Formulas Flashcards
Annual Equivalent Rate (AER)
CASH INVESTMENTS
SEE LATER CARD FOR MORE DETAILED EQUATION WHERE MORE FREQUENT INTEREST PAYMENTS USED
Annual rate = (1 + r)n
r = nominal rate of interest n = number of periods in which interest will be paid
Example: 3.6% paid quarterly
- 6% / 4 = 0.9
- 9 / 100 = 0.009
- 009 + 1 = 1.009
- 009 to the power of 4, which is:
(1. 009 x 1.009 x 1.009 x 1.009) = 1.03648
1.03648 - 1 = 0.03648
0.03648 x 100 = 3.648
Round up to 2 decimal places = 3.65%
Conversion Premium / Discount for Convertible Bonds
BOND INVESTMENTS
Calculation:
mb ( ------------ -1 ) x100 = x% (premium or discount) cr x ms
mb = market price of the bond cr = number of shares the bond stock will buy ms = market price of the ordinary shares
Example:
£110 ( ----------------- -1 ) x100 = 10% £25 x £4.00
Interest Yield
BOND INVESTMENTS
CALCULATION
DESCRIPTION
Calculation:
Coupon Interest Yield = ------------------- x 100
Clean price
Example:
Coupon = 8% Clean price (purchase price) = £124.27
8 6.44% = ------------------- x 100
£124.27
BOND INTEREST YIELD
- expresses the annual income from a bond as a percentage of the price an investor would pay for the bond
ISSUES
- can be misleading as bonds may create a capital gain or loss if held until redemption, depending upon the price at which they were purchased
- bonds may trade above or below their par or nominal value because their prices are not fixed
- if the coupon is above current interest rates and the issuer has a strong credit rating, the bond will trade above par
Redemption Yield (Part 1 of 2)
BOND INVESTMENTS
THIS IS ALSO SHOWN LATER ON (SIMPLIFIED)
Market Price (mp) Calculation:
Face value x clean price / 100 = mp
Example:
£1,000 x £124.27 / 100 = £1,242.70
Redemption Yield (Part 2 of 2)
BOND INVESTMENTS
Calculation:
(par - mp) / years to redemption)
Interest yield + ( ———————————————– x100)
mp
mp = market price
Step 1 = work out the INTEREST YIELD Step 2 = work out the MARKET PRICE Step 3 = do the calculation (as above) Negative figure = capital loss Positive figure = capital gains Step 4 = deduct the % answer to the above from the interest yield to get the redemption yield (if the figure from Step 3 is negative, ignore the minus and deduct such as IT 6.44% + - 4.88% = 1.56% RY)
Example:
(£1,000 - £1,242.70) / 4) 6.44% + ( --------------------------------------- x100) = 4.88%
£1,242.70
HIGHER REDEMPTION YIELD IS BETTER WHEN COMPARING
Duration
BOND INVESTMENTS
Duration allows the sensitivity of one bond verses another to be compared:
E Net present value of the cash flows to be received
Modified Duration 1 of 2
BOND INVESTMENTS
Modified Duration allows us to compare the sensitivity of a bond to changes in interest rates.
- This estimates how much a bond’s price will change if there is a change in interest rates
Duration --------------------------------------- (1 + Gross Redemption Yield)
Example:
- Duration of 2.88
- GRY of 5%
2.88 ------------------ = 2.74 (1 + 0.05)
Modified Duration 2 of 2
BOND INVESTMENTS
Can calculate what effect a % rise (say 1%) in yields will be on the bond’s price.
Our Duration of 2.74 means that the price should change by 2.74%.
