Time Value of Money Factors
- Single payment compound amount (F/P): F = P * (1+i)^n
- Single payment present worth (P/F): P = F * (1+i)^(-n)
- Uniform series sinking fund (A/F): A = F * i / [(1+i)^n - 1]
- Uniform series compound amount (F/A): F = A * [(1+i)^n - 1] / i
- Uniform series capital recovery (A/P): A = P * i*(1+i)^n / [(1+i)^n - 1]
- Uniform series present worth (P/A): P = A * [(1+i)^n - 1] / [i*(1+i)^n]
Gradient Series
- Arithmetic gradient present worth (P/G): P = G * [(1+i)^n - i*n - 1] / [i^2 * (1+i)^n]
- Arithmetic gradient uniform series (A/G): A = G * [1/i - n/((1+i)^n - 1)]
- Geometric gradient: P = A1 * [1 - (1+g)^n * (1+i)^(-n)] / (i-g) when i != g
- Geometric gradient when i = g: P = A1 * n / (1+i)
Project Evaluation Methods
- Net Present Value (NPV): sum of all discounted cash flows; accept if NPV > 0
- Internal Rate of Return (IRR): the i that makes NPV = 0; accept if IRR > MARR
- Annual Worth (AW): convert all cash flows to equivalent annual amount
- Benefit-Cost Ratio (B/C): B/C = PW(benefits) / PW(costs); accept if B/C > 1
- Payback period: time to recover initial investment (does not consider time value of money)
- Discounted payback: time to recover considering time value
Depreciation Methods
- Straight-line: D = (P - S) / n (P = initial cost, S = salvage, n = useful life)
- Book value: BV = P - accumulated depreciation
- Double declining balance (DDB): D_t = (2/n) * BV_(t-1)
- Sum-of-years digits (SYD): D_t = (remaining life / SYD) * (P - S)
- SYD = n*(n+1)/2
- MACRS: modified accelerated cost recovery system (IRS defined percentages per year)
Effective Interest Rates
- Effective annual rate: i_eff = (1 + r/m)^m - 1 (r = nominal, m = compounding periods per year)
- Continuous compounding: i_eff = e^r - 1
- Nominal rate: r = m * [(1 + i_eff)^(1/m) - 1]
Inflation
- Real (inflation-free) interest rate: i_r = (i - f) / (1 + f)
- Where i = market rate and f = inflation rate
- Use actual dollars with market rate or constant dollars with real rate