Table of Contents
a brief summary of financial equations
- 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 (????)
Nominal annual interest rate
- 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%
Present and Future values
- 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 )
Capital Investment Assessment Methods:
- 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
- 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.
maths/financial.txt · Last modified: 2021/07/24 11:38 by gary1