A bond priced at 97.28 would therefore fall (because the yield has risen) by:
97.28 - (97.28 x 0.0274) = 94.61
Ex-Rights Price
EQUITY INVESTMENTS
Example: Issue of 1 for2. Existing shares are £3 each:
Number of Shares Price Value
Before Issue 2 £4.50 £9
Rights Issue* 1 £3.00 £3
After Rights Issue** 3 £12
- Rights issue gives the right to subcribe for one new share at £3
- *After the rights issue, three shares are valued at £12
Ex-rights price is £12 / 3 = £4 a share
Rights Premium
EQUITY INVESTMENTS
Using the example from ‘Ex-Rights Price’:
Ex-Rights price of £4 - new share (rights issue) price of £3 = £1 (Rights Premium)
Bonus Issues & Share Splits
EQUITY INVESTMENTS
This is where the number of shares is increased either issuing more shares (bonus issue) or splitting the existing shares (share splits).
New share price is worked out as:
Value of the shares / the new number of shares
Initial Yield
PROPERTY INVESTMENTS
Returns on an investment in property are meansured by an INITIAL YIELD (which is a %) as follows:
Annual rental income Initial Yield = ----------------------------------- x 100
price of the property
- is used to compare property investments
- is inaccurate as a comparison measure because it does not allow for rental growth that a lease provides
- doesn’t take into account the growth resulting from future rent reviews
Unit Trust Buying & Selling Prices
Calculation:
NAV ------------------------------------------ = Buying & selling prices Number of units in existence
Gross Domestic Produce (GDP)
GDP Calculation:
GDP = C + I + G + (X - M)
C = Consumption (expenditure of households on goods and services) I = Invesment (expenditure of businesses and individuals for capital investment) G = Government spending X = Exports M = Imports
Capital Asset Pricing Model (CAPM)
CAPM derives the theoretical expected return for a risky security as a combination of the:
- return on a risk-free asset (such as a treasury gilt)
- risk premium (the compensation for holding a risky investment)
CAPM Equation:
E(Ri) = Rf + Bi (Rm - Rf)
E(Ri) = expected return on the risky investment
Rf = rate of return on risk-free asset
Rm - expected return of model portfolio
Bi = beta (sensitivity of investment to overall market)
(Rm - Rf) = market risk premium
Bi (Rm - Rf) = risk premium of the risky investment
Capital Asset Pricing Model (CAPM) - Assumptions
CAPM is based on a set of assumptions:
- investors are rational and risk adverse
- all investors have an identical holding period
- no one individual can affect the market price
- no taxes, transaction costs etc
- information is free and available to all investors
- all investors can borrow/lend unlimited money
- quantity of risky securities in the market is fixed
Holding Period Return - Calculation
HOLDING PERIOD RETURN CALCULATION:
D + V1 - V0 R = ------------------- x 100 to get a %
V0
R = holding period return D = income received during the period V0 = price/value at acquisition V1 = price on selling
EXAMPLE:
Investment costs £100, pays a dividend of £10 and is sold for £110 after six months
£10 + £110 - £100 R = ------------------- = 0.20 x 100 = 20%
£100
Holding Period Return - Description
HOLDING PERIOD RETURN
- compares returns on different investment
- encompasses the total return, including income and capital gains, over a period
- expressed as a percentage (%) of the original cost
- it equals all income received plus capital gains during the period as a % of the original investment
DISADVANTAGES:
- period looked at must be the same when comparing two investments
- does not take into consideration timing of cash flows or compounding of returns
Relative Return - Calculation
RELATIVE RETURN CALCULATION:
rREL = r - rB
r = the total holding period return rB = the benchmark return
EXAMPLE:
Portfolio has a total return of 12% and the benchmark rose by 10%
