Formulas & Ratios * some OEICs/ UT Etc Flashcards
What is the Theoretical ex- rights price formula?
(Existing value + Value of new
shares)/Total number of shares post issue
What does the Theoretical ex- rights price demonstrate?
The theoretical ex- rights pr ice is the
pr ice the original shares are
expected to move to as a result of
the rights issue.
The ex- rights pr ice will always be
lower than the cur rent pr ice, due to
the diluting effect of purchasing new
shares at a discount .
ABC Ltd have announced a 1 for 3
rights issue, with the new shares
discounted to £2 f rom the cur rent
share price of £2.50.
What is ex-rights price?
(3 x £2.50) + ( 1 x £2) = £9.50
Ex- rights price = £9.50/4 = £2.37
What is the Ex-bonus/scrip issue share price formula?
(Existing value of shares)/Total
number of shares post issue
What does the Ex-bonus/scrip issue share price demonstrate?
The ex-bonus/scrip issue price is the
price the original shares are expected to move to as a result of the issue.
As a bonus/scrip issue involves issuing additional shares at no cost , the effect will be to dilute the share price.
The total value of the shareholding
should be unaffected.
ABC Ltd have announced a 1 for 3 bonus issue. The current share price is £2.50.
Work out the Ex-bonus/scrip issue share price
(3 x £2.50)/4 = £1.87
Pre- issue holding = 3 x £2.50 = £7.50
Post - issue holding = 4 x £1.87 = £7.50
What is the Operating profit margin & Operating profit formula?
Operating profit margin
= (Operating profit/Sales) x 100%
Operating profit = Sales – Cost of Sales
Net profit margin calculation is very similar , but uses net profit on the numerator .
what does the Operating profit margin & Operating profit demonstrate?
Shows how efficiently a company is being run and how well they are using their operational resources (labour , materials etc. ) to generate sales.
A high operating profit margin suggests that the company has either increased sales or reduced the costs associated with sales.
XYZ Ltd made sales of £3,500,000.
Their operating costs for the year totalled £2,500,000.
work out the Operating profit margin & Operating profit
Operating profit = £3,500,000 -
£3,000,000 = £500,000
Operating profit margin
= (£500,000/£3,500,000) x 100% = 14.28%
What is the ROCE and capital employed formula?
Return on capital employed
(ROCE)
= (Profit before int . and
tax/capital employed) x 100%
Capital employed = Total Assets
– Current Liabilities
What does the ROCE demonstrate?
ROCE differs from ROE in that it shows the return, pre- tax and interest , the company is providing in relation to net total assets (which will include shareholder funds,
retained earnings and long term borrowing)
ROCE is a more comprehensive ratio than ROE and therefore is more useful when comparing to other companies.
ABC paid interest of £5,000 and tax of £12,500. They have total assets of £600,000 and cur rent liabilities of £75,000.
Work out the ROCE?
ROCE = (£50,000 + £12,500 + £5,000)/(£600,000 - £75,000) x
100% = 12.86%
What is the ROE and total equity formula?
Return on equity (ROE)
= (Net profit after tax/total equity) x 100%
Total equity = share capital + share premium + retained earnings
What does the ROE demonstrate?
Measures the return the company is providing on the funds provided by their shareholders.
A high ROE would demonstrate that the company is making best use of the funds raised f rom shareholders.
ABC Ltd has made net profit after tax of £50,000. The total equity of the company was valued at £500,000.
work out the ROE?
ROE = (£50,000/£500,000) x 100%
= 10%
What is the gearing ratio formula?
(Total Debt/Capital employed)
x 100%
What does the gearing ratio demonstrate
Indicates the sensitivity of the company’s profits to a change in interest rates.
Shows how highly leveraged a company is ( i.e. how reliant they are on borrowing to generate sales and profits) .
A high gearing rat io may lead to problems with further borrowing or may even lead to potential insolvency.
Total debt = £200,000 + £50,000 =
£250,000
Capital employed = £525,000
what is the gearing ratio?
