ENGINEERING ECONOMY (SEMI- FINAL COVERAGE)

Deferred Annuity, Annuity Due, Perpetuity, Uniform Gradient Cash Flow, Straight Line Depreciation, Sinking Fund Method, Declining Balance Method, Sum of the Years Digit Method (SOYD), Modified Accelerated Cost Recovery System (MACRS)

Payments start at any period after the first period

Deferred Annuity

Payment start at the beginning of each period starting from n=0

Annuity Due

Is an annuity that continues indefinitely

Perpetuity

G in the uniform gradient cash flow stands for ______

Gradient

It is the decrease in value of a property due to the passage of time

Depreciation

Annual Depreciation for a straight line depreciation

Annual Depreciation= (FC-SV)/n

Total depreciation after m years

D_m = mD

Book value after m years in straight line depreciation

BV= FC - D_m

Depreciation Rate

DR= D/FC

Salvage Rate

SR= SV/FC

n in the straight line depreciation stands for _____

life of the property or equipment

Annual Depreciation for the sinking fund method

D= (FC-SV)i / (1+i)ⁿ-1

Total depreciation of a sinking fund method after m years

D_m= D ((1+i)^m - 1 / (i))

Book value in a sinking fund method

BV= FC - D_m

Sunk cost of sinking fund method

Sunk Cost= BV - Actual Resale Value

Sunk cost of straight line method

Sunk Cost= BV - Actual Resale Value

constant ratio in declining balance method

k= 1 - (SV/FC)^1/n

Annual Depreciation for any year in declining balance method

D_n= k(FC)(1 - k)^n-1

Total Depreciation after n years (e.g. 5 years) in declining balance method

D_T5= D₁ + D₂ + D₃ + D₄ + D₅

Book value in declining balance method (e.g. 5 years)

BV= FC - D_T5

Book value in declining balance method after m years

BV_m= FC (1 - k)^m

What does SOYD stands for

Sum of the Years Digit Method

Formula for SOYD

SOYD= (1+n/2) n

Given n= 8 years, what is the formula for the depreciation for the first 5 years (SOYD)

D₁= (FC - SV) (8/36)

D₂= (FC - SV) (7/36)

D₃= (FC - SV) (6/36)

D₄= (FC - SV) (5/36)

D₅= (FC - SV) (4/36)

Total Depreciation after years (e.g. 5 years) (SOYD)

D_T5= D₁ + D₂ + D₃ + D₄ + D<sub>5

SHORTCUT METHOD:</sub>

D_T5= (FC - SV)(8+7+6+5+4/36)

Book Value after years (e.g. 5 years) (SOYD)

BV₅= FC - D_T5

What does MACRS means

Modified Accelerated Cost Recovery System

Depreciation charge for the first 5 years. (MACRS)

D₁= FC/n

D₂= 2/n (FC - D₁)

D₃= 2/n (FC - (D₁+ D₂))

D₄= 2/n (FC - (D₁+ D₂+ D₃))

D₅= 2/n (FC - (D₁+ D₂ + D₃ + D₄))

Book Value for the first 5 years. (MACRS)

BV₅= FC - (D₁+ D₂ + D₃ + D₄ + D₅)

Formula for the Present Worth in Deferred Annuity

P₁= R( (1+i)^{number of R}-1 / (1+i)^{number of R} i )

P= P₁/ (1+i)^{number of years from 0 to the day before P₁}

NOTE: P₁ is the year before the first R