

^stand7

%,

^and in a

seedling

^stand9 %. Ifaforest

improvement loan,

^{at a interest rate of}

only

^{3 % if}young forests are

being fertilized,

canbe obtainedthe

expected

^rate maybe somewhat lower. How ever, theloan ^is

relatively

^{short term and the}

fertilization investment must therefore be fi nanced with the forest owner's own

capital

within a few

years, it is

hardly

^{reasonable to} makethe

expected

^{interestrate lowerfor}young stands ^thanforoldforests. _Forest

improvement

loans

granted

^for fertilizationofoldforests_run

at a rate of5 %. Inthe

following calculations,

whichdeal with the

profitability

^of

fertilizing

forests

nearing

^{the final}

cutting

age, various rates ofinterest, 2, ^4and6percent, havebeen

applied.

3.INVESTMENT CALCULATIONS. The

present

value,

^{theinternalrate ofreturnand} the

pay-back period.

The

primary

^{methods used in investment} calculationsarethe present

value,

^or

discount, method,

theinternalrate ofreturnmethodand the

pay-back period.

^Underthepresent value

method,

^{the future returns and costs are dis} counted _to present values

according

^{to a}

given

rate of interest. The investment is

profitable

ifthepresent value ofreturns less the

present value of costs is zero ^or greater than zero.

The internal rate

of

^returnmethodseeks to determine the rate of interest at which the

returns and _costs of investment discounted _toa

given point

^intimeare

equal.

^{This method is}

usually preferred

^ifthe

enterprise

operateswith its_ownlimited

capital

^andthe

highest possible

relative _{return to} this

capital

^{is desired.But if} the

capital

^{available is}

relatively unlimited,

^the present ^{value method}maybe better since its

objective

^{is to secure the}

highest possible

net

returns without too muchconsideration of ^the

amountof

capital.

Since the futureis

always

^{uncertain, exact} calculations _are often omittedin

practice

^and

are

replaced by

^{various methodsof}

approxima

tion.Of

them,

^the

pay-back period

^is

perhaps

thebest

known;

aninvestment must beableto pay foritself^withina

given period.

^Thereason

why

^thismethodis

frequently

^usedis,^all

;gedly,

thatit

gives

^anideaofthe

liquidity

^oftheinvest

ment

(HONKO

1966, p.

107).

^{Some other} methodof

determining

^the

profitability

proper isoftenused

along

^{withthismethod.}

In

theory,

any of these methods can be

applied

^{to studiesofthe}

profitability

^offorest fertilization.

Usually, however,

^thepresent^value methodhasbeenusedincalculationsof

forestry

investment, ^and it will also be used in this

study.

4. ^{MEASURING THE RETURNS PRODUCED BY} FERTILIZATION

41.Short-term fertilization

411.The

felling

^valuemethod Oneway of

determining

^{thereturns to}

forest

fertilization is _to calculate the differences in

growing-stock felling

^{valuesofsimilar fertilized} and unfertilized stands

immediatly

^{after the} fertilization effect has terminated. ^This has ^been

done,

^for

example, by

^VIRO

(1966

^and

1967).

If the ^{fertilizedand} unfertilized ^{controlstands}

are clear cut as soon as the fertilization has

stopped producing

^an

effect,

^{such a}calculation is

relatively

easy.

Fig.

¹ illustratesthe

theory

which constitutes the basis ^for calculations made withthisso-called

felling

^valuemethod.

Fig.

^1.Theoreticalillustrationofthecalculationofreturns

produced by

^thefertilizationof_anindivid ualstand.

(ERKÉN

^1969,p.

66).

The increase in the

felling

^{value due to} fertilization

(A F)

^{is obtained}

by

subtraction:

the

product

^{oftheincreasedvolume1 obtained}

as a resultof fertilization

(Vf)

^{and the raised} stumpagevalueofacubicmetre

(Rf)

^minusthe

product

^{of the volume of the}

corresponding

unfertilized ^stand

(V

_Q

)

^andthestumpagevalue ofacubic_metre

(R

Q

).

