module Exonio
module Financial
# Calculates the future value of an annuity investment based on
# constant-amount periodic payments and a constant interest rate.
#
# @param rate [Float] The interest rate as decimal (not per cent) per period
# @param nper [Integer] The number of compounding periods
# @param pmt [Float] The number of payments to be made
# @param pv [Float] The present value
# @param end_or_begining [Integer] Whether payments are due at the end (0) or
# beggining (1) of each period
#
# @return [Float]
#
# @example
# Exonio.fv(0.05 / 12, 12 * 10, -100, -100) # ==> 15692.928894335748
#
def fv(rate, nper, pmt, pv, end_or_beginning = 0)
temp = (1 + rate) ** nper
fact = (1 + rate* end_or_beginning) * (temp - 1) / rate
-(pv * temp + pmt * fact)
end
# Calculates the payment on interest for an investment based on
# constant-amount periodic payments and a constant interest rate.
#
# @param rate [Float] The interest rate as decimal (not per cent) per period
# @param per [Integer] The amortization period, in terms of number of periods
# @param nper [Integer] The number of payments to be made
# @param pv [Float] The present value
# @param fv [Float] The future value remaining after the final payment has been made
# @param end_or_begining [Integer] Whether payments are due at the end (0) or
# beggining (1) of each period
#
# @return [Float]
#
# @example
# Exonio.ipmt(0.075 / 12, 8, 12 * 2, 5000) # ==> -22.612926783996798
#
def ipmt(rate, per, nper, pv, fv = 0, end_or_beginning = 0)
pmt = self.pmt(rate, nper, pv, fv, end_or_beginning)
fv = self.fv(rate, (per - 1), pmt, pv, end_or_beginning) * rate
temp = end_or_beginning == 1 ? fv / (1 + rate) : fv
(per == 1 && end_or_beginning == 1) ? 0.0 : temp
end
# Calculates the number of payment periods for an investment based on
# constant-amount periodic payments and a constant interest rate.
#
# @param rate [Float] The interest rate as decimal (not per cent) per period
# @param pmt [Float] The payment amount made each period
# @param pv [Float] The present value of the payments
# @param fv [Float] The future value remaining after the final payment has been made
# @param end_or_begining [Integer] Whether payments are due at the end (0) or
# beggining (1) of each period
#
# @return [Float]
#
# @example
# Exonio.nper(0.07 / 12, -150, 8000) # ==> 64.07334877066185
#
def nper(rate, pmt, pv, fv = 0, end_or_beginning = 0)
return (-pv - fv) / pmt if rate.zero?
z = pmt * (1 + rate * end_or_beginning) / rate
temp = Math.log((-fv + z) / (pv + z))
temp / Math.log(1 + rate)
end
# Calculates the periodic payment for an annuity investment based on
# constant-amount periodic payments and a constant interest rate.
#
# @param rate [Float] The interest rate as decimal (not per cent) per period
# @param nper [Integer] The number of payments to be made (number of periods)
# @param pv [Float] The present value of the annuity
# @param fv [Float] The future value remaining after the final payment has been made
# @param end_or_begining [Integer] Whether payments are due at the end (0) or
# beggining (1) of each period
#
# @return [Float]
#
# @example
# Exonio.pmt(0.075/12, 12*15, 200_000) # ==> -1854.0247200054619
#
def pmt(rate, nper, pv, fv = 0, end_or_beginning = 0)
temp = (1 + rate) ** nper
fact = (1 + rate * end_or_beginning) * (temp - 1) / rate
-(fv + pv * temp) / fact
end
# Calculates the present value of an annuity investment based on
# constant-amount periodic payments and a constant interest rate.
#
# @param rate [Float] The interest rate as decimal (not per cent) per period
# @param nper [Integer] The number of payments to be made (number of periods)
# @param pmt [Float] The amount per period to be paid
# @param fv [Float] The future value remaining after the final payment has been made
# @param end_or_begining [Integer] Whether payments are due at the end (0) or
# beggining (1) of each period
#
# @return [Float]
#
# @example
# Exonio.pv(0.05/12, 12*10, -100, 20_000) # ==> -2715.0857731569663
#
def pv(rate, nper, pmt, fv = 0, end_or_beginning = 0)
temp = (1 + rate) ** nper
fact = (1 + rate * end_or_beginning) * (temp - 1) / rate
-(fv + pmt * fact) / temp
end
# Calculates the interest rate of an annuity investment based on
# constant-amount periodic payments and the assumption of a constant interest rate.
#
# @param nper [Integer] The number of payments to be made (number of periods)
# @param pmt [Float] The amount per period to be paid
# @param pv [Float] The present value
# @param fv [Float] The future value remaining after the final payment has been made
# @param end_or_begining [Integer] Whether payments are due at the end (0) or
# beggining (1) of each period
# @param rate_guess [Float] An estimate for what the interest rate will be
#
# @return [Float]
#
# @example
# Exonio.rate(12, 363.78, -3056.00) # ==> 0.05963422268883278
#
def rate(nper, pmt, pv, fv = 0, end_or_beginning = 0, rate_guess = 0.10)
guess = rate_guess
tolerancy = 1e-6
close = false
begin
temp = newton_iter(guess, nper, pmt, pv, fv, end_or_beginning)
next_guess = (guess - temp).round(20)
diff = (next_guess - guess).abs
close = diff < tolerancy
guess = next_guess
end while !close
next_guess
end
# Calculates the net present value of an investment based on a
# series of periodic cash flows and a discount rate.
#
# @param discount [Float] The discount rate of the investment over one period
# @param cashflows [Array] The first future cash flow + additional future cash flows
#
# @return [Float]
#
# @example
# Exonio.npv(0.281, [-100, 39, 59, 55, 20]) # ==> -0.00661872883563408
#
def npv(discount, cashflows)
total = 0
cashflows.each_with_index do |cashflow, index|
total += (cashflow.to_f / (1 + discount.to_f) ** (index + 1))
end
total
end
# Calculates the internal rate of return on an investment based on a
# series of periodic cash flows.
#
# @param cashflows [Array] An array containing the income or payments
# associated with the investment
#
# @return [Float]
#
# @example
# Exonio.irr([-100, 39, 59, 55, 20]) # ==> 0.28094842116...
#
def irr(values)
func = Helpers::IrrHelper.new(values)
guess = [ func.eps ]
nlsolve( func, guess)
guess[0]
end
private
# This method was borrowed from the NumPy rate formula
# which was generated by Sage
#
def newton_iter(r, n, p, x, y, w)
t1 = (r+1)**n
t2 = (r+1)**(n-1)
((y + t1*x + p*(t1 - 1)*(r*w + 1)/r) / (n*t2*x - p*(t1 - 1)*(r*w + 1)/(r**2) + n*p*t2*(r*w + 1)/r + p*(t1 - 1)*w/r))
end
end
end