6.10.3 Probabilistic Models
A probabilistic model is decision making under risk and involves the use of statistics and probability. The most popular is Monte Carlo sampling and simulation analysis.
The simulation approach to engineering economic analysis is summarized as follows (Blank and Tarquin, 2002):
1. Formulate alternative(s) and select the measure of worth to be used.
2. Select the parameters in each alternative to be treated as random variables and estimate values for other definite parameters.
3. Determine whether each variable is discrete or continuous and describe a probability distribution for each variable in each alternative.
4. Develop random samples.
5. Compute n values of the selected measure of worth from the relation(s) in step 1 using the defi- nite estimates made and n sample values for the varying parameters.
6. Construct the probability distribution of the measure computed in step 5 using between 10 and 20 cells of data and calculate measures such as the mean, the root-mean-square deviation, and other relevant probabilities.
7. Draw conclusions about each alternative and decide which is to be selected.
The results of this approach can be compared with decision-making when parameter estimates are made with certainty.
FV (Future Value)
● FV (rate, nper, pmt, pv, type).
● Calculates the FW for a periodic payment at a specific interest rate:
rate: Interest rate per compounding period.
nper: Number of compounding periods.
pmt: Constant payment amount.
pv: The PV amount. The function will assume that pv is zero if omitted.
type: (optional) Either 0 or 1. A 0 represents end-of-the-period payment, and 1 represents beginning-of-the-period payment. If omitted, 0 is assumed.
IPMT (Interest Payment)
● IPMT (rate, per, nper, pv, fv, type).
● Calculates the interest accrued for a given period on the basis of constant periodic payment and interest rate:
rate: Interest rate per compounding period.
per: Period for which interest is to be calculated.
nper: Number of compounding periods.
pv: The PV amount. The function will assume that pv is zero if omitted.
fv: The FV (a cash balance after the last payment is made). If omitted, the function will assume it to be 0.
type: (optional) Either 0 or 1. A 0 represents end-of-the-period payment, and 1 represents beginning-of-the-period payment. If omitted, 0 is assumed.
IRR (Internal Rate of Return)
● IRR (values, guess).
● Calculates the IRR between 100% and infinity for a series of cash flows at regular periods:
values: A set of numbers in a spreadsheet row or column for which the rate of return will be calculated. There must be at least one positive (cash inflow) and one negative (cash outflow) number.
guess: (optional) Guess a rate of return to reduce the number of iterations. Change the guess if #NUM! error appears.
MIRR (Modified Internal Rate of Return)
● MIRR (values, finance rate, reinvest rate).
● Calculates the MIRR for a series of cash flows and reinvestment of income and interest at a stated rate:
values: A set of numbers in a spreadsheet row or column for which the ROR will be calculated.
There must be at least one positive (cash inflow) and one negative (cash outflow) number.
finance rate: Interest rate of money used in the cash flows.
reinvest rate: Interest rate for reinvestment on positive cash flows.
NPER (Number of Periods)
● NPER (rate, pmt, pv, fv, type).
● Calculates the number of periods for the PW of an investment to equal the FV specified:
rate: Interest rate per compounding period.
pmt: Amount paid during each compounding period.
pv: Present values.
fv: (optional) The future value (a cash balance after the last payment is made). If omitted, the function will assume it to be 0.
type: (optional) Either 0 or 1. A 0 represents end-of-the-period payment, and 1 represents beginning-of-the-period payment. If omitted, 0 is assumed.
NPV (Net Present Value)
● NPV (rate, series).
● Calculates the net present worth (NPW) of a series of future cash flows at a particular interest rate:
rate: Interest rate per compounding period.
series: Series of inflow and outflow setup in a range of cells in the spreadsheet.
PMT (Payments)
● PMT (rate, nper, pv, fv, type).
● Calculates equivalent periodic amounts based on PW or FW at a stated interest rate:
rate: Interest rate per compounding period.
nper: Number of compounding periods.
pv: The PV amount. The function will assume that pv is 0 if omitted.
fv: The future value (a cash balance after the last payment is made). If omitted, the function will assume it to be 0.
type: (optional) Either 0 or 1. A 0 represents end-of-the-period payment, and 1 represents beginning-of-the-period payment. If omitted, 0 is assumed.
PPMT (Principal Payment)
● PPMT (rate, per, nper, pv, fv, type).
● Calculates the PMT on the principal based on uniform payments at a stated interest rate:
rate: Interest rate per compounding period.
per: Period for which interest is to be calculated.
nper: Number of compounding periods.
pv: The PV amount. The function will assume that pv is 0 if omitted.
fv: The FV (a cash balance after the last payment is made). If omitted, the function will assume it to be 0.
type: (optional) Either 0 or 1. A 0 represents end-of-the-period payment, and 1 represents beginning-of-the-period payment. If omitted, 0 is assumed.
PV (Present Value)
● PV (rate, nper, pmt, fv, type).
● Calculates the PW of a future series of equal cash flows and a single lump sum in the last period at a stated interest rate:
rate: Interest rate per compounding period.
nper: Number of compounding periods.
pmt: Cash flow at regular intervals. Inflows are positive and outflows are negative.
fv: The FV (a cash balance after the last payment is made). If omitted, the function will assume it to be 0.
type: (optional) Either 0 or 1. A 0 represents end-of-the-period payment, and 1 represents beginning-of-the-period payment. If omitted, 0 is assumed.
RATE (Interest Rate)
● RATE (nper, pmt, pv, fv, type, guess).
● Calculates the interest rate per compounding period for a series of payments or incomes:
nper: Number of compounding periods.
pmt: Cash flow at regular intervals. Inflows are positive and outflows are negative.
pv: The PV amount. The function will assume that pv is 0 if omitted.
fv: The FV (a cash balance after the last payment is made). If omitted, the function will assume it to be 0.
type: (optional) Either 0 or 1. A 0 represents end-of-the-period payment, and 1 represents beginning-of-the-period payment. If omitted, 0 is assumed.
guess: (optional) Guess a ROR to reduce the number of iterations. Change the guess is #NUM!
error appears.
SLN (Straight-Line Depreciation)
● SLN (cost, salvage, life).
● Calculates the straight-line depreciation of an asset for a given year:
cost: First cost or basis of the asset.
salvage: Salvage value.
life: Recovery period.
SYD (Sum-Of-Year-Digits Depreciation)
● SYD (cost, salvage, life, period).
● Calculates the SOYD depreciation of an asset for a given year:
cost: First cost or basis of the asset.
salvage: Salvage value.
life: Recovery period.
period: The year for which the depreciation is to be calculated.
VDB (Variable Declining Balance)
● VDB (cost, salvage, life, start-period, end-period, factor, no-switch).
● Calculates the depreciation schedule using the DB method with a switch to SLN in the year in which straight line has a larger depreciation amount. This function can be used for MACRS depre- ciation schedule computations.
cost: First cost or basis of the asset.
salvage: Salvage value.
life: Recovery period.
start-period: First period for depreciation to be calculated.
end-period: Last period for depreciation to be calculated.
factor: (optional) Enter 1.5 for 150% DB and so on. The function will use 2.0 for 200% DB if omitted.
no-switch: (optional) If omitted or entered as FALSE, the function will switch from DB or DDB to SLN depreciation when the latter is greater than DB depreciation. If entered as TRUE, the function will not switch to SLN depreciation at any time during the depreciation life.