ODC 651.7

237.4

## FOLIA FORESTALIA _{<4}

### METSÄNTUTKIMUSLAITOS

^{•}INSTITUTUM FORESTALE FENNIAE • HELSINKI 1970

KARI KEIPI JA ^{OTTO}^{KEKKONEN}

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} ^{Folia}^{Forestalia} ^{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}_{per}unity^{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 ^{season}1965/66.2,^{—}
No27 Kullervo Kuusela: Helsingin, Lounais-Suomen, Satakunnan, Uudenmaan-Hämeen,Pohjois-

Hämeen ja ^{Itä-Hämeen}metsävarat 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 ^{the}swamps 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 ^{season}1965/66. 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 ^{vuonna}1965 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 ^{the}cutting season 1966/67.2, ^{—}
No40 Jorma Sainio—Pentti Sorrola: Eri polttoaineet teollisuuden lämmön ja ^{voiman} ^{sekä}

kiinteistöjen ^{lämmön}kehittämisessävuonna 1965.

Differentfuels in the generation^{of} ^{industrial}^{heat} ^{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-Sa}^{and} ^{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., ^{a}newforest 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;

^{it}

^{is}

### appropriate

^{that}

^{the}

### Depart

ment of Forest Economics and the authors

### hereby formally

express their### appreciation

^{to}these

### people.

^{The}

^{authors}

^{would}

^{also}

^{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}

^{internal}

^{rate}

^{of}

^{return}

^{and}

^{the}

### pay-back period,

54. MEASURING THE RETURNS PRODUCED BY FERTILIZATION 6

41.Short-termfertilization _{5}
411.The

### felling

^{value}

^{method}6

412.Themethodbasedonshortenedrotation g

42.

### Long-term

fertilizationg 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

_{on}the

### felling

^{value}

^{method}12 53. Results

^{obtained}with the method

^{based}onshortenedrotation 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,

^{the}

^{industrial}compa

### ny's

^{or}

^{the}

### private

^{forest}

^{owner's.}

^{The}

^{decision}

### making authority

^{in}

^{the}

^{government}

### integrates

the treatment of forests in the total national economy.### Wood-using industry

^{sees}fertilization

asameansof

### securing

^{its}

### supply

^{of}

^{raw}

^{material.}

Fortheforest_{owner,} fertilization ispart ofhis
management

### practice.

The present

### study

^{will}

^{review}

^{forest}

^{fertili}zation from the

### point

^{of}

^{view}

^{of}

^{a}

### 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

^{will}

^{be}

^{discussed.}

^{These}

^{calcu}lationmethods will be

### applied

^{to}

^{the}

### 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

_{as}

_{to}observe the

### development

^{of}

^{the}

### advantages

^{of}

^{fertili}zationinmaturestandswith

### increasing growing

stock d.b.h. Thepart### played by

^{the}stumpage

### price

^{level}

^{in}

^{the}

### profits

^{obtainable}

^{from}

^{fertili}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

^{of}

^{studies}

^{of}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

^{the}

^{owners}of the

### capital

^{and}

### production

^{factors}

^{used}

### by

an

### enterprise

^{must}

^{obtain}

^{in}

^{order}

^{to}

^{make}

^{the}

### 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}

^{arise}

^{when}

^{the}

### 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}

^{fertilizer}

^{and}

### usually

^{also}from

### transporting

^{it}

^{to}

^{the}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

_{use}ofhired

_{manpower.}In

### addition,

fertilization entails the cost of interest onthe### capital,

^{either}

### explicit

^{of}

### implicit.

^{In}

^{this}con

text

### explicit

^{and}

### implicit

^{costs}

^{are}

^{not}

### separated.

The fertilization cost proper ^{can}

### usually

^{be}estimatedwith afair

### degree

^{of}accuracy. The determinationof interest on

### capital

^{is}

^{more}

### complicated

^{and}

^{will}

^{be}

^{discussed}

### separately

later.### Only

^{the}differencesbetweenalternativesare

of

### importance

^{in}

^{investment}calculations

### (DEAN 1960,

p.### 562;

^{HONKO}

### 1966,

p.### 42;

^{VIRKKU}NEN

### 1965,

p.### 67).

