Functions for Formulas

abs

The absolute value of a number

avg

The arithmetic mean (average) of the inputs. Can also be used as avgif.

Example: avg(1, 2, 3) = 2avg(if Var[all] % 2 = 0 then Var[all] else none = avg of all even values

first_nonzero_­value

The first value that is not zero or empty

Example: first_nonzero_value­(0,none,4,6) = 4

log

Natural logarithm (base e)

Example: log(e^2) = 2

log10

Common logarithm (base 10)

Example: log10(100) = 2

max

The highest of the given values

Example: max(1, 2, 3) = 3; max([1, 2, 3]) = 3

min

The lowest of the given values

Example: min(1, 2, 3) = 1; min([1, 2, 3]) = 1

mod

The remainder of a division.You can also use mod as "%"

Example: mod(5, 2) = 15 % 2 = 1reccurence every 4 months: if timeStep % 4 = 0 then 1 else 0

reverse

Reverses the order of an array.

Example: reverse([1, 2]) = [2, 1]

round

Rounds the number to the closest integer. Optionally, you can specify the decimal places as the second argument.

Example: round(2.3) = 2, round(2.5) = 3, round(2.26, 1) = 2.3

rounddown

Rounds the number down, toward 0. Optionally, you can specify the decimal places as the second argument.

Example: rounddown(2.8) = 2, rounddown(-2.8) = -2, rounddown(2.88, 1) = 2.8

roundup

Rounds the number up, away from 0. Optionally, you can specify the decimal places as the second argument.

Example: roundup(2.2) = 3, roundup(-2.2) = -3, roundup(2.22, 1) = 2.3

signchange

Timestep on which the first sign change occurs

Example: signchange​(Var[all])

spread

Spreads a value over a time period.

Example: spread(New Customers[0:t], Payments[0:t])

sqrt

Square root of a value

Example: sqrt(4) = 2

sum

The sum of the inputs. Can also be used as sumif or countif.

Example: sum(1, 2, 3) = 6. sum(if Var[all] % 2 = 0 then Var[all] else 0) = sum of all even values

sumproduct

Multiplies two or more arrays together and returns the sum of products.

Example: sumproduct(Var1[all], Var2[all])

exp

Exponential function

Example: exp(2) = e^2

date

The timestep number of a date. Timesteps start with 0.

Example: date(2021,12,24) = 11 in a monthly model that starts in Jan 2021

month_from_­date

Extracts the month of a date or timestep.

Example: month_from_date( date(2021,12,24) ) = 12

year_from_date

Extracts the year of a date or timestep.

Example: year_from_date( date(2021,12,24) ) = 2021

cumipmt

Cumulative interest paid.

Example: cumipmt(rate, periods, value, start, end, type)

finance.AM

Amortization

Example: finance.AM(principal, rate, period, yearOrMonth, payAtBeginning)

finance.CAGR

Compound annual growth rate

Example: finance.CAGR(beginning value, ending value, number of periods)

finance.CI

Compound interest

Example: finance.CI(rate, compoundings per period, principal, number of periods)

finance.DF

Discount factor (returns an array; must index array to obtain values -- to see all values of array, see working example above).

Example: finance.DF(rate, number of periods)[index]

finance.FV

Future value

Example: finance.FV(rate, nper, pmt, pv, type)

finance.IAR

Inflation-adjusted return

Example: finance.IAR(investment return, inflation rate)

finance.irr

Internal rate of return.

Example: finance.IRR(Cashflows[all], [guess])

finance.LR

Leverage ratio

Example: finance.LR(total liabilities, total debts, total income)

finance.NPV

Net present value

Example: finance.NPV(rate, initial investment, cash flows[all])

finance.PI

Profitability index

Example: finance.PI(rate, initial investment, cash flows[all])

finance.PMT

Payment for a loan based on constant payments and a constant interest rate

Example: finance.PMT(fractional interest rate, number of payments, principal)

finance.PP

Payback period

Example: finance.PP(number of periods, cash flows[all])

finance.PV

Present value

Example: finance.PV(rate, nper, pmt, [fv], [type])