rREL = 12% - 10% = 2%
Relative Return - Description
RELATIVE RETURN
- is the return from an investment/portfolio measured against the return from a benchmark index
- shows how well the investment/portfolio has performed relative to a benchmark
- measures whether a fund manager had added value above the index return
MWR - Calculation
MONEY WEIGHTED RATE OF RETURN CALCULATION
D + V1 - V0 - C MWR = -----------------------
V0 + (C x n / 12)
n = number of months remaining in the year C = the new money introduced during the year V0 = the price or value at acquisition V1 = the price on selling
EXAMPLE
V0 = £20,000 V1 = £24,000 D = nothing as no income paid out Money In = £3,000 in March Money Out = £2,000 in September (withdrawal)
D + V1 - V0 - C MWR = -------------------------------------------
V0 + (C x n / 12) + (C x n /12)
0 + 24,000 - 20,000 - 1,000 MWR = ---------------------------------------------------
[20,000 + (3,000x9/12) + (-2,000x3/12)]
3,000 MWR = --------------------------------- = 0.1379 x 100 = 13.79%
20,000 + 2,250 - 500
MWR - Description
MONEY WEIGHTED RATE OF RETURN
- a modified form of the holding period return
- adjusts for cash inflows into the portfolio
ISSUES
- not considered appropriate when trying to compare different portfolios
- strongly influenced by the timing of cash flows
- does not identify whether the overall return for the investor is due to the ability of the fund manager or as a result of when additional funds were invested
TWR - Calculation
TIME WEIGHTED RATE OF RETURN CALCULATION
1 + R = (1 + r1) (1 + r2) (1 + r3) (1 + r4) … (1 + rn)
R = TWR ri = holding period return in each sub-period
EXAMPLE
- Portfolio starting value of £100m
- Value after 6 months is £110m
- £2m cash dividend paid out
- Value at end of 12 moths is £130m
- HOLDING PERIOD
D + V1 - V0 R = ------------------- x 100 to get a % V0
R = holding period return D = income received during the period V0 = price/value at acquisition V1 = price on selling
2 + 110 - 100 r1 = --------------------- = 0.12 x 100 = 12%
100
130 - 110 r2 = --------------------- = 0.1818 x 100 = 18.18%
110
- LINK THE RETURNS TO CALCULATE THE TWR
1 + R = (1 + r1) (1 + r2)
1 + R = (1.12) (1.1818)
1 + R = 1.3236
R = 1.3236 - 1 R = 0.3236 or 32.36% (0.3236 x 100)
TWR - Description
TIME WEIGHTED RATE OF RETURN
- can compare the performance of one fund manager to another by eliminating distortions caused by the timing of new money
- does this by breaking down the return for a particular period into sub-periods
Investment Bond - Redemption Yield
SIMPLIFIED CALCULATION
REDEMPTION YIELD CALCULATION:
gain or loss / years to maturity
to maturity Interest Yield + or - ------------------------------------------- x100
clean price
EXAMPLE
- stock purchased for £126.85 per £100
- at redemption there will be a capital loss of £126.68 - £100 = £26.85
- five years to redemption
- capital loss each year is £26.85 / 5 = £5.37
- reduction in return is:
- 5.37
- ——– x 100 = -4.23
126. 85 - interest yield of 6.31% - -4.23 = redemption yield of 2.08%
Investment Bond - Redemption Yield
DESCRIPTION
BOND REDEMPTION YIELD
- is a more accurate calculation of the yield on a bond
- takes into account the income payments from a bond and the capital gain or loss from holding the bond until maturity
- adjusts the value of each payment according to when it is received
- assumes the bond is held to maturity and that coupons can be reinvested at the redemption yield
- assumes that the investor reinvests each interest payment
Sharpe Ratio
CALCULATION
SHARPE RATIO CALCULATION:
standard deviation of the return on the investment
EXAMPLE:
Return = 10%
Risk-free return = 4%
Standard Deviation = 8%
10 - 4 Sharpe Ratio = ------------ = 0.75 (or 0.75%)
8
Portfolio earned a 0.75% return above the risk-free investment.
