Investment Calculations Flashcards
Simple interest formula?
FV = Original principal amount x [1 + (rxn)]
Compound interest formula?
FV = PV (1 + r) ^n
Discounting formula?
PV = FV / (1 + r) ^n
Internal rate of return, key points and definition?
(IRR)
- Natural extension of discounting and compounding is that each invstment has a NPV (net present value).
- NPV is the point at which an investment becomes favourable and the investment becomes positive.
- This break even point is the IRR
Exact definitio of IRR =
IRR is the interest rate that makes the net present value of an investment zero when applying the interest rate over a set period. This rate of return is the break-even point.
Series of payments: accumulation and annuities - calculating the FV of an accumulated sum of money accrued from a series of paymens:
FV = PV [(1 + r) ^n -1) / r]
Steps:
- (1 + r) ^n-1
- Ans / r
- Ans x PV
Annuity formula?
A = P [1 - (1+r) ^-n] / r
For a given level of interest rates, the PV of the annuiy is calculated by discounting the annual cashflows back to today’s value.
A = present value of whole annuity
P = is the regular annuity payment, paid at the end of the year
r = is the interest rate (normally annual) over the lifetime of the annuity
n = number of periods (normally years) annuity will run for
Mortgage payments - key points and formula?
- Effectively a reverse annuity
25 year repayment mortgage of £100,000 at 7.5% interest p.a.
R = 7.5%
N = 25 years
A = £100,000
Steps:
- 1 - ( + 0.075) ^-25 = 0.836020939
- Ans / 0.075 = 11.14694586
- P x 11.14694586 = £100,000
£100,000 / 11.14694586 = £8,971.07
Annual Equivalent Rate or Annual Percentage Rates - key points and formula?
APR = AER = EAR
- APR normally used for borrowing, AER for returns
- Equal to a periodic rate converted into annual terms on a compounded basis
Formula =
(1 + r/n) ^n - 1
APR calculated from a monthly rate of interest can be worked as:
APR = (1 + monthly rate) ^12 - 1
APR monthly rate formula?
If the APR is already known, i.e, for a credit card deal, the monthly rate would be calulated using the following formula:
Monthly rate = (1 + APR) ^1/12 - 1
Annualised returns - key points and formula:
- Anualised returns involves taking a return period which isn’t in years and turning returns into annualised figures
Formula =
An = [(A/P) ^1/n - 1] x 100
Where:
An = % annualised return
A = Accumulation (the amount accumulated over time)
P = Principal (original amount invested)
n = number of investment periods = years (this is the whole period in years or periods of 12 months).
Compounded annual return (CAR): annualised return - key points and formula?
- involves establishing a total return over a number of periods
- Work out each annualised return and multiply
(Year 1 x Year 2 x Year 3 - 1) = total return over a 3 year period
Real vs nominal rate of return - formula:
Rreal = Rnominal - Rinflation
Or
(1 + nominal) / (1 + inflation) - 1 = real rate of return
Holding period return formula?
R = (D + V1 - V0) / V0
D = additional returns generated (income/ dividends paid out)
V0 = starting price
V1 = end price
Money weighted return formula?
MWR = (D + V1 - V0 - C) / V0 + (C x n/12)
C = net cash inflow into the portfolio If there is a net cash outflow, C will be negarive.
n = the number of months remaining in th eyear at the time the addition / withdrawal took place.
Money weighted return is influenced by cash flows into and out of the fund/ portfolio which is outside control of fund manager.
Full MWR return formula?
D + V1 - V0 - C / V0 + (+C x n/12) + (-C x n/12)
Where C is an inflow it is +
Where C is an outflow it is -
Top line growth is calculated by:
- Takinh value at end of holding period + dividends
- Deducting original investment amount
- Deducting net cash inflow into the investment