Ifthe increaseinreturns

produced by

^fertili zation, ^A F, exceeds the fertilization- cost

1) ^Inthisstudyvolumeissolid_measure

and _m

3means

solid cubic metre.

convertedto the_same

point

ⁱⁿtime,thefertili zationis a

paying proposition.

The

felling

^valuemethod

gives systematically

erroneous results in certain _cases; In mature

stands itover-estimates

profitability

^unlessfinal

cutting

^is

planned

^{to take}

place immediately

after fertilization loses its

effect,

i.e., unless the

resulting

^{increaseinvalueisrealizedimme}

diately.

^{This seems to be}

particularly

^{true if} transitionfrom

pulpwood

^{to saw timber is} at its

highest just

^when fertilization takes effect

(see Fig. 6).

^{In a}youngstandthesituationisthe

reverse. Themethod basedon shortenedrota tionthen

gives

^a

higher though

^{more uncertain}

result,

^which

apparantly

^ismorecorrect atleast in _a

young stand with

no

felling

^{value at all.}

412. The method based on shortened rotation

Assuming,

^as

suggested by

^CARBONNIER

(1962),

^{thatthe returns dueto} fertilization if the rotationis shortened accurein the form ^of

saved interestcosts, fertilizationisaneconomic

proposition

^{iftheincreaseinthediscountvalue} of the stand exceeds the cost of fertilization.

■A

F=Vf Rf

^—V0

*R

0

7 Thismethodwas

proposed by

^EINOLA

(1964,

p.

61)

^{and PEIPPO}

(1965,

p.

20)

^for use in youngforests.

Ifvolumeincrement of thestandisusedasa

parameter, the

shortening

^{of the rotation is:}

n=number of _years

by

^{which the rotation}

is shortened

k=increase in volumeincrement _{as a} result offertilization

(during

^{thewholeeffective}

period)

i =annual volume ^increment of the stand after the fertilizationlosesits direct effect.

Since in

practice

^{the rotation can}

only

^be shortened

by

^wholeyears,the

problem

^ishow

to

proceed

^{iftherotationisshortened}

by

^some fraction of a year. As was obvious from the

above, however,

it makeslittledifferencewheth

er we assume that_more timberisgrownwithin the same

period

^{of rotation or the same}

quantity

^{of timber is} grownwithin ashorter

period

^{ofrotation,since theeffect ofone-time} fertilization _onmineralsoilsis

usually relatively

small.

Consequently,

^the calculations _may as sumethat^{therotationis}shortened

by

^anumber ofmonths

although,

ⁱⁿ

practice,

^a

correspond ingly larger quantity

^oftimberis grownwithin the same unshortened rotation.

The formulas for

calculating

fertilization

returns on thebasis of shortenedrotation_are

presented

^below.

They

^are

adapted

^{from for} mulas derived

by

^EINOLA

(1964,

p.

53)

^for

determining

^the

optimum regeneration

^time.

Only

^{returns and variable costs}

relating

^{to a}

single

^standare

considered;

^{fixedcosts are not} included because

they

^{are not affected}

by

decisions

concerning

fertilization.Theformulas estimate the contribution

margin

^{values of} fertilized andunfertilized stands. Thedifference between the contribution

margin

^{values indi}

cates the increasein discountedreturns net of variable costs

(but

^not

including

fertilization

costs) produced by

fertilization.¹

T 0

⁼ contribution

margin value,

unfertilized stand

Tf

⁼ contribution

margin value,

^{fertilizedstand}

a ⁼ revenue fromfinal

cutting

c ⁼ costof

regeneration

d

x

= netrevenue from

thinning

^atage ^x d

x

>

=net revenue from

thinning

at age x',

assuming

^thatx'=x—n

Only

^{thereturns andcosts}

arising

^atorafter the _moment of fertilization_are considered in

calculating

^thecontribution

margin

^value.FertiT

lization is

profitable

^{if the increase in the} contribution

margin

^value

(Tf

^—T_Q

)