Sharpe Ratio
DESCRIPTION
SHARPE RATIO
- is a measure of the risk-adjusted return of a stock
- measures the excess return for every unit of risk that is taken in order to achieve the return
WHAT IT MEASURES
- the higher the sharpe ratio the better the return on an investment compensates an investor for the risk taken
i. e. the better it’s risk-adjusted performance has been - a negative sharpe ratio indicates that a risk-free asset would have performed better
Alpha
CALCULATION
ALPHA CALCULATION
a = actual portfolio return - [Rf + Bi (Rm - Rf)]
BODMAS: 1. Rm - Rf 2. Bi x (Rm - Rf) etc
Rf = risk-free rate of return
Rm = market return
Bi = beta of the fund or portfolio
EXAMPLE
Portfolio return = 12%
Beta of fund = 1.5
Market return = 8%
Risk-free rate = 2%
Alpha
DESCRIPTION
ALPHA (JENSEN’S ALPHA)
- the difference between the return that would be expected from a security, given its beta, and the return it actually produced
- is the part of a return that cannot be explained by movements in the overall market
- sometimes referred to as ‘value added’
WHAT IT SHOWS
- positive alpha shows that the investment has performed better than expected given its beta
- negative alpha indicates that it has performed worse than expected given its beta
i. e. for a portfolio it allows us to quantify the value added or taken away by a manager through active management
Information Ratio
CALCULATION
INFORMATION RATIO CALCULATION
Rp - Rb Information Ratio = -------------------------
tracking error
Rp = portfolio return Rb = benchmark return
EXAMPLE
Fund return = 13%
Benchmark return = 10%
Fund tracking error = 6%
13 - 10 Information Ratio = ------------------------- = 0.5
6
Information Ratio
DESCRIPTION
INFORMATION RATIO
- used to assess the risk-adjusted performance of active portfolio managers
- shows the consistency to which they beat the benchmark index
- measures the relative return achieved by an investment manager divided by the amount of risk the manager has taken relative to a benchmark
NEGATIVE INFORMATION RATIO
- investor would have received a better return by matching the benchmark using tracker fund
Compound Interest
(Working out Future Value)
CALCULATION
COMPOUND INTEREST FORMULA:
FV = PV x (1 + r)n
FV = Future Value PV = Present Value r = Interest rate (shown as a decimal so 5% = 0.05) n = Time Period
Example:
PV = £5,000 r = 4% n = 5 years
Step 1 = 4% is 0.04. 0.04 + 1 = 1.04 or (1 + r)
Step 2 = 1.04 x 1.04 x 1.04 x 1.04 x 1.04 = 1.2167
or (1 + r)n or (1.04)5
Step 3 = £5,000 x 1.2167 = £6,083.50
or £5,000 x (1.04)5
or PV x (1 + r)n
Compound Interest
(Working out multiple interest rates and periods)
CALCULATION
CALCULATION:
FV = PV x (1 + r1)n1 x (1 + r2)n2
Example:
PV = £5,000 r1 = 5% n1 = 2 Years r2 = 7% n2 = 3 years
£5,000 x (1 + r1)n1 x (1 + r2)n2
£5,000 x (1.1025) x (1.225043)
£6,753.05
Effective Annual Rate
(When interest is paid more frequently than annually)
Same as APR or AER (se below)
CALCULATION
CALCULATION:
EAR = (1 + r/n)n - 1
Example:
r = 8% n = Quarterly
Step 1 = r/n or 0.08 / 4 = 0.02 Step 2 = (1 + 0.02) or 1.02 Step 3 = (1.02)4 or 1.02 x 1.02 x 1.02 x 1.02 = 1.0824 Step 4 = 1.0824 - 1 = 0.0824 Step 5 = 0.0824 x 100 = 8.24%
Annual Percentage Rate or Annual Equivalent Rate (APR or AER)
(When interest is paid more frequently than annually)
Same as EAR (see above)
CALCULATION
CALCULATION:
APR or AER = (1 + r/n)n - 1
Example:
r = 24% n = Monthly
Step 1 = r/n or 0.24 / 12 = 0.02 Step 2 = (1 + 0.02) or 1.02 Step 3 = (1.02)12 or 1.02 x 1.02 x 1.02 x 1.02 x 1.02 x 1.02 x 1.02 x 1.02 x 1.02 x 1.02 x 1.02 x 1.02 = 1.2682 Step 4 = 1.2682 - 1 = 0.2682 Step 5 = 0.2682 x 100 = 26.82%
Present Value
(Working out what amount to invest to get a certain amount at a certain point in the future with a certain interest rate)
