Engineering Economics Formula Sheet

1. ©Haris H.
Engineering Economics Formula Sheet
The future amount of present amount 𝐹 = 𝑃 (1 + 𝑖) 𝑛
The present value of a future amount: 𝑃 = 𝐹 (1 + 𝑖)−𝑛
= 𝐹
1
(1+𝑖) 𝑛
The factor (1+i)-n
is sometimes called the present worth factor, 𝑃𝑊𝐹(𝑖, 𝑛). Thus, P = F(1+i)-n
= F PWF(i,n)
Future Value of a Series of Payments
The future value, F, of a series of equal annuities A, that accrue interest at a rate, I, over n periods is:
𝐹𝑉𝑛 =
 
i
1i)(1A n

Present Value of a Series of Annuities
𝑃𝑛 = present value of n payments of amount A = present amount that is equal to a series of payments, A, for n years
𝑃𝑉𝑛 = 




  
i
i)(11
A
n
=
(1+𝑖)
𝑛
−1
𝑖(1+𝑖)
𝑛
Uniform Gradient Series Annual Equivalent Amount
Annual equivalent amount of a series with an amount of A1 at the end of 1st year & with an equal increment (G)
𝐴 = 𝐴1 + 𝐺
(1+𝑖) 𝑛−𝑖𝑛−1
𝑖(1+𝑖) 𝑛−𝑖
Revenue-Dominated cash flow analysis
P = Initial investment Rn = Net revenue at the end of nth year S = Salvage value at the end of nth year
𝑃𝑊 = −𝑃 + 𝑅1
1
(1 + 𝑖)1
+ ⋯ + 𝑅 𝑛
1
(1 + 𝑖) 𝑛 + 𝑆
1
(1 + 𝑖) 𝑛
Future Worth Criterion Cost-Dominated cash flow analysis
𝐹𝑊 = 𝑃(1 + 𝑖) 𝑛 + 𝐶1(1 + 𝑖) 𝑛−1 + 𝐶1(1 + 𝑖) 𝑛−2 + ⋯ + 𝐶𝑗(1 + 𝑖) 𝑛−𝑗 + 𝐶 𝑛 − 𝑆
Rate of Return (IRR): I𝑅𝑅 = 𝐼𝐿 +
𝑃𝑊 𝐿
𝑃𝑊 𝐿−𝑃𝑊 𝐻
(IH − IL)
If IRR > MARR, accept the project. If IRR = MARR, remain indifferent. If IRR < MARR, reject the project.
Depreciation
Straight Line Depreciation Method:
𝐷𝑡 =
𝑃−𝑆
𝑛
𝐵𝑡 = 𝑃 − 𝑡 [
𝑃−𝑆
𝑛
] = 𝑃 − 𝑡𝐷𝑡
Declining Balance Depreciation Method
𝐷𝑡 = 𝐾 × 𝐵𝑡−1 = 𝐾 (1 − 𝐾) 𝑡−1
× 𝑃 = 𝐾 ×
𝐵𝑡
1−𝐾
𝐵𝑡 = (1 − 𝐾) × 𝐵𝑡−1 = (1 − 𝐾) 𝑡
× 𝑃
Sum-of-years' digits method
𝐷𝑡 =
𝑛−𝑡+1
𝑛(𝑛+1)
2
(𝑃 − 𝑆) 𝐵𝑡 = ( 𝑃 − 𝑆)
(𝑛−𝑡)
𝑛
(𝑛−𝑡+1)
(𝑛+1)
+ 𝑆
Sinking Fund method of depreciation
𝐷𝑡 = ( 𝑃 − 𝑆) [
𝑖
(1+𝑖) 𝑛−1
] (1 + 𝑖) 𝑡−1
𝐵𝑡 = 𝑃 − ( 𝑃 − 𝑆) [
𝑖
(1+𝑖) 𝑛−1
]
(1+𝑖) 𝑡−1
𝑖
= 𝑃 − 𝐷𝑡
(1+𝑖) 𝑡−1
𝑖(1+𝑖) 𝑡−1
Conventional Benefit / Cost (B/C) Ratio with Present Worth
𝐵
𝐶
𝑅𝑎𝑡𝑖𝑜 =
𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠 − 𝐷𝑖𝑠𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠
𝐶𝑜𝑠𝑡
=
𝐵 − 𝐷
𝐶
Make or Buy Decisions
Formula for Purchase model (EOQ) and TC for each model are given as:
𝐸𝑂𝑄 = √
2(𝐴𝑛𝑛𝑢𝑎𝑙 𝑈𝑠𝑎𝑔𝑒 𝑖𝑛 𝑢𝑛𝑖𝑡𝑠)(𝑂𝑟𝑑𝑒𝑟 𝐶𝑜𝑠𝑡)
(𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝐶𝑜𝑠𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡)
𝑄1 = √
2𝐶0 𝐷
𝐶 𝑐
𝑇𝐶 = 𝐷𝑃 +
𝐷𝐶0
𝑄1
+
𝑄1 𝐶 𝑐
2
Manufacturing model
𝑄2 = √
2𝐶0 𝐷
𝐶 𝑐(1−𝑟/𝑘)
𝑇𝐶 = 𝐷𝑃 +
𝐷𝐶0
𝑄2
+
𝑄2 𝐶 𝑐(𝑘−𝑟)
2𝑘
Break-even point
𝐵𝐸𝑃 =
𝐹𝐶
𝑆𝑒𝑙𝑙𝑖𝑛𝑔 𝑐𝑜𝑠𝑡/𝑢𝑛𝑖𝑡 − 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐶𝑜𝑠𝑡/𝑈𝑛𝑖𝑡
= 𝑋 =
𝐹𝐶
𝑃 − 𝑉
0 1 2 3 n
A