Calculations Flashcards
(44 cards)
Interest (AKA Current/Flat/Running) Yield
Coupon/Clean price x 100
A: 8%/£105 x 100 = 7.62%
B: 8%/£95 x 100 = 8.42%
Gross Redemption Yield
Interest Yield + or - gain or loss to maturity/number of years to maturity/clean price x 100
A: 7.62% - (5/4/£105x100) = 7.62 - 1.19 = 6.43
B: 8.42% + (5/4/£95x100) = 8.42 + 1.32 = 9.74
If redemption yield is less than interest yield (A) there will be a capital loss, if redemption yield is more (B) there will be a capital gain if held to maturity.
Stamp Duty
Colin buys £2,583 worth of share using a stock transfer form - how much stamp duty does he pay?
£2,583 x 0.5% = £12.915
Rounded up to the nearest £5 is £15.
Stamp Duty Reserve Tax
Colin buys £2,583 worth of shares using CREST - how much stamp duty does he pay?
£2,583 x 0.5% £12.915
Rounded up to the nearest penny is £12.92.
Dividend Taxation
First £2000 tax free
Sums above taxed at the following:
- 5% Basic-Rate Taxpayers
- 5% Higher-Rate Taxpayers
- 1% Additional-Rate Taxpayers
Higher rate taxpayer received £5,000 in dividend income - £2,000 falls within allowance, remaining £3,000 is taxed at 32.5% = £3,000 x 32.5% = £975
Capital Gains Tax (CGT)
Internal capital gains within an authorised unit trust are exempt from CGT.
Total annual exemption of £12,300 in 2020/21
Taxable gain is remaining after annual exemption is taxed at 10%/20% depending on other income for the year.
A higher rate taxpayer has made a gain on Unit Trust of £30,000. Assuming she has already used annual exemption, how much CGT will she have to pay?
£30,000 x 20% = £6,000
Earnings Per Share (EPS)
Tells us how much of the company’s profit has been paid out to ordinary shareholders.
Net Profits attributed to shareholders/No. of shares
Net Profits: £2 million
No. of shares: 10 million
2m/10m = 20p
Dividend Yield
Net dividend per share/Current share price (%)
8p / £1.90 x 100% = 4.21%
Dividend Cover
Earnings Per Share/Dividends Per Share
20p/8p = 2.5
This means the dividend can be paid out 2.5x from current earnings.
Price earnings P/E ratio
Current Share Price/Earnings Per Share
Current Share Price: £1.90
Earnings Per Share (£2m/10m): 20p
190/20 = 9.5
Net Asset Value (NAV) Per Share
Net Assets attributable to shareholders/No. of shares
Net Assets: £18m
No. Shares: 10m
18/10 = 1.8
This positive figure means that their assets exceed liabilities.
Stamp Duty Land Tax
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Rental Yield
Rent - expenses / Value of property + costs x 100
£1,200 - £350 x 12 / £200,000 + £6,000 x 100 = 4.95%
Standard Deviation
If an investment has a standard deviation of 5 and an expected return of 8%.
A movement of 1 standard deviation would be a return of 5% more or less than 8%, therefore a range of 3% to 13%.
The standard deviation only works if returns from investments fall within a particular pattern, that is most returns are close to the expected return with just a few at the extremes.
If this is the case we can expect 68% of historic returns to fall within 1 standard deviation of the mean. We can also expect 95% of historic returns to fall within 2 standard deviations of the mean.
The greater the standard deviation, the greater the volatility, the greater the risk.
Correlation
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Capital Asset Pricing Model (CAPM)
The CAPM suggests that the sensitivity of an investment to the market that is the appropriate measure of risk.
The sensitivity of a security relative to the market is expressed in terms of its beta.
The market has a beta of one.
A beta of less that 1 means the investment is less volatile than the market.
A beta of more than 1 means the investment is more volatile than the market.
The CAPM equation is usually expressed as:
E(Ri) = Rf + Bi (Rm - Rf)
E(Ri) - Expected return on the risky investment
Rf - Rate of return on a Risk free asset
Rm - Expected return of the market
Bi - The measure of sensitivity of the investment to movements in the overall markets
Bi (Rm - Rf) is the risk premium on the risky investment
Time Value of Money (How much will an amount of money be worth in a number of years time?)