CALCULATION
CALCULATION:
FV PV = ----------
(1 + r)n
Example:
FV = £1,000 r = 5% n = 5 years
Step 1 = (1 + r)n
or 1 + 0.05 = 1.05 x 1.05 x 1.05 x 1.05 x 1.05 = 1.276281562
Step 2 = £1,000 / 1.276281562 = £783.53
PV = £783.53
Accumulation of Regular Savings
(Regular savings and how interest is accumulated to give a Future Value)
Regular payments made at the END of each year
CALCULATION
CALCULATION
{ (1 + r)n -1 } FV = regular payment x { ------------ }
{ r }
Example
regular payment = £100
r = 8%
n = 10 years
Step 1: 0.08 + 1 = 1.08
or (1 + r)
Step 2: 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 = 2.1589
or (1 + r)n which is (1 + 0.08)10
Step 3: 2.4589 - 1 = 1.4589 / 0.08 = 14.48625
(1 + r)n - 1 2.1589 - 1 1.1589
or —————- which is —————— or ————
r 0.08 0.08
Step 4: 100 x 14.48625 = £1,448.63
{ (1 + r)n -1 } or FV = regular payment x { ------------ }
{ r }
{ (1.08)10 -1 } or £1,448.63 = 100 x { -------------- }
{ 0.08 }
Accumulation of Regular Savings
(Regular savings and how interest is accumulated to give a Future Value)
Regular payments made at the START of each year
CALCULATION
CALCULATION
[ { (1 + r)n+1 -1 } ] FV = regular payment x [ { ------------ } -1 ]
[ { r } ]
Example (Using calculation from previous card)
Step 2 is altered: 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 = 2.3316
or (1 + r)n+1 which is (1 + 0.08)10+1 or (1 + 0.08)11
Step 3 is altered:
2.3316 - 1 = 1.3316 / 0.08 = 16.6455 - 1 = 15.6455
Step 4 is therefore:
100 x 15.6455 = £1,564.55
Annuity Payment
(Sum of money needed to make regular payments, plus interest, over a fixed period and at a fixed rate of interest)
Payments made at the END of the year
CALCULATION
CALCULATION
[ 1 - (1 + r)-n ] PV of annuity = A x [ ------------------ ]
[ r ]
A = annuity paid each year r = rate of interest n = number of periods that the annuity will run for
Example:
A = £100 r = 8% n = 10 years
Remember: That because of -n, when you do the 1.08 / 1.08, you need to put a ‘1’ first like so:
1 / 1.08 / 1.08 / 1.08 / 1.08 / 1.08 / 1.08 / 1.08 / 1.08 / 1.08 / 1.08 = 0.4632
[ 1 - 0.4632 ] PV of annuity = £100 x [ ------------------ ]
[ 0.08 ]
Which is 1 - 0.4632 = 0.5368 / 0.08 = 6.71 x 100 = £671
Basic Formula for the Accumulation of Capital
CALCULATION
CALCULATION
FV = PV X (1 + r)n
Example:
PV = £1,000 r = 5% n = 4 years
Step 1: 1 + 0.05 = 1.05
Step 2: 1.05 x 1.05 x 1.05 x 1.05 = 1.2155
Step 3 : £1,000 x 1.2155 = £1,215.50
FV is therefore £1,215.50
Net Present Value
CALCULATION
CALCULATION:
CF1 CF2 NPV = CF0 + ------ + -------- etc
(1 + r) (1 + r)2
NPV = Net Present Value
CF0 = expected cash flow at the beginning of the investment period (usually negative and the cost of the investment)
CF1, 2 etc = the expected cash flows in the period. It is positive if it is a cash outflow being paid TO the investor and negative if it is a cash inflow being paid BY the investor
r = the investor’s required return
Example:
Ones Calculated
Year 0 -150 -150 (or CF0)
Year 1 25 22.7
Year 2 50 41.3
Year 3 55 41.3
Year 4 40 27.3
Year 5 60 37.3
NPV = 19.9 (add up years 1 -5 and subtract year 1)
Internal Rate of Return
CALCULATION
CALCULATION
CF1 CF2 0 = CF0 + ----------- + ------------- ETC
(1 + IRR) (1 + IRR)2
IRR = Internal Rate Of Return CFn = Expected cash flow in the period (n)
Example:
- Same as the Net Present Value
Internal Rate of Return
DESCRIPTION
INTERNAL RATE OF RETURN
- is the single number that represents the rate of return from an investment when there are a number of cash flows into/out of the investment
- used to decide whether a project has an attractive rate of return
- sometimes referred to as the effective interest rate and for a bond, the redemption yield
- it is calculated by finding the discount rate that will make the present value of the cash flows from the investment equal to the present value of the costs