^{Investment}

^{in}fertilization is

### considered,

^{in}

^{the}present

### study,

^{to}

^{affect}

^{the}

returns and _{costs}ofthe ^{stand}whichis

### 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,

^{and}

^{when}

^{the}

^{financial}

### plan

is drafted the status ofthewholeforest_{enter}

### prise

^{must}

^{be}

^{taken}

^{into}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}

^{in}

^{two}

^{different}ways. First,

astandwitha

### given

^{rotation}maybe 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^{been}

^{obtained}

^{without}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

^{volume}

^{of}

^{wood}

^{to}

^{be}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}

^{size}

^{of}

^{the}

trees and thatafterthefertilizationis_{no}

### longer

effective^{the}

^{stand}continuesits

### development

^{in}the same way

^{as}

^{an}unfertilized standof the

same size. Thismethodwas

### proposed by

^{CAR}BONNIER

### (1962).

In the_{event}that 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

_{to}arisefromanartificial

### improvement

^{of}site

### quality.

^{As}

^{a}

### result,

^{the}

^{site}

^{will}

### yield

moretimber ^{than} before ^{while} at the _{same}
time the rotationis shortened.On thebasis
of ^{the} ^{results,}of fertilization

### experiments

^{to}datewecannotyet

^{discribe}

^{the}influenceofsev eralconsecutive fertilizationsonthe

### productive capacity

^{of}

^{the}

^{soil.}

^{It}

^{is}

^{not}

^{known}

^{whether}there is

any ^{sense} in

### expecting

^{a}

### "permanent improvement

^{of}

^{the}

^{site"}

^{as}

^{a}

^{result}

^{of}

^{fertili}zation. It is

### believed,

^{for}

### example,

^{that}

^{fertili}zationwith

### nitrogen

^{alone}maybefore

### long

^{lead}

to a deficit ofother nutrients

### (VIRO

^{1967,}p.

### 122).

22. Period of investment

The

### period

^{of}

^{investment}

### equals

^{the}

^{remain}

### ing length

^{of}

^{the}

^{rotation}

^{of}

^{the}

^{fertilized}stand. If

a

### cutting

^{of}

^{the}

^{increment}

^{increase}

### produced by

fertilization_{is}made

### immediately

afterthedirectactionoffertilization_{ceases,}the result

maybe astandthatcontainslessthan^{the}

### optimum density suggested by

^{the}

### growth

^{and}

### yield

^{tables.}

### Rather,

^{it}

^{is}

^{often}

### 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

^{of}

^{invest}

ment

### (HONKO

^{1966,}p. 62;EINOLA 1960,

_{p.}

### 81).

^{In}

^{this}case,

### therefore,

^{the}

^{economic}rotationwillbe usedincalculations

### concerning

the### stand,

^{as}

^{has}

^{been}

^{done}

### previously

^{in}

^{forest}value calculations

### [e.g.,

^{HEIKKILÄ}1930,

_{p.}

### 815).

^{1}

### Owing

^{to}

^{the}calculation methods

### used, however,

^{this}can be

### applied only

^{to}

^{an}

^{unferti}lized stand.

23. Calculative _{rate} of interest

A characteristic of forest

### fertilization,

^{and}ofinvestmentin

### general,

^{is}

^{the}

^{time}

^{dimension.}

### Consequently,

^{the}

### expenditure required

^{for}

^{and}theincome

### produced by

^{an}

^{investment}

^{are}

^{not}

1) Seefootnote2onpage7.

### comparable,

^{but}

^{must}

^{be}

^{either}

### compounded

or discounted to the same

### point

^{in}

^{time}

^{with}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

^{would}

^{earn}

^{in}

^{an}alternativeuse.

