Engineering Decision Analysis

Engineering Economics

What dose the symbol “P” mean?

Present value (money at time 0)

What dose the symbol “F” mean?

Future value (money at time n)

What dose the symbol “A” mean?

Uniform annual amount (same payment each period)

What dose the symbol “G” mean?

Arithmetic gradient (increase by constant amount each year)

What dose the symbol “g” mean?

Geometric gradient (increase by % each year

What dose the symbol “i” mean?

interest rate per period

What dose the symbol “n” mean?

number of periods

How do you determine “n”

number of periods (n = years x m)

How do you determine “i”

interest rate per period (i = r/m)

How do you determine “r”

nominal annual interest rate

How do you determine “m”

compounding periods per year

How do you calculate the coupon payment of a bond?

A = (Coupon Rate × Face Value) / payments per year

What equation determines the price of a bond?

P = A(P/A,i,n) + F(P/F,i,n)

(PV of coupons + PV of face value)

Meaning: initial cost + annual flows + salvage value

General present worth equation

PW = Benefits − Costs

PW = -P + A(P/A,i,n) + F(P/F,i,n)

When do you include the P/F term in PW calculations?

Use P/F when there is a single future amount.

Ex: PW = -P + A(P/A,i,n) + F(P/F,i,n)

Equation for loan payment

A = P(A/P,i,n)

Meaning: payment required to repay loan

Remaining balance after k payments

Bk = A(P/A,i,n-k)

Where:

Bk = balance after k payments

n = total payments

k = payments made

How do you calculate payoff amount after a payment?

1) Bk = A(P/A,i,n-k)

2) Payoff = Bk(F/P,i,t)

Where: t = number of periods between the balance time and the payoff time

What equation is used for costs increasing by constant amount each year?

Arithmetic Gradient: PW = A(P/A,i,n) + G(P/G,i,n)

What equation is used when cash flows grow by a percent each year?

Geometric Gradient: PW = A1[(1 - ((1+g)/(1+i))^n)/(i-g)]

How much must be invested today to reach a future value?

P = F(P/F,i,n)

How do you choose between two alternatives?

Compute: PW_A & PW_B

Decision Rule: Choose highest PW

How do you find the crossover rate between two alternatives (range of MARR)

1) PW_A = PW_B

2) Solve for i