- if the IRR exceeds the required return, the investment will increase the investor’s wealth
- if the IRR is less than the required return, it will reduce the investor’s wealth compared to the alternative investments
- the hurdle rate is a minimum rate which the IRR must exceed to make the investment attractive
Annual Depreciation Charge
CALCULATION
ANNUAL DEPRECIATION CHARGE CALCULATION
(STRAIGHT-LINE METHOD):
original cost - expected residual value Depreciation p.a. = ------------------------------------------------------
expected useful life
Example:
Original cost of tractor = £10,000
Useful life = 5 years
Expected resale/residual value = £1,000
Step 1: £10,000 - £1,000 = £9,000
Step 2: £9,000 / 5 = £1,800 (Annual Depreciation charge)
Financial Statement Calculations
CALCULATIONS & DESCRIPTIONS
SHAREHOLDER FUNDS & LIABILITIES
Its construction is underpinned by the accounting equation:
Assets = Liabilities + Equity
INCOME STATEMENT
Gross Profit Calculated:
Gross Profit = Revenue - Cost of Sales
Operating Margin
CALCULATION & DESCRIPTION
OPERATING MARGIN
- provides information about the profitability of a firm’s core business
- operating profit is the profit made after paying the operating costs of goods sold as well as general and administration expenses
CALCULATION:
Operating Profit Operating Margin = ---------------------------- x 100
Sales
Net Margin
CALCULATION & DESCRIPTION
NET MARGIN
- measures the percentage of net income of an entity to its net sales
- used to compare the profit of competitors in the same industry
- net margin represents the proportion of sales that is left over after all relevant expenses have been adjusted
CALCULATION:
Net profit after taxation Net Margin = ----------------------------------- x 100
Sales
Return on Equity (ROE)
CALCULATION & DESCRIPTION
ROE - Return on Equity
- is a measure of the profitability of the shareholder’s investment
- measures the percentage return the company is achieving on the amount of funds provided by shareholders
- with the funds provided by shareholders coming from two sources:
1. share capital and share premium (funds being paid by investors)
2. retained earnings (profits not paid out as dividends) - The higher the ROE the better
- ROE is heavily affected by differences in company capital structure
CALCULATION:
Net profit after tax ROE = ------------------------------ x 100
Total Equity
Earnings Compared to Capital Employed (ROCE)
CALCULATION & DESCRIPTION
ROCE (Earnings Compared to Capital Employed)
- determines how much the company has earned from the total of the different types of capital it has employed
- measures the percentage return achieved on the capital employed in the business
- ROCE is a better comparison between companies than ROE
- ROCE includes long-term finance and is therefore a more comprehensive test of profitability than ROE
- ROCE is limited though in that it does not account for depreciation
CALCULATION:
Profit before interest and tax ROCE = ------------------------------------------- x 100
Capital Employed
ROCE - Splitting it into two parts
- Means that you can identify which element/part is responsible for a fall or rise in ROCE
1. ASSET TURNOVER
2. PROFIT MARGIN
CALCULATION
PART 1: ASSET TURNOVER
- this shows how much of the return arises from good asset utilisation
Sales
CALCULATION: —————————
Capital Employed
PART 2: PROFIT MARGIN
- how much arises from profit and cost management
Profit
CALCULATION: —————————
Sales
THE FORMULA LINKING ALL THREE:
Profit before interest & tax ROCE = ------------------------------------------
Capital Employed
Sales Profit = --------------------------- x -----------------
Capital Employed Sales
Financial Leverage (Gearing) - CALC 1