### According

^{to}

^{HONKO}

### (1966,

p.### 65), however,

the rate of interest tobe used in calculations### ultimately equals

^{the}

^{return}

### expected

^{from}

^{the}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 ^{used}^{in} calcula
tions is

### being

determined:thecostof### financing;

the relative

### uncertainty

^{of}

^{the}investment; the

### liquidity

^{of}

^{the}

### investment;

^{and}

### possibly

^{also}the effect of taxation

_{on}the returns from different investments. The rate,

### therefore, ultimately depends

^{on}

^{the}

^{forest}

^{owner's}

### judge

ment,^{on}the

^{basis}of whichatarget

^{rate}

^{of}

return is defined in each _{case} before _{an}invest-

ment is made

### (JÖRGENSEN

1962;^{HONKO}

### 1966;

^{DUE}

^{&}

^{CLOWER}

### 1966).

In young forests the

### uncertainty

^{associated}withthefertilization

### yield

^{is}

^{also}

^{much}greater thanin old

### Liquidity

^{is}poorerfor

^{the}fertilization of

_{young}stands than for mature

forests. Hence,^{the} rateofinterest

### expected by

theforest_{owner}is

### obviously higher

^{the}younger the forest to be fertilized. For

### example,

^{in}

^{a}stand

### approaching maturity

^{the}

### expected

^{rate}

### might

^{be}

^{5}

^{%,}

^{in}

^{a}

### middle-aged

^{stand}

^{7}

### %,

^{and}in a

### seedling

^{stand}

^{9}%. 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 fewyears, it is

### hardly

^{reasonable}

^{to}makethe

### expected

^{interest}

^{rate}

^{lower}

^{for}young stands

^{than}foroldforests.

_{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,^{4}

^{and}6percent, havebeen

### applied.

3.INVESTMENT CALCULATIONS. The

present

### value,

^{the}

^{internal}

^{rate}

^{of}

^{return}

^{and}the

### pay-back period.

The

### primary

^{methods}

^{used}

^{in}

^{investment}calculationsarethe present

### value,

^{or}

### discount, method,

theinternalrate ofreturnmethodand the### pay-back period.

^{Under}

^{the}present 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 thepresent
value of costs is zero ^{or} greater than zero.

The internal rate

### of

^{return}

^{method}seeks to determine the rate of interest at which the

returns and _{costs} of investment discounted _{to}_{a}

### given point

^{in}

^{time}are

### equal.

^{This}

^{method}

^{is}

### usually preferred

^{if}

^{the}

### enterprise

operateswith its_{own}limited

### capital

^{and}

^{the}

### 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

netreturns without too muchconsideration of ^{the}

amountof

### capital.

Since the futureis

### always

^{uncertain,}

^{exact}calculations

_{are}often omittedin

### practice

^{and}

are

### replaced by

^{various}

^{methods}

^{of}

### approxima

tion.Of### them,

^{the}

### pay-back period

^{is}

### perhaps

thebest### known;

aninvestment must beableto pay foritself^{within}a

### given period.

^{The}

^{reason}

### why

^{this}

^{method}

^{is}

### frequently

^{used}is,

^{all}

### ;gedly,

thatit### gives

^{an}

^{idea}

^{of}

^{the}

### liquidity

^{of}

^{the}

^{invest}

ment

### (HONKO

1966, p.### 107).

^{Some}

^{other}methodof

### determining

^{the}

### profitability

proper isoftenused### along

^{with}

^{this}

^{method.}

In

### theory,

any of these methods can be### applied

^{to}

^{studies}

^{of}

^{the}

### profitability

^{of}

^{forest}fertilization.

### Usually, however,

^{the}present

^{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

^{value}

^{method}Oneway of

### determining

^{the}

^{returns}

^{to}

### forest

fertilization is _{to} calculate the differences in

### growing-stock felling

^{values}

^{of}

^{similar}

^{fertilized}and unfertilized stands

### immediatly

^{after}

^{the}fertilization effect has terminated.

^{This}has

^{been}

### done,

^{for}

### example, by

^{VIRO}

### (1966

^{and}

### 1967).

If the ^{fertilized}^{and} unfertilized ^{control}^{stands}

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

^{value}

^{method.}

### Fig.

^{1.}Theoreticalillustrationofthecalculationofreturns

### produced by

^{the}fertilizationof

_{an}individ ualstand.

### (ERKÉN

^{1969,}p.

