Finance Equations

•

• 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 (????)
• 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%
• 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 (??)

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.