a brief summary of financial equations

see also:

• a brief summary of mathematical principles and tools
• History of Mathematics
• mensuration - how to measure area, volume, etc of various shapes
• Algebra
• Calculus
• Circular functions
• Coordinate geometry, parabolae, etc
• Logarithmic, exponential and hyperbolic functions
• Probability theory

• interest rate per year = (redemption value - principal)/principal X (365/no.days)

• compound value = principal (1 + int.rate)^^no.periods
• interest rate = exp(ln(compound value/principal)/no.periods) - 1 (????)

• effective interest rate = (1+(Nominal Rate/no.compounding periods/yr))^^{(no.compounding periods/yr -1)}
• ie. if 4 compounding periods per year and effective rate is 5.3543%/yr then nominal rate s 5.25%

• Future Value = present value (1 + int.rate)^^no.periods
• Present Value = future value (1 + int.rate)^^{-(no.periods)}
  • =amount needed to invest now @ int.rate to give a FV @ n periods.

• Annuities: = equal periodic payments over equal periods of time
  • ordinary: = payments at end of each period
  • annuity due: = payments at beginning of each period
  • deferred anuity: = payments are delayed
  • perpetuity: = anuity continues forever (ie. n → infinity)
  • future value = [ payment (1 + int.rate)^^no.periods - 1] / int.rate
    • eg. $1000 invested @ end yr for 5yrs @ 10%pa ⇒ FV = $6105
  • present values (PV):
    • ordinary annuity = [ payment (1-(1+int.rate)^^{-(no.periods)})] / int.rate
    • annuity due = PV (ord.annuity) * (1+int.rate)
    • perpetuity = payment / int.rate (as n → infinity )

• Payback period:
  • if equal annuity: = init.investment /annual cash flow
  • if mixed then work out manually
• Average Rate Of Return: = av. after tax profits / av. investment
  • = % return on average investment
  • rarely used as no account of time value of money!
• Discounted Cash Flow Methods:
  • recognises time value of money;
  • appropriate discount factor is max. rate of return required (RROR) by firm to invest in such a project.
  • a) NPV = (PV cash flows discounted at RROR) - initial investment (II)
    • if < 0, then reject project!
    • = sum (cash flowi * (1+k)^-i - II, k = RROR, i = cash flow period;
  • b) IRR = internal rate of return
    • = discount rate that equates PV cash flows with initial investment
    • ie. solves for k by making II = PVcash flows;
    • if IRR < RROR then project is rejected.
  • c) PI = profitability index = benefit-cost ratio
    • = PV cash inflows / initial investment
• Modified Internal Rate Of Return (MIRR):
  • = int. rate that relates FV with initial outlay over the period
  • = (PV/FV)^n - 1 (??)

• Measures of risk (the greater value the greater risk, ? in order of importance):
  • 1) range
  • 2) variance
  • 3) st. dev.
  • 4) coeff. of variation
• Eg.
  • Forecast Pr(forecast) Return (R) Mean Average Weighted Value       Pr * R (R-mean av.)2 * Pr Pessimistic 0.25 13% 3.25 1 Most likely 0.50 15% 7.50 0 Optimistic 0.25 17% 4.25 1 sum 1.00   15 2 = variance         1.41% = st.dev.