### 66).

The increase in the

### felling

^{value}

^{due}

^{to}fertilization

### (A F)

^{is}

^{obtained}

### by

subtraction:the

### product

^{of}

^{the}

^{increased}

^{volume}

^{1}

^{obtained}

as a resultof fertilization

### (Vf)

^{and}

^{the}

^{raised}stumpagevalueofacubicmetre

### (Rf)

^{minus}

^{the}

### product

^{of}

^{the}

^{volume}

^{of}

^{the}

### corresponding

unfertilized^{stand}

### (V

_{Q}

### )

^{and}

^{the}stumpagevalue ofacubic

_{metre}

### (R

Q### ).

Ifthe increaseinreturns

### produced by

^{fertili}zation,

^{A}F, exceeds the fertilization- cost

1) ^{In}^{this}studyvolumeissolid_{measure}

and _{m}

3means

solid cubic metre.

convertedto the_{same}

### point

^{in}time,thefertili zationis a

### paying proposition.

The

### felling

^{value}

^{method}

### gives systematically

erroneous results in certain _{cases;} In mature

stands itover-estimates

### profitability

^{unless}

^{final}

### cutting

^{is}

### planned

^{to}

^{take}

### place immediately

after fertilization loses its### effect,

i.e., unless the### resulting

^{increase}

^{in}

^{value}

^{is}

^{realized}

^{imme}

### 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

^{is}

^{more}correct atleast in

_{a}

young stand with

no

### felling

^{value}

^{at}

^{all.}

412. The method based on shortened rotation

### Assuming,

^{as}

### suggested by

^{CARBONNIER}

### (1962),

^{that}

^{the}

^{returns}

^{due}

^{to}fertilization if the rotationis shortened accurein the form

^{of}

saved interestcosts, fertilizationisaneconomic

### proposition

^{if}

^{the}

^{increase}

^{in}

^{the}

^{discount}

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

■A

### F=Vf Rf

^{—}

^{V}0

*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

^{the}

^{whole}

^{effective}

### period)

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

Since in

### practice

^{the}

^{rotation}

^{can}

### only

^{be}shortened

### by

^{whole}years,the

### problem

^{is}

^{how}

to

### proceed

^{if}

^{the}

^{rotation}

^{is}

^{shortened}

### by

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

### above, however,

it makeslittledifferencewhether we assume that_{more} timberisgrownwithin
the same

### period

^{of}

^{rotation}

^{or}

^{the}

^{same}

### quantity

^{of}

^{timber}

^{is}grownwithin ashorter

### period

^{of}

^{rotation,}

^{since}

^{the}

^{effect}

^{of}

^{one-time}fertilization

_{on}mineralsoilsis

### usually relatively

small.### Consequently,

^{the}calculations

_{may}as sumethat

^{the}

^{rotation}

^{is}shortened

### by

^{a}

^{number}ofmonths

### although,

^{in}

### practice,

^{a}

### correspond ingly larger quantity

^{of}

^{timber}

^{is}grownwithin the same unshortened rotation.

The formulas for

### calculating

fertilizationreturns 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

^{stand}are

### considered;

^{fixed}

^{costs}

^{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,

^{fertilized}

^{stand}

a ^{=} revenue fromfinal

### cutting

c ^{=} costof

### regeneration

dx

= netrevenue from

### thinning

^{at}age

^{x}d

x

>

=net revenue from

### thinning

at age x',### assuming

^{that}

^{x'}

^{=}

^{x}

^{—}

^{n}

### Only

^{the}

^{returns}

^{and}

^{costs}

### arising

^{at}

^{or}

^{after}the

_{moment}of fertilization

_{are}considered in

### calculating

^{the}contribution

### margin

^{value.}

^{Ferti}T

lization is

### profitable

^{if}

^{the}

^{increase}

^{in}

^{the}contribution

### margin

^{value}

### (Tf

^{—}

^{T}

_{Q}

### )

^{exceeds}

^{the}

costof fertilization. As

### pointed

^{out}

### earlier,

^{the}basis

_{to}be used in the calculations is the

economic an unfertilized

### stand;

thatfor^{which}^{the}contribution

### margin

^{value}

^{at}the

### beginning

^{of}

^{the}

^{rotation}

^{is}

^{maximum.}

1)^{1.}op^{u}refers _{to}therateofinterest factor(1+i)^{v},

in which i ^{=}

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

in theprofitability calculations (e.g.^{HEIKKILÄ}1930;

KELTIKANGAS 1962). ^{Because} ^{in}^{this} study only ^{the}
relative, notthe absolute,profitability ^{of}^{forest}^{fertili}
zation will be scrutinized,the concept existing ^{in} ^{the}
original manuscript ^{has}notbeen changed.

