Calculations Flashcards
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.
Compound interest
P (1 + r / n) power n
Asset Cover & Hurdle Rate
If a trust has a hurdle rate of 3.5% and asset cover of 0.9 what does this tell you about the trust?
The trust needs to grow by 3.5% per year if it is to meet its liabilities at the end of its term. At present its assets only cover 90% of its liabilities.
Offshore - Reporting Fund
Must report all income
Must apply annually for Reporting Fund Status
Dividends are paid to investors gross.
Capital Gains made by the individual investor are subject to CGT and annual exemption applies along with other gains made
Distributor status is given annually
Taxed as normal
Offshore - Non Reporting Fund
Income is accumulated
Gain on disposal are taxed as Income tax and therefore no annual exemption can be utilised
Gain = sale proceeds less purchase price
Taxed as income tax and therefore up to 45%
No CGT to pay so no offset permitted
Qualifying Policy
Fund taxed on income and gains at an assumed rate of 20%
No further tax payable on encashment providing the policy has been in force for 10 years or 3/4 of the term if sooner.
Maximum that can be paid into a qualifying policy is £3,600.
To be classed as qualifying it must meet the criteria:
- Must secure a capital sum on maturity, death or earlier disability.
- Premiums must be payable annually or more frequently.
- Premiums must be paid for at least 10 years or until earlier death.
- For term assurance policies the sum assured must not be less than 75% of the premiums payable during the term of the policy.
- For whole of life policies the sum assured must not be less than 75% of the total premiums payable should death occur at age 75.
- Premiums payable in any one year must not be more than 1/8th of total premiums payable in any other year.
Friendly Societies
Premiums of a policy must not exceed £270 per annum (for annual premiums) or £300 per annum for more frequent premiums (£25 per month or £5.70 per week).
These contribution limits are applied to the total plans held by an investor.
Policies are available from age 18 to a maximum age of 70 in the individual’s own name.
Policies can be taken out for children from birth.
Non Qualifying Policies
Policies which do not meet the qualifying criteria are called non-qualifying policies.
All single premium bonds are non-qualifying as they do not meet the requirement of regular premiums.
With non-qualifying policies there is the possibility of a tax liability for policyholders in the higher rate tax brackets when a chargeable event occurs.
Tax is charged at 20% of the net gain for higher rate tax payers and 25% of the net gain for additional rate tax payers.
Any gain may also affect any entitlement to income related allowances/benefits.
Bond holders are allowed to withdraw up to 5% of their original capital each year, for a maximum of 20 years, without incurring an immediate tax charge. This is known as taking ‘tax deferred income’.
Chargeable Events
D - Death
A - Assignment for money
M - Maturity
E - Excess on partial surrender over 5%
S - Surrender
Top Slicing
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Onshore Bond Taxation
Pay net income
Additional tax due on net income
Can offset expenses against tax bill
Fund rolls up net
Fund benefits from indexation relief
Offshore Bonds Taxation
Pay gross income
Additional tax due on gross income
No tax bill to offset expenses against
Fund rolls up gross
Withholding tax on non-UK dividends is non-reclaimable
Property Authorised Investment Funds (PAIFs)
In a PAIF, rental profits and property related income is ring-fenced and exempt from corporation tax.
It is distributed to the investor net of 20% tax. Non tax payers can reclaim this. Higher and Additional rate tax payers must pay an extra 20% and 25% of the gross income respectively.
Enterprise Investment Scheme (EIS)
An investor who has realised a gain from an investment can get CGT deferral relief if he invests the gain within the timeframe of 12 months before the gain arose and 35 months afterwards.
Under an EIS the investor may also obtain income tax relief at 30% on the amount invested up to a total of £1,000,000 for shares issued in any one tax year.
Relief can be claimed up to a maximum of £2m, providing any amount in excess of £1m is invested in knowledge-intensive companies and the investor has income tax liability of at least the amount being claimed.
Must be held for 3 years.
Dividends taxable.
CGT on disposal free after 3 years.
Seed Enterprise Investment Scheme (SEIS)
Tax relief is given at a rate of 50% on investments up to £100,000 with the same requirement to hold the shares for three years and the other reliefs being the same as those for EIS.
Venture Capital Trusts (VCT)
VCT’s are companied listed on the London Stock Exchange.
Income tax relief is available at a rate of 30% in the tax year when the investment is made into VCT shares.
The maximum amount which can attract this relief is £200,000 and the shares must be held for 5 years.
Dividends not taxable.
CGT free on disposal from outset.
No CGT deferral relief on initial investment.
Child Trust Funds
There are 3 types of CTF account:
- Savings
- Share accounts
- Stakeholder accounts
Contributions can be made to existing CTFs by parents, relations and friends of up to £9,000.
Holding Period Return
The holding period return allows comparisons of returns to be made between different investments over the same time period.
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Sharpe Ratio
The Sharpe ratio is a measure of the risk adjusted return of an investment.
It measures the excess return for every unit of risk that has been taken in to achieve the return.
(Return on the investment - risk free return)
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Standard Deviation of the return on the investment
Alpha
a = actual portfolio return - (Rf + Bi (Rm - Rf))
Rf - Risk free rate of return
Bi - Beta of the fund or portfolio
Rm - Market return
Information Ratio
Rp - Rb
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Tracking error
Rp - Portfolio return
Rb - Benchmark return