FV = PV (1 + r) n
FV = The future value of money PV = The present value of money r = The rate of interest n = The number of years invested
Client has £1,000 which he wants set aside for two years time.
You find him an account paying 5% interest annually.
How much will client receive at the end of the two years?
FV = PV (1 + r)n
FV = £1000 (1 + 0.05) power 2
FV = £1000 (1.05) power 2
FV = £1000 (1.1025)
FV = £1,102.50
If interest is paid in advance formula would be:
FV = PV (1 + r) n+1
Time Value of Money (What return has been earned on an investment?)
To find out the interest rate applicable to an investment given the amount invested at the start of the term and the amount accumulated at the end of the term we use the same basic formula of FV = PV (1 + r) n but in a slightly different way.
Your client invested £5,000 into an OEIC 4 years ago.
Its current value is £7,892.62.
What compound rate of return has it achieved?
FV = PV (1 + r) n
£7,892.62 = £5,000 (1 + r) power 4
£7,892.62 / £5,000 = (1 + r) power 4
- 5789 = (1 + r) power 4
(1. 5789) power 1/4 = 1 + r
(1. 5789) power 0.25 = 1 + r - 121 = 1 + r
r = 1.121 - 1
r = 0.121
Expressed as a percentage = 12.1%
Time Value of Money (What is the true rate of interest achieved?)
Where interest is payable more often than annually, we need to take into account the number of payments made in the year in our formula as shown in the example below.
Your client has £1,000 which he wants set aside for 2 years time.
You find him an account paying 5% interest half yearly.
How much will your client receive at the end of the 2 years?
FV = PV (1 + r) n
On this occasion n = 4 because there will be 4 interest payments over the course of the two year term so:
FV = £1,000 (1 + 0.025) power 4
FV = £1,000 (1.025) power 4
FV = £1,000 (1.1038)
FV = £1,103.80
Effective Annual Rate of Interest (APR)
Where interest is payable more often than annually, it is helpful to be able to work out the effective annual rate of interest. This shows as a percentage by which the client benefits having interest paid more frequently and gives a more accurate figure. The formula is:
(1 + r / n) power n - 1
r = The rate of interest n = The number of interest payments in the year
What is the effective rate of interest on an account that pays 7% quarterly?
Effective rate of interest = (1 + r / n) power n - 1
Effective rate of interest = (1 + 0.07 / 4) power 4 - 1
Effective rate of interest = (1 + 0.0175) power 4 - 1
Effective rate of interest = (1.0175) power 4 - 1
Effective rate of interest = (1.0718) - 1 = 0.0718 or 7.18%
Time Value of Money (How much is needed to invest?)
To work out the amount that needs to be invested now to generate a set amount of money at a future date based on a specific interest rate use the following formula:
PV = FV / (1 + r) power n
Your client requires £12,000 in 5 years time.
You have found an account that pays an annual interest rate of 6%.
How much does your client need to invest to achieve her objective?
PV = FV / (1 + r) power n
PV = £12,000 / (1 + 0.06) power 5
PV = £12,000 / (1.06) power 5
PV = £12,000 / 1.338
PV = £8,968.61
Real Returns vs Nominal Returns
Real Returns adjust the value of a return for inflation purposes.
Real returns are important for investors as they represent the increase (or decrease) in the purchasing power of their investment portfolio.
The real return is approximately the nominal return from the investment minus the inflation rate but is more accurately calculated as the nominal return discounted by the inflation rate. The formula is:
Rreal = Rnom - Rinf
Rreal - The real return
Rnom - The nominal return
Rinf - The inflation rate
If a return of 11% had been achieved over the last year and inflation had been 3% per year, what is the real return adjusted for inflation?
Rreal = Rnom - Rinf
Rreal = 11% - 3% = 8%
Personal Savings Allowance (PSA)
Basic-rate taxpayer can earn up to £1,000 in savings income tax free.
Higher-rate taxpayers are able to earn up to £500
There is no allowance for additional-rate taxpayers
Gearing of trusts
To work out how geared a trust is:
Total Gross Assets / Net Assets x 100
A fund has gross assets of £140m and total net assets of £110m.
To what extent has the fund geared?
£140m / £110m x 100 = 127.27
This means the fund is 27.7% geared, i.e. 27.27% of the total assets are borrowed funds.