Gearing ratio = (£250,000/£525,000)
x 100%
= 47.62%
What is the interest cover ratio formula?
= Profit before interest and
tax/Gross interest
What does the interest cover demonstrate?
Indicates the sensitivity of the company’s profits to a change in interest rates.
Shows how many times the interest payment could have been made of
the company’s profits.
A high interest cover shows that the
company can sustainably meet their debt servicing, even in times of declining profits.
The main limitation is that this measure is a snap-shot in time.
Profit before interest and tax =
£50,000 + £12,500 + £5,000 =
£67,500
work out the interest cover?
Interest Cover = £67,500/£5,000 =
13.5 times
What is the current ratio / working capital formula
= Current Assets/Current Liabilities
Current Assets are those which
are expected to be liquidated and
utilized within 12 months ( i.e. stock, cash) .
Current Liabilities are those which are expected to be paid within 12 months ( i.e. short term loans, tax payable) .
What is the liquidity ratio formula?
(Current Assets – Stock)/Current Liabilities
What does the current ratio and liquidity ratio demonstrate?
Measures the liquidity within a
company, i.e. whether sufficient cash can be generated through normal business/liquidating stock to repay short term liabilities when they arise.
The liquidity ratio goes an additional step and takes stock out of the equation to focus predominantly on the company’s cash business.
A low ratio ( less than 1.5 for working
capital or 1 for liquidity ratio) would suggest that the company could suffer insolvency in the near future.
A high working capital ratio may suggest that the company is currently holding too much stock.
DEF Ltd has valued thei r cur rent
stock at £850,000 and holds cash in
the bank of £800,000. The company
has short term loans worth
£1,000,000.
Work out the liquidity ratio and current ratio
Working capital ratio
= (£850,000 + £800,000)/
£1,000,000 = 1.65
Liquidity ratio
= £800,000/£1,000,000 = 0.8
What is the interest yield formula?
= (Coupon/Clean Price) x 100%
What does the interest yield on a bond demonstrate?
The annual income provided by the bond as a per centage of what you would currently have to pay for it.
Used as a measure of performance to evaluate against other securities /investments .
Peter is interested in a bond which is
currently pr iced at £98 per £100 nominal. It has a coupon of 5%.
Interest yield = (5/98) x 100% = 5.1%
What is the redemption yield formula?
Work out the gain or loss at maturity as a % of the current price;
((Nominal Value – Clean Price) /Clean price) x 100%
Divide this by the number of years to maturity to work out the annual gain/ loss as a %;
% Gain (or loss) at maturity/Term to maturity
Add (for a gain) or subtract (for a loss) f rom the interest yield.
Interest yield +(-) % gain (or loss) /Term to maturity
What does the redemption yield demonstrate
measure of performance/return which
takes not only income/ coupon payment s
into consideration but al so capital gain
or loss if held to maturity .
If the RY < IY, then the bondholder will
make a loss if they hold the bond to maturity .
If the RY > IY, then the bondholder will make a gain if they hold the bond to maturity .
Peter is interested in a bond which is
currently pr iced at £98 per £100
nominal. It has a coupon of 5%.
Let us assume the bond has 5 years to maturity.
what is the redemption yield
Gain or loss at maturity as % of current price
= ((£100 - £98) /£98) x 100% = 2.04%
Annual gain/ loss
= 2.04%/5 years = 0.41% per year
Redemption yield
= 5.1% + 0.41% = 5.51%
As the RY is higher than the IY, Peter
stands to make a gain if he holds the
bond to maturity.
What is the modified duration formula?
Duration/ (1 + GRY)
Duration refers to the length of time in years i t will take to repay the bond pr ice with cash-flows from it (coupons and redemption value). I t is sometimes refer red to as Macaulay Duration.
What does modified duration demonstrate?
The modified duration provides an
indication of the bond’ s sensitivity to changes in interest rates .
In particular, the modified duration relates to the percentage fall expected
in a bond price should interest rates increase by 1%
Redemption yield = 5.51%
lets assume the duration
of his bond was 4.54 years.
