**Finance
Equations**

- see also:

**Simple Interest:**- interest rate per year = (redemption value - principal)/principal X (365/no.days)

**Compound Interest:**- compound value =
principal (1 + int.rate)^
^{no.periods} - interest rate = exp(ln(compound value/principal)/no.periods) - 1 (????)

- compound value =
principal (1 + int.rate)^
**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%

- effective interest
rate = (1+(Nominal Rate/no.compounding
periods/yr))^
**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 )

- ordinary
annuity = [ payment (1-(1+int.rate)^

**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 (??)

**Risk Assessment:**

- 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.**