finance.R72

Rule of 72

Example: finance.R72(rate)

finance.roi

Return on investment

Example: finance.ROI(Cashflows[all])

finance.WACC

Weighted average cost of capital

Example: finance.WACC(market value of equity, market value of debt, cost of equity, cost of debt, tax rate)

finance.xirr

Internal rate of return for a schedule of cash flows

Example: finance.xirr([-10,11], [0,12], 12) = 10%

fv

Future value

Example: v(rate, nper, pmt, pv, [type])

fvifa

Future value interest factor of an annuity

Example: fvifa(rate, nper)

ipmt

Interest portion of a given loan payment

Example: ipmt(rate, per, nper, pv, [fv], [type])

pmt

Periodic payment for a loan

Example: pmt(rate, nper, pv, [fv], [type])

ppmt

Principal portion of a given loan payment

Example: ppmt(rate, per, nper, pv, [fv], [type])

pv

Present value

Example: pv(rate, nper, pmt, fv, [type])

pvif

Present value interest factor

Example: pvif(rate, nper)

rate

Interest rate per period of an annuity

Example: rate(nper, pmt, pv, [fv], [type], [guess])

beta

Beta distribution

Example: beta(alpha, beta)

binominal

Binomial distribution

Example: binomial(n, p)

cauchy

Cauchy distribution

Example: cauchy(local, scale)

chisq

Chi-squared distribution

Example: chisq(k)

exponential

Exponential distribution

Example: exponential(rate)

gamma

Gamma distribution

Example: gamma(shape, scale)

invgamma

Inverse-gamma distribution

Example: invgamma(shape, scale)

lognormal

Log-normal distribution

Example: lognormal(μ, σ^2)

lognormal_from

Log-normal distribution

Example: finance.LR(total liabilities, total debts, total income)

normal

Net Present Value

Example: finance.NPV(rate, initial investment, cash flows[all])

normal_from

Log-normal distribution

Example: lognormal_from_interval­​ (from, to, confidence_percent)

pareto

poisson

Poisson distribution

Example: poisson(λ)

stdev

The standard deviation of an array

Example: stdev(Var[all])

triangle

Triangle distribution

Example: triangle(from, to, confidence_percent)

uniform

Uniform distribution

Example: uniform(from, to)

variance

The variance of an array

Example: variance(Var[all])

error

Error to assert an invalid state

Example: error()

flat_cohort_​forecast

Forecasts cohort data without the cohort dimension.

Example: flat_cohort_forecast​(oldCohorts[all],​ newCohorts[all], retentionRates[all],​ lastDataDate, t, [additionalChurn])

gaussian​_ramp

Ramps up a value over a time period in the shape of a gaussian bell curve.

Example: gaussian_ramp​(timestep,date(2022,10), 2, 100)

if_error

If the first argument evaluates to an invalid number error, we return the second argument. Otherwise, we return the first argument.

Example: if_error(Y/X, Z) - useful where the denominator X is 0, and so the first argument would result in a divided by 0 (invalid number error)

is_data

Evaluates to 1 if argument is derived from a datasource, and otherwise to 0.

Example: is_data(Variable[all])

is_locked

Evaluates to 1 if argument is a locked dimension item, and otherwise to 0.

Example: is_locked​(dimensionitem)

last_data_​timestep

Returns the last timestep that is derived from a datasource.

Example:last_data_​timestep​(Var[all])

logistic_ramp

Ramps up a value over a time period in an S-shape (logistic function).

Example: logistic_ramp​(timestep, date(2022,1),​ date(2022,10), 1.8, 100, 200)

quadratic_​ramp

Ramps up a value quadratically over a time period.

Example: quadratic_ramp​(timestep,date(2022,1),​ date(2022,10) [startValue],​ [endValue])

ramp

Ramps up a value linearly over a time period.

Example: ramp(timestep, date(2022,1), date(2022,10), 100, 200)

ramp_​normalized

A ramp with the cumulative sum of 1. Useful for distributing a fixed value over a time period.

Example: ramp_normalized​(timestep, date(2022,1),​ date(2022,10)