Work out the modified duration
Modified duration = 4.54/ (1.0551) =
4.30%.
This means that the price of the bond would be expected to fall by 4.30% if interest rates increase by 1%.
What is the EPS formula?
Profit attributable to ord shareholders
Number of ordinary shares in issue
what does the EPS demonstrate?
Trends in the company ’ s profitability
How the company measures up to other
companies in relation to profitability
ABC Ltd made profits of £10,000,000 in
2016. They have 750,000 ordinary shares in
issue.
work out the EPS?
EPS = £10,000,000/750,000 = £13.33 per
share
what is the P/E ratio formula?
= Cur rent share price/EPS
what does the P/E Ratio demonstrate
Shows how highly the investors value the
earnings of the company .
A high P/E ratio typical l y demonstrates that
The investors are willing to pay more for
shares and that demand is high, or
The share price may be over valued based upon the profits generated
ABC Ltd made profits of £10,000,000 in
2016. They have 750,000 ordinary shares in
issue.
current share price us £100
work out the P/E Ratio?
P/E ratio = £100/£13.33 = 7.5
what is the DPS formula?
= Total Dividend paid/No of shares in
issue
what does the DPS demonstrate
The level of profits distributed to the
shareholders .
ABC Ltd made profits of £10,000,000 in
2016. They have 750,000 ordinary shares in
issue. In 2016, they paid a total dividend of £5,000,000.
work out the DPS
DPS = £5,000,000/750,000 = £6.66 per share.
what is the dividend yield formula?
= (DPS/Current share price) x 100%
what does the dividend yield demonstrate?
Shows the return that investors are receiving from the shares in the way of annual income.
A high Dividend Yield would demonstrate that the investor i s receiving a good return from the shares , but does not necessarily mean that the level of profit distribution is sustainable.
ABC Ltd made profits of £10,000,000 in
2016. They have 750,000 ordinary shares in
issue.
share price £100
DPS £6.66
work out the dividend yield
Dividend Yield = £6.66/£100 = 6.66%
what is the dividend cover formula?
= EPS/DPS
Or
= Profit attributable/Dividend paid
what does the dividend cover demonstrate
Shows how many times the dividend could have been paid from the period’ s profits .
A dividend cover of less than 1 would suggest that the company has to utilise reserves .
DPS £6.66
EPS £13.33
work out the dividend cover?
Dividend Cover = £13.33/£6.66 = 2 times
what is the NAV per share formula?
= Net assets att to ord shareholders
Number of ordinary shares in issue
what does the nav per share demonstrate?
The value of the company for accounting
purposes .
Reflects the true value of the company , based on the balance sheet (as set s les s liabilities ) as oppose to market sentiment.
ABC Ltd. The net asset
attributable to ordinary shareholders is
£50,000,000.
They have 750,000 ordinary shares in
issue.
work out the nav per share?
NAV ps = £50,000,000/750,000 = £66.66 per
share
what is the premium/discount to nav ps formula?
= (Current price – NAV per share) /NAV
per share x 100%
+ve result = premium
-ve result = discount
what does a premium or discount to NAV per share demonstrate?
This measure i s used to determine how
accurately a share price represent s the
underlying value of the company .
A premium suggests that you would currently pay more than the true value, whereas a discount suggests you would currently pay less than the true value.
The main driver here i s suppl y and demand for the shares (prices wil increase due to low suppl y or high demand).
The current share price of ABC Ltd is £70 per share. NAV per share is £66.66
work out the premium?
Difference = £70 - £66.66 = £3.33, which
means the shares are trading at a premium.
Premium = (£3.33/£66.66) x 100% = 5%
what is the rental yield formula
= (Gross rent /Market price) x 100%
Or
= (Gross rent – expenses) x 100%
(Market price + costs of buying)
what does the rental yield demonstrate
The return, as a %, generated by renting out an investment property .
A high rental yield would demonstrate that the investor is receiving a good return from the property , but the sustainability of the yield will be reliable on the qual it y of tenant and the cost of ongoing maintenance.
what is the HPR formula
= D + V1 – V0 / V0
D = Income paid out (Dividend)
V1 = Value at end of the period
V0 = Value at star t of the period
what does the HPR demonstrate
The holding period return shows the
return on an investment, taking account
of the capital growth and income
generated.