### n=-L

1

### (a-c)+ld

x### -1.0p

^{v}

-x

### (a-c) +£

^{d}x

• 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,

unfertilizedi' ^{=} rotation in a fertilized

### stand, assuming

that u'=u—nn ^{=} ageof^{stand}^{in}the_{year}offertilization
i = rate of interest used in calculations

### i

^{=}

### shortening

^{of}

^{the}

^{rotation}

^{as}

^{a}

^{result}

^{of}

r. _

8

42.

### Long-term

fertilization Iffertilization has a### long-term effect,

^{or}

^{if}

several consecutive fertilizations take

### place

^{and}theaggregate

### profitability

^{of}

^{the}various fertili zationsis to be

### calculated,

^{the}

^{situation}

^{is}

^{simi}lar

_{to}thatwhen the

### profitability

^{of}

### drainage

^{is}

### calculated;

^{there}

^{is}

^{a}

### long-term improvement

in the site### quality

^{which}

^{must}

^{be}

^{taken}

^{into}

account.

Iffertilization is

### begun

^{in}

^{the}yearthestand 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,

^{that}

^{a}

^{Vaccinium}

### site-type

^{is}

^{converted}

### by

fertilizationinto a### Myrtillus site-type,

^{the}present value of the returns to fertilization

### equals

^{the}

^{difference}

^{between}

^{the}contribution

### margin

^{values}

^{of}

### Myrtillus

^{and}

^{Vaccinium}

^{sites.}

### Any advantages

^{of}fertilization

^{become}

^{evident}whenthis increase incontribution

### margin

^{value}is

### compared

^{with}fertilization

_{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

^{when}

^{the}

^{stand}

^{is}50 years old

### (for example)

^{and}

### continuing

^{for}

an unlimited

### period,

^{then}

^{the}presentvalue of the

_{returns}

_{to}fertilization will

### equal

^{the}

^{dif}ference

### resulting

^{when}

^{the}contribution

### margin

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

^{stand.}

^{Yield}

^{tables}

^{show}

^{that}

^{a}

^{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

^{stand}

^{minus}

^{that}

^{of}

^{the}

^{50-}yearold Vaccinium

### pine

^{stand.}

Iffertilizationistobecontinued

### only

^{to}

^{the}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,

^{can}

^{be}

### expressed by

^{formulas}

^{as}

^{follows:}

T q

= contribution

### margin value,

unfertilizedstand### Tf

^{=}contribution

### margin value,

^{"}

^{new"}

^{stand}on

### improved

^{site}

r ^{=} economic

ageofthe^{"}_{new"}standinthe

yearoffertilization

a ^{=} final

### cutting

^{revenue}

c ^{=} cost of

### regeneration

y^{=}rotation

_{on}the

### improved

^{site}

v = rotationunfertilized

d =

### thinning

revenue atagex,^{or}fertilizedatage

^{z}

m =

### biological

ageofstandintheyearoffertilization
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,

^{which}presupposes several consecutive fertilizations within

^{the}

### remaining period

^{of}rotation,

^{is}

### probably

notoften

### required

^{for}adecision

### concerning

^{fertili}zation. Each

^{decision}most often

### applies

to a### single fertilization,

^{with}

^{a}

^{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

^{d}z

• 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 ^{the}calculations
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

^{value}

^{method}

^{and}

^{the}method

^{based}on shortened rotation.

The

### primary yield

^{of}

^{the}

^{stands}

^{was}

^{calcula}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^{of}

^{the}

^{62nd}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

^{results}

^{which}

^{are}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

^{the}

^{effect}

^{of}fertilization were

carried _{out} five

years after ^{the} fertilization.

### Average growing-stock

^{data}

### concerning

^{all}

^{the}

### sample

^{stands}

^{are}

### given

^{below.}

The trials were 2^{3} _{or} 2^{4} factor trials. The
total number of

### sample plots

was 152. The nutrients used_{were}

### nitrogen, phosphorus

^{and}limein the2

^{3}trials andin the 2

^{4}

### trials,

^{also}

### potassium. Appendix

^{3}illustratesthe

arrange
mentof_{a2}^{3} trial.