^exceedsthe

costof fertilization. As

pointed

^out

earlier,

^the basis _to be used in the calculations is the

economic an unfertilized

stand;

thatfor^whichthecontribution

margin

^valueat the

beginning

^{of the rotation is maximum.}

1)^1.op^urefers _totherateofinterest factor(1+i)^v,

in which i ⁼

2)Opinions ^differwidely ^{whether or}not touse this kind of "economicrotation" on"financial maturity"

in theprofitability calculations (e.g.^HEIKKILÄ1930;

KELTIKANGAS 1962). ^{Because inthis} study only ^the relative, notthe absolute,profitability ^{offorestfertili} zation will be scrutinized,the concept existing ^{in the} original manuscript ^hasnotbeen changed.

n=-L

1

(a-c)+ld

x

-1.0p

^v

-x

(a-c) +£

^dx

• 1.0p

v"x+

m 1.0_P^v— 1

0

~

1.0p v"m

v» ;

(a-c)+ld

x

•

1.0p

^v

"x

(a-c)

^{+ d}x

> ^•1.0p

v^"x + -

m 1.0p

v

— 1 f

,

1.0p

^v"m

i ⁼

rotation,

unfertilized

i' ⁼ rotation in a fertilized

stand, assuming

that u'=u—n

n ⁼ ageof^standinthe_yearoffertilization i = rate of interest used in calculations

i

⁼

shortening

^{of the rotation as a resultof}

r. _

8

42.

Long-term

fertilization Iffertilization has a

long-term effect,

^{or if}

several consecutive fertilizations take

place

^and theaggregate

profitability

^ofthevarious fertili zationsis to be

calculated,

^{thesituationissimi} lar _to thatwhen the

profitability

^of

drainage

^is

calculated;

^{thereis a}

long-term improvement

in the site

quality

^{which must be taken into}

account.

Iffertilization is

begun

^intheyearthestand is established and continued for not less than the first rotation, the present ^value of the

returns to fertilizationless the present ^value of fertilization _expenses

equals

^{the increase} in the contribution

margin

^value

produced by

fertilization. ^If it is

estimated,

^{for ex}

ample,

^{thata Vaccinium}

site-type

^isconverted

by

fertilizationinto a

Myrtillus site-type,

^the present value of the returns to fertilization

equals

^{the differencebetween the} contribution

margin

^{values of}

Myrtillus

^{and Vaccinium sites.}

Any advantages

^offertilization ^{becomeevident} whenthis increase incontribution

margin

^value is

compared

^withfertilization _expenses.

If fertilization is initiated when the standis

older,

^the calculationis more

complicated.

^If

it is assumed as before that a Vaccinium site canbe converted

by

fertilization into_a*

Myrtil

lus site, fertilization

starting

^{whenthe standis} 50 years old

(for example)

^and

continuing

^for

an unlimited

period,

^thenthe presentvalue of the _{returns to} fertilization will

equal

^{the dif} ference

resulting

^whenthecontribution

margin

value of the Vaccinium stand with no fertili zation is subtracted from that of the"new"

Myrtillus

^{stand. Yield tables show thata 50-} year old Vaccinium

pine

^stand

approximately equals

^a

42-year

^old

Myrtillus pine

^{stand in}

height

^{and volume.}

Consequently,

^the _present value of the returns to fertilization wouldbe the contribution

margin

^{value of the}

42-year

old

Myrtillus pine

^{standminusthatofthe 50-} yearold Vaccinium

pine

^stand.

Iffertilizationistobecontinued

only

^tothe end of the rotation, the

succeeding

^rotations should be calculated

according

to the unferti lized

alternative,

^{i.e., the Vaccinium}

pine

^stand in both _cases. This

alternative,

fertilization

during only

onerotation

cycle,

^canbe

expressed by

^{formulasas follows:}

T q

= contribution

margin value,

unfertilizedstand

Tf

⁼ contribution

margin value,

^"new"standon

improved

^site

r ⁼ economic

ageofthe^"_new"standinthe

yearoffertilization

a ⁼ final

cutting

^revenue

c ⁼ cost of

regeneration

y ⁼ rotation_onthe

improved

^site

v = rotationunfertilized

d =

thinning

revenue atagex, ^orfertilizedatage^z

m =

biological

ageofstandinthe

yearoffertilization p ^{= rate}ofinterest usedincalculations

Fertilization, therefore,

is

profitable

^if

Tf—T

_Q exceeds the fertilization costs discounted tothe datewhen the fertilization_was first carried_out.

