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OGUNKA UCHENNA EMMANUEL

100404048MECHANICAL ENGINEERING

GEG 501- ENGINEERING

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With appropriate mathematical equations define all the following concepts

1) Effective Rate (Effective Yield): This is the interest rate of the interest gained over n

periods, ie an interest that is compounded more frequentl! in a !ear

i=

(1+

r

M

)

M

1

Where " # effective interest rate

$ # %um&er of su&periods per !ear

R # nominal interest rate

') traight ine *epreciation: The depreciation per !ear is the cost minus the salvage

value divided &! the !ears of life The straight line method of depreciation interprets a

fi+ed asset as an asset that offers its services in a uniform fashion The asset provides

an equal amount of service in each !ear of its useful life The straightline method

charges, as an e+pense, an equal fraction of the net cost of the asset each !ear, as

e+pressed &! the relation:

Where *- # depreciation charge during !ear n

. # .ost of the asset, including installation e+penses

n # alvage value at the end of the asset/s useful life

% # num&er of useful !ears

3) Present Value of an Ordinary Annuity: This is the va!e "# a

st$ea% "# e&'e(te "$ '$"%ise #!t!$e 'a*%e+ts that have ,ee+

is("!+te t" a si+e e.!ivae+t va!e t"a*/

The %athe%ati(a $e'$ese+tati"+ "# this is

2"a A

[(1( 1(1+i )n ))

i

]he$e 2"a $ese+t va!e "# a+ "$i+a$* a++!it* A A%"!+t "# ea(h 'a*%e+t

I is("!+t $ate 'e$ 'e$i"

N +!%,e$ "# 'e$i"s

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0) um of the Years*igits *epreciation: n accelerated method for calculating an

asset2s depreciation This method ta3es the asset2s e+pected life and adds together the

digits for each !ear

um of the !ears2 digits method of depreciation is one of the accelerated depreciation

techniques which are &ased on the assumption that assets are generall! more

productive when the! are new and their productivit! decreases as the! &ecome old

The formula to calculate depreciation under Y* method is:

Y* *epreciation #

*eprecia&le 4ase 5Remaining 6seful ife

um of the Years2 *igits

"n the a&ove formula, deprecia&le &ase is the difference &etween cost and salvage

value of the asset and sum of the !ears2 digits is the sum of the series:

1, ', 7, n8 where n is the useful life of the asset in !earsum of the !ears2 digits can &e calculated more convenientl! using the following

formula:

um of the Years2 *igits #n(n91)

'

um of the !ears2 digits method can also &e applied on monthl! &asis, in which case

the a&ove formula to calculate the sum of the !ears2 digits &ecomes much useful

5) $ese+t 2a!e "# a Si+e A%"!+t is a+ a%"!+t t"a* that is

e.!ivae+t t" a #!t!$e 'a*%e+t6 "$ se$ies "# 'a*%e+ts6 that has

,ee+ is("!+te ,* a+ a''$"'$iate i+te$est $ate/

Mathe%ati(a $e'$ese+tati"+ "# this is

PV=FV[ 1(1+i )n ]he$e 2 $ese+t 2a!e

72 7!t!$e 2a!e

i I+te$est Rate 'e$ e$i"

+ N!%,e$ "# C"%'"!+i+ e$i"s

) e$'et!ities a+ Ca'itai9e C"st e$t!it* is a+ a++!it* that has +"

e+6 "$ a st$ea% "# (ash 'a*%e+ts that ("+ti+!es #"$eve$/ It isa+ a++!it* i+ :hi(h the 'e$i"i( 'a*%e+ts ,ei+ "+ a ;&e ate a+

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("+ti+!e i+e;+ite*/ It is s"%eti%es $e#e$$e t" as a 'e$'et!a

a++!it*/ 7i&e ("!'"+ 'a*%e+ts "+ 'e$%a+e+t* i+veste

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, where

lternativel!, E. can &e o&tained &! multipl!ing the %; of the pro-ect &! the ?loan

repa!ment factor?

The annual cost of owning an asset over its entire life Equivalent annual cost is often used &!

firms for capital &udgeting decisions Eqivalent annual cost is calculated as:

@) .apitali

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i # effective interest rate with inflation accounted for (real interest rate)

f # inflation rate for the item under consideration

1C) in3ing Dund Dactor: This is the process corresponding to the

inverse of series compounding is referred to as a sinking

fund; ie, what si

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The discounted cash flow formula is derived from the future valueformula for

calculating the time value of mone! and compounding returns

Thus the discounted present value (for one cash flow in one future period) is

e+pressed as:

where

DPVis the discounted present value of the future cash flow (FV),

orFVad-usted for the dela! in receipt8

FVis the nominal value of a cash flow amount in a future period8

ris the interest rate or discount rate, which reflects the cost of t!ing up

capital and ma! also allow for the ris3 that the pa!ment ma! not &e received

in full8G0H

nis the time in !ears &efore the future cash flow occurs

Where multiple cash flows in multiple time periods are discounted, it is necessar!

to sum them as follows:

10) %et resent ;alue: The net difference of the present time equivalent value of all thecosts and &enefits incurred during the !ears of the s!stem

%; # ; (4enefits) I ; (.osts)

1J) *iscounted 4rea3Even eriod:

"n the &rea3even point (4E) in economics, &usiness, and specificall! cost

accounting, is the point at which total cost and total revenue are equal: there is no net

loss or gain, and one has ?&ro3en even? profit or a loss has not &een made,

although opportunit! costs have &een ?paid,? and capital has received the ris3

ad-usted, e+pected return "n short, all costs that needs to &e paid are paid &! the firm&ut the profit is equal to C "n the linear .ost;olumerofit nal!sis model (where

http://en.wikipedia.org/wiki/Future_valuehttp://en.wikipedia.org/wiki/Discounted_cash_flow#cite_note-4http://en.wikipedia.org/wiki/Future_valuehttp://en.wikipedia.org/wiki/Discounted_cash_flow#cite_note-4

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marginal costs and marginal revenues are constant, among other assumptions),

the &rea3even point (4E) (in terms of 6nit ales (K)) can &e directl! computed in

terms of Total Revenue (TR) and Total .osts (T.) as:

where:

TD. is TotalDi+ed .osts,

is 6nit ale rice, and

; is 6nit ;aria&le .ost

The 4rea3 Even oint can alternativel! &e computed as the point where .ontri&ution

equals Di+ed .osts The quantit!, , is of interest in its own right, and is called

the 6nit .ontri&ution $argin(.): it is the marginal profit per unit, or alternativel! the

portion of each sale that contri&utes to Di+ed .osts Thus the &rea3even point can &emore simpl! computed as the point where Total .ontri&ution # Total Di+ed .ost:

To calculate the &rea3even point in terms of revenue (a3a currenc! units, a3a

sales proceeds) instead of 6nit ales (K), the a&ove calculation can &e multiplied &!

rice, or, equivalentl!, the .ontri&ution $argin Ratio (6nit .ontri&ution $argin over

rice) can &e calculated:

R#., Where R is revenue generated,

. is cost incurred ie Di+ed costs 9 ;aria&le .osts or L M (rice per unit) # TD. 9L M ;. (rice per unit),

http://en.wikipedia.org/wiki/Fixed_Costshttp://en.wikipedia.org/wiki/Fixed_Costshttp://en.wikipedia.org/wiki/Contribution_marginhttp://en.wikipedia.org/wiki/Fixed_Costshttp://en.wikipedia.org/wiki/Contribution_margin

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L M L M ;. # TD.,

L M ( ;.) # TD., or,

4rea3 Even nal!sis L # TD.=c=s ratio#4rea3 Even