Table 1

### specifies

^{the}fertilizersused inthe

### trials,

^{their}

^{nutrient}

^{content}

^{and}

^{the}

### quantities

of fertilizer### spread

^{over}

^{the}

### sample plots.

Before

### determining

^{the}

^{increase}

^{in}

^{increment}

### produced by

^{the}

^{different}

### fertilizers,

^{the}

^{homo}

### genity

^{of}

^{the}

^{material}

^{was}

### analyzed.

^{The}

^{blocks}

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

^{of}

^{variance}

^{was}

^{used}

^{to}

### 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}

_{groups}orin

### larger

^{ones.}

^{Nor}

^{were}

### significant

differences recorded foraverage

### Growing

^{stock}

Vaccinium

### pine

^{stands}

### Myrtillus

sprucestandsige

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 ^{used}inthe

### trials,

^{their}

^{nutrient}content,andthe

### quantities spread

^{over}

### sample plots, kg/ha.

1) 313kg/ha^{of}^{urea}wasspreadoverone2^{3}block.

### growth

^{of}

^{the}unfertilized

### sample plots

^{before}and

### during

^{the}

^{trial.}

^{This}

^{showed}

^{that}

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

The effect of the different fertilizers _{was}
verified

### by

^{the}

^{usual}

^{method}

^{used}

^{for}

^{calculat}

### ing

^{the}

^{results}

^{of}

^{factor}tests

### (see,

^{for}

### example,

COCHRAN & COX### 1964,

pp.### 155-161).

^{The}

### degrees

^{of}

^{the}

### principal

^{and}

_{aggregate}

^{effects}

^{of}the fertilizers

_{were}tested with the F test. The calculations showed

^{that}in the

### five-year

^{trial}

### period

^{the}

### nitrogen

fertilization inallcasescauseda

### highly significant

^{increment}

^{increase}

### (at

^{the}risk of0.1 per

### cent).

^{The}

### principal

^{effects}

^{of}

theother fertilizers were not

### significant (at

^{the}risk of5 per

### cent).

^{Nor}

^{did}

^{the}fertilizers show

anaggregate

### increasing

^{effect}on

### growing-stock

increment.On thecontrary,^{in}some ofthe2

^{4}

### trials,

^{the}aggregate fertilizer effect on the

### sample plots

^{treated}

^{with}

^{all}

^{four}

^{nutrients}was

### negative.

The

### following figures

^{show}

^{the}averageincre 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 _{years}in
the

### pine

^{stands}

### averaged

^{5.3}

^{m}

^{3}

### /ha,

^{in}spruce stands fertilized with

_{urea,}5.7 m

3

### /ha,

^{and}

^{in}spruce stands fertilized with ammonium sul

### phate,

^{7.5}

^{m}

^{3}

### /ha.

On the basis of the results of fertilization

### trials,

^{the}correlationbetweenthe fertilization effect

### produced by nitrogen

^{and}some stand characteristicswas

### analyzed.

^{In}

^{this}

^{case}

^{the}age ofthe standshowed

_{no}correlation. The stand, volume

### proved

^{to}

^{be}

^{a}poor

### explaining

^{variable}and the

### pre-fertilization

^{increment}

^{did}

^{not}

### adequately explain

^{the}

^{increment}

^{increase}

^{due}

to fertilization.

Theinsertion of increment and stand volume in a

### regression

^{model}

^{with}

^{two}

### independent

variables showed that _{even}

### together they only slightly explained

^{the}

^{increment}

^{increase}

^{due}

^{to}fertilization. Thelinearmodel

E=increment increase due to fertilization 1=

### growing

^{stock}

^{increment}

### prior

^{to}

^{fertili}

zation

### V=growing

^{stock}

^{volume}A, B, C=constants

### proved

^{to}

^{be}

^{the}

^{most}serviceableofsixlinear and three non-linear models. The

### degree

^{of}

### determination,

^{on}

### application

^{of}

^{the}

### 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