This does not take ac count of
withdrawals or additional investments
over the period, nor does it take
ac count of the timing of withdrawals /additional investments ,
however it is often used for making
simple performance comparisons .
Fiona invested £100,000 at the star t of the
year . Half-way through the year , she
received a dividend of £5,000. At the end of
the year , the investment was valued at
£135,000.
work out the HPR
Holding return = £5,000 + £135,000 - £100,000 / £100,000
Holding return = £40,000/£100,000
= 0.4 = 40%
what is the MWR formula?
= D + V1 – V0 – C / V0 + (C x (n/12))
D = Income paid out (Dividend)
C = New money introduced (-C) or
money out (+C)
V1 = Value at end of the period
V0 = Value at star t of the period
n = Number of months remaining
in the year
what does the MWR demonstrate
The money weighted rate of return
shows the return on an investment,
taking ac count not only of capital
growth and income generated, but al so
cash-flows in and out of the investment.
It therefore prov ides a more ac curate
reflection of investment performance
than the holding period return.
Limitations
Strongly influenced by timing of
additional investments /withdrawal s
Additional investments /withdrawal s are
often out s ide of the investment
manager’s control and therefore cannot
be mitigated.
Doesn’t show whether the return is
down to management skill or the impact
of additional investments /withdrawals .
Fiona invested £100,000 at the star t of the
year . Half-way through the year , she
received a dividend of £5,000. At the end of
the year , the investment was valued at
£135,000.
3 months into the year , she invested
a further £20,000.
what is the MWR?
MWR = £5,000 + £135,000 - £100,000 - £20,000 / £100,000 + (£20,000 x 9/12)
MWR = £20,000/£115,000 = 0.1739 = 17.93%
This is considerably lower than the holding
period return, which demonstrates that a
huge component of the performance was the additional investment .
what is the TWR formula
= (1 + HPR 1) x (1 + HPR2 )…x
Where each HPR is calculated by
breaking the period into sub-periods valued at each capital investment or withdrawal.
what does the TWR demonstrate
The time weighted rate of return
prov ides a more accurate rate of return
by removing distortions caused by the
timing of cash-flows .
TWR is used for comparing performance
with other investments .
Fiona invested £100,000 at the star t of the
year . Half-way through the year , she
received a dividend of £5,000. At the end of
the year , the investment was valued at
£135,000.
3 months into the year , she invested
a further £20,000.
just prior to her investing a further
£20,000, her investment was valued at
£105,000.
work out the TWR
HPR 1
(£5,000 + £105,000 - £100,000) /£100,000 = 0.1 = 10%
HPR 2
£135,000 – £105,000 - £20,000 / £105,000 + £20,000 = 0.08 = 8%
TWR = (1.10) x (1.08) = 1.188 = 18.8%
Given that the TWR is higher than the MWR,
this tells us that the rate of return was
heavily influenced not only by the size of
the additional investment but also the
timing of it .
What is the CAPM formula?
E(R ) = Rf + (β x (Rm – Rf))
E(R ) = Expected return on the risky
investment
Rf = Rate of return on a risk-free asset
β = Measure of sensitivity of the investment to movements in the market
Rm = Expected return of the market
portfolio
what does the CAPM demonstrate
Shows the expected return on a stock/ security
with reference to it s market and the return
that could be achieved through a risk-free
as set.
The higher the beta, the more volatile the
stock/ security in relation to its market
A beta of les s than 1 suggests that the
s tock/ security is defensive.
A beta of greater than 1 suggests that the
s tock/ security exaggerates market
movements .
A beta equal to 1 suggests that the
s tock/ security moves exactly in line with the market.
The expected return on a Treasury bill is
2.5% and the market portfolio is expected
to return 6%. Assume the beta of ABC Ltd is
0.7.
work out the CAPM
E(R ) = 2.5% + (0.7 x (6% - 2.5%)) = 4.95%
Let us now assume that a stock has an
expected return of 5%, compared to the
expected market portfolio return of 3.5%
and a Treasury Bill return of 3%.