CALCULATION & DESCRIPTION
FINANCIAL LEVERAGE
- the extent to which a company uses borrowed money
- carries a risk of bankruptcy
- but can lead to increased returns
CALCULATION:
(Long-term loans + preference shares) Gearing = ----------------------------------------------------------
(Total equity - preference shares)
- Debt to equity ratios of more than 100% are considered too high in the UK
- High gearing is usually more acceptable in the utilities sector
Financial Leverage (Gearing) - CALC 2
CALCULATION & DESCRIPTION
ALTERNATIVE METHODS TO CALCULATE GEARING
CALCULATION:
(Long-term loans + PS + short-term loans) Gearing = ----------------------------------------------------------
(Total assets - current liabilities)
PS = Preference shares
Interest Cover
CALCULATION & DESCRIPTION
INTEREST COVER
- How many times could the interest bill be paid out of current profits?
CALCULATION:
Profit before interest and tax
Interest Cover = ——————————————-
Gross interest payable
Working Capital (‘Current’) Ratio
CALCULATION & DESCRIPTION
CURRENT RATIO
- most investors like to see a cushion to protect a company against a downturn in sales
- generally, investors prefer to see that sufficient cash will be generated from current assets in the course of a normal business day to pay off creditors
- as a generalisation, the ratio should be between 1.5 and 2
CALCULATION:
Current assets Current Ratio = --------------------------
Current liabilities
Liquidity Ratio
CALCULATION & DESCRIPTION
LIQUIDITY RATIO
- this ratio is more cautious
- only measures those assets that can be quickly and definitely turned into cash
- the liquidity ratio should be at least 1
CALCULATION:
Current assets - stock Liquidity Ratio = -----------------------------------
Current liabilities
Working Capital
CALCULATION & DESCRIPTION
WORKING CAPITAL (NET CURRENT ACCOUNT ASSETS)
- represents the money that circulates through the business automatically
- i.e. money being spent on goods and services to enable production to take place and money being received as customers pay for their purchases
- when many small transactions are taking place very rapidly, working capital levels can grow unnecessarily large
CALCULATION:
Current assets - current liabilities = Net current assets
Debtor Turnover
CALCULATION & DESCRIPTION
DEBTOR TURNOVER
- is the ratio of a business’ net credit sales to its accounts receivable during a given period
- is an activity ratio that estimates the number of times a business collects its average accounts receivable balance during a period
- measures the efficiency of a business in collecting its credit sales
- HIGH FIGURE more favourable
- usually calculated on an annual basis
CALCULATION:
Sales Debtor Turnover = -------------
Debtors
Debtor Collection Period In Days
CALCULATION & DESCRIPTION
DEBTOR COLLECTION PERIOD IN DAYS
- expressed in days to represent the number of days that it takes the company to collect its invoices
- benchmark to beat is 60 days
CALCULATION:
Debtors
Debtor collection period in days = ————— x 365
Sales
Stock Turnover
CALCULATION & DESCRIPTION
STOCK TURNOVER
- is a ratio used to assess how efficiently a business is managing its inventories
- a high inventory turnover indicates efficient operations
- stock turnover is a measure of the number of times inventory is sold or used in a given time period, such as over one year
CALCULATION:
Cost of sales
Stock Turnover = ———————-
Stock
365 days / the answer gives how many days the stock is held for on average
Creditor Turnover
&
Creditor Payment Period in Days
CALCULATION & DESCRIPTION
CREDITOR TURNOVER
- evaluates how fast a company pays off its creditors (suppliers)
- the ratio shows how many times in a given period the company pays its accounts payable