This typeof

calculation,

^whichpresupposes several consecutive fertilizations within ^the

remaining period

^of rotation, ^is

probably

not

often

required

^for adecision

concerning

^fertili zation. Each ^decision most often

applies

to a

single fertilization,

^{witha new decision}

being required

^{in due} course

concerning

^refertili

zation.

v

(

^a"c

)

v

+

IV

^I-0P^U

"X

_

(a-c)u +L

^d_x^{* 1.0}p

u"x+

T o

™

1.0p^u—1

1.0p

^v-m

y

(a-c)

_v

+r

^d_x^•

1.0p

^v"x

(a-c) +f

^dz

• i.o

Py-^z + ⁰

Tf

^{= T}

__

1.0

pu-x

^_i i.oPy-^r

5. CALCULATIONS CONCERNING THE PROFITABILITY OF A

SINGLE FERTILIZATION IN STANDS OVER 60 ^YEARS OLD

51.Sourcematerialsandframework of ^thecalculations 511.Growthand

yield

^tables

The calculations

concerning profitability

^of fertilization were carried out for forests _near

ing

^{the final}

cutting

age

using

^{the methods} describedabove for

calculating

^the

profitability

offertilization:the

felling

^{valuemethodandthe} method ^basedon shortened rotation.

The

primary yield

^{ofthe standswascalcula} ted

according

^{to the}

growth

^and

yield

^tables worked out

by'

^NYYSSÖNEN

(1954)

^for

pine stands,

^{treated with}

repeated thinnings,

^on Vaccinium sites and

by

^VUOKILA

(1956)

^for

managed

spruce stands _on

Myrtillus

^sites.The

sample plots

^{of both authors} were

mainly

situatedinsouthern

Finland,

south^ofthe62nd latitude. The tables _were

grouped together by

KOIVISTO

(1959),

^{but are not}

fully

compar able. For this _reason, the tables oftheabove studies _{were not} usedas such inthe

following

calculations: SIVONEN

complemented

^and revised

them, producing

^{resultswhichare}yet^to be

published.

^These

growth

^and

yield

^tables

concern stands which _grow

fully-stocked

^to final

cutting

^and are treated with

repeated

low

thinnings. Appendices

^{1 and 2}

provide

informationonthese tables.

512. Fertilization trial material and the increase in increment obtained

The Forest Research Institutein the

Depart

ment of Soil Sciencehas carriedoutextensive forest-fertilization ^trials since 1958.Anumber of

sample plot

systemsestablishedinVaccinium

pine

^{stands and}

Myrtillus

spruce stands

aged

over 60 years and situated in southern and

central Finland _were selected for _use. Measure ments to

verify

^{theeffect of}fertilization were

carried _out five

years after ^the fertilization.

Average growing-stock

^data

concerning

^{all the}

sample

^standsare

given

^below.

The trials were 2³ _or 2⁴ factor trials. The total number of

sample plots

was 152. The nutrients used_were

nitrogen, phosphorus

^and limein the2³ trials andin the 2⁴

trials,

^also

potassium. Appendix

³ illustratesthe

arrange mentof_a2³ trial.

Table 1

specifies

^the fertilizersused inthe

trials,

^{their nutrientcontent and the}

quantities

of fertilizer

spread

^{over the}

sample plots.

Before

determining

^{theincreaseinincrement}

produced by

^thedifferent

fertilizers,

^thehomo

genity

^{ofthematerialwas}

analyzed.

^Theblocks

fertilized with ammonium

sulphate

^and urea, on the _one

hand,

^{and those fertilized with}

"Kotka"

phosphate

^and "fine"

phosphate,

^on the

other,

were

grouped

^into groups of2—4 blocks

according

^to age, dominant

height

^and volume increment at the timeof fertilization.

