calculation of ror

8/18/2019 Calculation of ROR

1/18

PROFITABILITY

Term used to measure the amount of profit from a certain investment

Total Profit cannot be used as meansof comparing investments.

Example:

Investment Profit

$ 100,000 10,000$/yr

$ 1,000,000 2,000$/yr

The second investment has a larger profit. !o"ever,

"hen the profit is compared to the investment, thefirst investment loo#s better.


2/18

METHODS OF PROFITABILITY

EVALUATION

1) RATE OF RETURN (ROI )

%I& TCI ) PAT ( Taxes After ofit Pr

'If (epreciation is not included in P)T, use*)+! -% instead

+ince euipment depreciate, it is betterto use average values over the life of

the proect.

%I& TCI Averaged ofit Pr Annual Averaged

)veraged T*I & *I +alvage 3alue 4 or#ing *apital


3/18

RETURN BASED ON CAPITAL

RECOVERY WITH MINIMUM

PROFIT

Incorporate a certain 5inimum Profitdesired as a fictitious e6pense

%I&Income Expense Min ofit

TCI− − .Pr

eturn calculated in this manner gives theRISK EARNING RATE

Caution: It is better to use *)+! -%instead of I7*%5889P87+8

eturn of Investment is a point value.

*alculations are done for a particular oraverage year.

: 7o time value of money is included


4/18

ROI BASED ON DISCOUNTED

CASH FLOW

)ssume1 ) loan at interest i is used to finance

the proect.2 The cash flo" of the proect is used

to pay principal and interest.

Then %I & i

EXAM!E:

*I & $100,000 ;ear ** & $ 10,000 1 $


5/18

+&CFa

a 1

n

=

∑'14 ina

*a ? predicted cash flo" for year a

e calculate no" the amount of moneyneeded to pay the loan ?

3& 110,000 '14 i& T*I'14 in

Therefore, the future "orth of proceedscorrected for salvage value and "or#ingcapital 'recovered at the end should beeual to 3

3&+43+4*

110,000 '14 i &


6/18

This is a polynomial of degree n. +olve it,i.e. find the root.

or the e6ample i &0.20@ %I&20.@A

Note? i corresponds to Bero future value of proceedsas compared to the *I.


7/18

DCF Referred to Present Time

"e#ent $alue o% In&e#tment '"e#ent $alue o% Ca# Flo#

T*I &

CFaa 1

n

=

∑'14ia 4'3+4*'14in

+o, if the cash flo" is eual for all years 'thesimplest situation possible, then

T*I &* a 1

n

=∑

'14ia 4'3+4*'14in


8/18

NET PRESENT WORTH

Present value of annual cash flo"s initial investment.

EXAM!E ? +ame data as before.

)ssume the capital of the company isnormally put at 1A interest.

;ear *ash lo" Present 3alue 1 $


9/18

CAPITALIED COST

PROFITABILITY

Eseful for comparing alternatives "ithin asingle proect. 'ecall the stainless steel vs.5ild steel reactor e6ample

F)+I* 8GE)TI%7 ?

H & *3 4

CiR n( )1 1+ −

Fut *3 & *43+. Then

H &C i

iR n

n( )

( )1

1 1+

+ − 4 3+

( )( )

11 1

++ −

ii

n

n ? *apitaliBed *ost factor.


10/18


11/18

Exten#ion to in*lu+e Ope"atin, Co#t#

*onsider operating costs as a piece ofeuipment that lasts for one year andhas Bero scrap value.

*alculate the present value of each yearscost 'as in net present "orth method and

then calculate the capitaliBed cost of theseannual cash e6penses. 'H%.

EXAM!E ? )ssume i &1A and thefollo"ing %perating *osts.

;ear %p. *osts Present 3alue1 $


12/18

H% & $ 100,=

( . )

( . )

115

115 1

5

5 − & $ 200,000


13/18

Therefore?

7et present "orth of annual %p. *osts?

Ciaa

n

a=∑

+1

11( )

*apitaliBed *ost of annual %p. costs

H%&

( )( )

11 1

++ −

ii

n

n

Ciaa

n

a=∑

+1

11( )

If *a is eual for all years, then ?

H%&( )

( )1

1 1+

+ −i

in

n C

i11

Gene"al %o"mula

*ap. *ost & H 4 H%4 or#ing *apital


14/18

PAYOUT PERIOD

5inimum length of time needed torecover the investment in a form ofcash flo".

Payout &

FCI

Average Cash Fo!

Ote" name# a"e? Paybac#, Payoff, *ashecovery period.

In*lu#ion o% Inte"e#t

Payout &

FCI Interest on TCIAverage Cash Fo!

+

Interest on T*I is calculated as annualcash flo"s discounted at interest rate I to

get an average annual value.


15/18

ACCEPTABLE RETURNS

7eed to compare "ith otherinvestments and their ris#s

In&e#tment Retu"n Ri#-

Jovernment @A )lmostFonds none

Preferred +toc# @D A +ome

*ommon +toc# KD A !igher


16/18

INVESTMENT COMPARISON

EXAM!E

In&e#tment "o%it ROI $ 1,200,000 $ 2>0,000 20 A$ 2,000,000 $


17/18

FOR!SAVIN"S INVESTMENTS

EXAM!E : *onsider a heat e6changerinstallation to recover energy. )ssume thereare > alternatives.

)-T. *I %P8. 3)-E8 % *%+T !8)T +)38(

1 $10,000 $100 $>,100 2 $1=,000 $100 $=,000 < $20,000 $100 $=,D00 > $2=,000 $100 $C,C0

)ssume a depreciation of 20A/yr and a minimum %Iof 10 A Then

+avings&3aluedepreciation%perating costs

)-T. +)3I7J+ %I I7*8587T)-'over )-T 1

1 $2,000 20 A 2 $2,@00 1=.DA 11.@A < $2,C00 1> A 2.A > $


18/18

Pic# )lternative 2

calculation of ror

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