- a higher value indicates that a company was able to pay them off quickly
CALCULATION:
Cost of sales Creditor turnover = -----------------------
Trade creditors
CREDITOR PAYMENT PERIOD IN DAYS
CALCULATION:
Trade creditors
Creditor payment period in days = ———————– x 365
Cost of Sales
Earnings Per Share (EPS)
CALCULATION & DESCRIPTION
EARNINGS PER SHARE (EPS)
- is a measure of the profitability of a company or the profit available to shareholders
- expressed as an amount per share
- this is so comparisons can be made between different shares and/or companies
CALCULATION:
Net Income EPS = ------------------------------------------
Number of Shares in Issue
Net Income = may be written as ‘Profit for the year’
Number of Shares in Issue = may be written as weighted average number of shares
TWO OTHER VERSIONS OF EPS:
- EBIT - calculated before the impact of interest payments and taxation
- EBITDA - provides a way for company earnings to be compared internationally
Price-Earnings Ratio (PE)
CALCULATION & DESCRIPTION
PRICE-EARNINGS RATIO
- measures how highly investors value a company in its ability to grow its income stream
- a company with a high PE ratio relative to its sector average reflects investors expectations that the company will achieve above-average growth
Reasons why a company may have a higher PE ratio:
- greater perceived ability to grow its EPS than others
- producing higher quality earnings than others
- being a potential takeover target
- experiencing a temporary fall in profits
CALCULATION:
Share Price PE = -------------------
EPS
Dividend Yield
CALCULATION & DESCRIPTION
DIVIDEND YIELDS
- give investors an indication of the expected return in a share
- can then be compared with other shares
- high dividend yield implies low dividend growth
CALCULATION:
Dividend per share
Dividend yield = —————————- x 100 = x%
Share price
Dividend Cover
CALCULATION & DESCRIPTION
DIVIDEND COVER
- the ability of the company to keep paying dividends at the current level
- looks at how many times the company can pay out that level of dividend based on profit for the year
- the higher the dividend cover the less likely it is that the company will have to reduce dividends if profits fall
CALCULATION:
EPS
Dividend Cover = ——————————
Dividend per share
Price To Book Ratio
CALCULATION & DESCRIPTION
PRICE TO BOOK RATIO
- measures the relationship between the company’s share price and the net book
- how much the shareholders are paying for the net assets of the company
- if the share price is lower than its book value, it can indicate that it is undervalued
- higher than book value means that it has above-average growth potential
CALCULATION:
Share price
Price to book ratio = ————————
NAV per share
Share Valuation
CALCULATION & DESCRIPTION
SHARE VALUATION
- expected return of a share based on anticipated dividends
- Gordon’s growth model is used to calculate
Drawbacks to Gordon’s growth model:
- only a few factors are considered in the valuation
- it assumes a single constant growth rate for dividends
CALCULATION:
Dividend
Share price = —————————————————–
(Return required - dividend growth)
Dividend: expected dividend one year from now
Return required: required rate of return for an equity investor
Dividend growth: growth rate of the dividends
Net Asset Value (NAV)
CALCULATION & DESCRIPTION
NET ASSET VALUE (NAV)
- represents the NAV per share attributable to ordinary shareholders
Useful for assessing the following:
- minimum price at which a company’s shares should theoretically trade
- the underlying value of a property company
- the underlying value of an investment trust
CALCULATION:
(Total Assets - Liabilities - Preference Shares) NAV = ------------------------------------------------------------------
Number of Shares in Issue