One-way analysis

^{ofvariancewasusedto}

study

whether _any

significant

differences ^existed in the average

growth

^{of the} _groups ^{before the} trial. No such differences _were recorded either in these^small_groupsorin

larger

^ones.Norwere

significant

differences recorded for

average

Growing

^stock

Vaccinium

pine

^stands

Myrtillus

sprucestands

ige

lominant

height

'olume

including

^bark

:urrent annual volume ncrement

excluding

^bark

90yrs 19.9 m

132.6m 3

/ha

3.2m 3

/ha

90 yrs 20.0 m

136.7m 3

/ha

3.6m 3

/ha

Table1. Fertilizers ^usedinthe

trials,

^{theirnutrient}content,andthe

quantities spread

^over

sample plots, kg/ha.

1) 313kg/ha^ofureawasspreadoverone2³block.

growth

^{of the}unfertilized

sample plots

^before and

during

^{thetrial.This showedthatmeasured} results could be used in later calculations without correction for increment fluctuations.

The effect of the different fertilizers _was verified

by

^{the usualmethodusedforcalculat}

ing

^{theresults offactor} tests

(see,

^for

example,

COCHRAN & COX

1964,

pp.

155-161).

^The

degrees

^ofthe

principal

^and_aggregate^effectsof the fertilizers _were tested with the F test. The calculations showed ^that in the

five-year

^trial

period

^the

nitrogen

fertilization inallcasescaused

a

highly significant

^{incrementincrease}

(at

^the risk of0.1 per

cent).

^The

principal

^{effects of}

theother fertilizers were not

significant (at

^the risk of5 per

cent).

^{Nordid the}fertilizers show

anaggregate

increasing

^effect on

growing-stock

increment.On thecontrary, ⁱⁿsome ofthe2⁴

trials,

^the aggregate fertilizer effect on the

sample plots

^{treatedwithallfournutrients}was

negative.

The

following figures

^showtheaverageincre ment increase due _to

nitrogen

fertilization

during

^the

five-year

^trial

period.

^Ammonium

sulphate

fertilization was used both in the

Myrtillus

spruce stands and Vaccinium

pine

stands. Ureawas used

only

^{to fertilize}

Myrtillus

spruceblocks.

Thetotalincrementincreaseinfive _yearsin the

pine

^stands

averaged

^{5.3 m3}

/ha,

ⁱⁿ spruce stands fertilized with _urea, 5.7 m

3

/ha,

^{and in} spruce stands fertilized with ammonium sul

phate,

^7.5m3

/ha.

On the basis of the results of fertilization

trials,

^the correlationbetweenthe fertilization effect

produced by nitrogen

^and some stand characteristicswas

analyzed.

^{Inthiscase the}age ofthe standshowed _nocorrelation. The stand, volume

proved

^{tobe a}poor

explaining

^variable and the

pre-fertilization

^{increment did not}

adequately explain

^{the incrementincreasedue}

to fertilization.

Theinsertion of increment and stand volume in a

regression

^{model with two}

independent

variables showed that _even

together they only slightly explained

^{theincrementincrease dueto} fertilization. Thelinearmodel

E=increment increase due to fertilization 1=

growing

^{stock increment}

prior

^{to fertili}

zation

V=growing

^stockvolume A, B, C=constants

proved

^{to be themost} serviceableofsixlinear and three non-linear models. The

degree

^of

determination,

^on

application

^ofthe

equation, averaged

^{0.194 and the common} correlation coefficient was0.44.

E=A + B^•1 + C'V

Fertilizer Nutrient _content

Quantity used, kg/ha Nitrogen fertilizers

⁴⁰⁰

ammonium

sulphate

urea

20.5 % ^N 46.3 % N

400 200

(313)

¹

Phosphorus fertilizers

"Kotka"

phosphate

fine"

phosphate

23.5%

P2O5

33.0% ^"

400 200

Potassium

fertilizer

potassium

^{salt 50.0%K}2 0 400

Limestone

powder

²⁰⁰⁰

■erti

fertilizer Vaccinium

Myrtillus pine

^stands spruce stands

m3

excluding bark/ha/year

urea

mmonium

sulphate

1.14

1.06 1.50