Formulas Flashcards
1
Q
Annual Equivalent Rate (AER)
CASH INVESTMENTS
SEE LATER CARD FOR MORE DETAILED EQUATION WHERE MORE FREQUENT INTEREST PAYMENTS USED
A
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%
2
Q
Conversion Premium / Discount for Convertible Bonds
BOND INVESTMENTS
A
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
3
Q
Interest Yield
BOND INVESTMENTS
CALCULATION
DESCRIPTION
A
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
4
Q
Redemption Yield (Part 1 of 2)
BOND INVESTMENTS
THIS IS ALSO SHOWN LATER ON (SIMPLIFIED)
A
Market Price (mp) Calculation:
Face value x clean price / 100 = mp
Example:
£1,000 x £124.27 / 100 = £1,242.70
5
Q
Redemption Yield (Part 2 of 2)
BOND INVESTMENTS
A
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
6
Q
Duration
BOND INVESTMENTS
A
Duration allows the sensitivity of one bond verses another to be compared:
E Net present value of the cash flows to be received
7
Q
Modified Duration 1 of 2
BOND INVESTMENTS
A
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)
8
Q
Modified Duration 2 of 2
BOND INVESTMENTS
A
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
9
Q
Ex-Rights Price
EQUITY INVESTMENTS
A
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
10
Q
Rights Premium
EQUITY INVESTMENTS
A
Using the example from ‘Ex-Rights Price’:
Ex-Rights price of £4 - new share (rights issue) price of £3 = £1 (Rights Premium)
11
Q
Bonus Issues & Share Splits
EQUITY INVESTMENTS
A
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
12
Q
Initial Yield
PROPERTY INVESTMENTS
A
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
13
Q
Unit Trust Buying & Selling Prices
A
Calculation:
NAV ------------------------------------------ = Buying & selling prices Number of units in existence
14
Q
Gross Domestic Produce (GDP)
A
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
15
Q
Capital Asset Pricing Model (CAPM)
A
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
16
Q
Capital Asset Pricing Model (CAPM) - Assumptions
A
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
17
Q
Holding Period Return - Calculation
A
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
18
Q
Holding Period Return - Description
A
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
19
Q
Relative Return - Calculation
A
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%
20
Q
Relative Return - Description
A
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
21
Q
MWR - Calculation
A
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
22
Q
MWR - Description
A
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
23
Q
TWR - Calculation
A
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)
24
Q
TWR - Description
A
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
25
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%
26
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
27
Sharpe Ratio
CALCULATION
SHARPE RATIO CALCULATION:
return on the investment - risk free return
--------------------------------------------------------------
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.
28
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
29
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%
30
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
31
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
32
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
33
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
34
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
35
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%
```
36
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%
```
37
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
38
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 }
39
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
40
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
41
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
42
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)
43
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
44
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
45
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)
46
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
47
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
48
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
49
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
50
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
51
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
52
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
53
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
54
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
55
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
56
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
57
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
58
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
59
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
60
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
61
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
62
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:
1. EBIT - calculated before the impact of interest payments and taxation
2. EBITDA - provides a way for company earnings to be compared internationally
63
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
64
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
65
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
66
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
67
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
68
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