Using the CAPM formula what is the beta?
5% = 3% + (β x (3.5% - 3%))
2% = β x 0.5%
β = 4
What is the alpha formula?
= Actual portfolio return – CAPM
CAPM = Rf + (β x (Rm – Rf))
what does Alpha demonstrate?
The alpha shows whether the investment has outperformed or underperformed its ’
benchmark in light of its ’ beta.
It is another way of demonstrating the
skill/quality of the investment manager
The expected return on a Treasury bill is
2.5% and the market portfolio is expected
to return 6%. Assume the beta of ABC Ltd is
0.7
Let ’s assume the
market was expected to return 4%. The
beta is 1.5. The actual return was 5%.
what is the Alpha?
CAPM = 3% + (1.5 x (4% - 3%)) = 4.5%
Alpha = 5% - 4.5% = 0.5%
Harpal’s portfolio has outperformed in
light of its beta.
what is the SD formula?
Step 1 – Calculate the average/mean
return over the sample
Step 2 – Calculate the variance of
each individual return to the average/mean
Step 3 – Square each output f rom
step 2 (x or ^ then ‘2’ on the calculator ).
Step 4 – Total up the squared variances
Step 5 – Divide by the number of
returns observed (n)
Step 6 – Square root the output from
step 5 (x or ^ then ‘0.5’ on the calculator ).
what does SD demonstrate
Measures the volatility of the investment
around it’ s mean/average return.
Often used as an indicator of the investment risk associated with an investment, so a high standard deviation would typify a high risk investment.
Over the last three years, an investment
has provided returns of 4%, -2% and 1.5%.
Step 1 – The average return will be
(4% - 2% + 1.5%) /3 = 1.17%
Step 2 – The individual variances will be
4% - 1.17% = 2.83%
-2% - 1.17% = -3.17%
1.5% - 1.17% = 0.33%
Step 3 – The squared variances will be
(2.83) = 8.01%
(-3.17) = 10.05%
(0.33) = 0.11%
Step 4 – The total of the squared variances is
8.01% + 10.05% + 0.11% = 18.17%
Step 5 – Divide by n
18.17%/3 = 6.06%
Step 6 – Standard Deviation will
therefore be
(6.06%) = 2.46%
what is the sharpe ratio formula
Actual Return – risk-free return /
Standard deviation
what does the sharpe ratio demonstrate
The Sharpe ratio is essentially the risk adjusted return on an investment, and shows the additional return achieved by an
investment over and above what could have
been achieved by taking no risk at all .
The higher the Sharpe ratio, the more
value/ skill is being added by the investment manager.
Harpal is interested in an investment that
has an investment return of 5% and a
standard deviation of 10%. The return he
could achieve on a Treasury Bill is 3%.
work out the sharpe ratio
Sharpe ratio = (5% - 3%) /10% = 0.2%
Therefore, Harpal achieved a return of 0.2%
for each unit of risk taken.
what is the information ratio formula
Actual return – benchmark return /
Tracking error
The tracking error is essentially the
standard deviation, but relative to a
benchmark as opposed to the average
return of the investment .
what does the information ratio demonstrate
The information ratio essentially shows the value added through active management as
opposed to a more passive, index tracking
approach.
The t racking error on Harpal’s portfolio is
7% and the benchmark returned 4%.
work out the information ratio
Information rat io = (5% - 4%) /7% = 0.14
Whilst Harpal’s portfolio has outperformed
the benchmark, it has done so by taking a
significant amount of risk.
what is the formula for Future value of a lump sum investment
= PV (1 + r) n
r = annual rate of interest / return
n = number of years
Present value of a future lump sum formula?
= FV/ (1 + r )n
r = annual rate of interest / return
n = number of years
What does the future and present value formulas demonstrate?
Based on an assumed interest rate, this
shows the future value of a lump sum
investment today , or alternatively the
value required as a lump sum today to
achieve a specified future value.
