Investment Calculations Flashcards

1
Q

Simple interest formula?

A

FV = Original principal amount x [1 + (rxn)]

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Compound interest formula?

A

FV = PV (1 + r) ^n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Discounting formula?

A

PV = FV / (1 + r) ^n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Internal rate of return, key points and definition?

(IRR)

A
  • 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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Series of payments: accumulation and annuities - calculating the FV of an accumulated sum of money accrued from a series of paymens:

A

FV = PV [(1 + r) ^n -1) / r]

Steps:

  1. (1 + r) ^n-1
  2. Ans / r
  3. Ans x PV
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Annuity formula?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Mortgage payments - key points and formula?

A
  • 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. 1 - ( + 0.075) ^-25 = 0.836020939
  2. Ans / 0.075 = 11.14694586
  3. P x 11.14694586 = £100,000

£100,000 / 11.14694586 = £8,971.07

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Annual Equivalent Rate or Annual Percentage Rates - key points and formula?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

APR monthly rate formula?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Annualised returns - key points and formula:

A
  • 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).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Compounded annual return (CAR): annualised return - key points and formula?

A
  • 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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Real vs nominal rate of return - formula:

A

Rreal = Rnominal - Rinflation

Or

(1 + nominal) / (1 + inflation) - 1 = real rate of return

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Holding period return formula?

A

R = (D + V1 - V0) / V0

D = additional returns generated (income/ dividends paid out)

V0 = starting price

V1 = end price

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Money weighted return formula?

A

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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Full MWR return formula?

A

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:

  1. Takinh value at end of holding period + dividends
  2. Deducting original investment amount
  3. Deducting net cash inflow into the investment
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Time weighted return formula?

A

1 + TWR = (1 + r) x (1 + r2) x (1 + r3) …. (1 + rn)

Where TWR = TWR

r = holding period return

TWR breaks up the total period, say a year into little sub periods. Simply take the HPR for each period and multiply together.