Jack would like to invest £1,000 for
10 years at an annual rate of interest
of 5%.
work out the future value
FV = £1,000 x (1.05) 10 = £1,628.89
Jack would like to invest £1,000 for
10 years at an annual rate of interest
of 5%.
Let us now assume that Jack would
like to achieve a lump sum of £1,000
in 10 years’ time and he can save at
an annual interest rate of 5%
what is the present value
PV = £1,000/ (1.05) 10 = £613.91
what is the AER formula
= ((1 + r /n) – 1) x 100%
r = quoted rate of interest (annual)
n = frequency of interest payments
what does the AER demonstrate?
Where an interest rate i s quoted
annually , but i s paid more frequently ,
the AER shows the actual rate of
interest paid to the investor annual l y .
The more frequent the payment, the
higher the AER will be in comparison to
the quoted rate.
The AER makes the return on an
investment more comparable with other
types of investment.
ack’s savings account has a nominal
annual rate of interest of 4%.
Interest is paid to his account
quarterly.
work out the AER
AER = ((1 + 0.04/4) 4 – 1) x 100%
AER = ((1.01) 4– 1) x 100%
AER = 4.06%
what is the annualized return formula
= ((1+r ) – 1) x 100%
r = rate of return over a specified period/ term
n = number of years invested
what does the annualised return demonstrate
Where an investment return has been
provided over a specified term (e.g. 3
year s ), the annual i sed return i s a means
of working out the return the investment would have achieved on an annual basis .
This makes the investment more
comparable with other investments and
may be used as a means of benchmarking the performance of the investment.
Marvin has held an investment for 5
years and over that period it has
achieved a return of 12%.
work out the annualised return
Annualised return = ((1 + 0.12) – 1) x 100%
Annualised return = (1.0229-1) x 100%
Annualised return = 2.29%
I CHARTERED
These spines can be used to approach the following types of AF4 question;
Additional information required to assess the suitability of an assessment
Factors to consider when investing in an asset class or collective investment
Features of an asset class or collective investment
Direct v Direct; Direct v Indirect; Indirect v Indirect comparisons (features, benefits
and drawbacks)
Wrapper v Wrapper; Wrapped v Unwrapped
Indexes (Benchmarks)
Costs/charges
How to buy….
Aims/Objectives of the investment
Recompense/Repayment (FCSC et
al)
Taxation
Examples (Options & Types)
Risk
Ease of access to funds (liquidity)
Dealing/Trading
Collectives specific elements:
GRAMS
These spines can be used to approach the following types of AF4 question;
Additional information required to assess the suitability of an assessment
Factors to consider when investing in an asset class or collective investment
Features of an asset class or collective investment
Direct v Direct; Direct v Indirect; Indirect v Indirect comparisons (features, benefits
and drawbacks)
Wrapper v Wrapper; Wrapped v Unwrapped
Wrappers:
TOP HAT
These spines can be used to approach the following types of AF4 question;
Additional information required to assess the suitability of an assessment
Factors to consider when investing in an asset class or collective investment
Features of an asset class or collective investment
Direct v Direct; Direct v Indirect; Indirect v Indirect comparisons (features, benefits
and drawbacks)
Wrapper v Wrapper; Wrapped v Unwrapped
what benchmark would you use for Cash, Fixed Int, Property and Equities
what are the costs/charges when dealing with cash / fixed interest, property and equity
How can you buy Cash, Fixed Interest, Property and Equities
what are the aims / objectives of Cash, Fixed Int, Equities and property
Cash, Fixed Int, Equities and property
what is the FSC protection on Cash, Fixed Int, Equities and property
Examples and options of Cash, Fixed Int, Equities and property
CASH / FI/ EQ/ PROP
Risks of Cash, Fixed Int,
CASH / FI/ EQ/ PROP
Liquidity of Cash, Fixed Int,
CASH / FI/ EQ/ PROP
Dealing and trading of Cash, Fixed Int, Equities and property
CASH / FI/ EQ/ PROP
