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J10 - Discretionary Investment Management > Formulas > Flashcards

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

  1. 6% / 4 = 0.9
  2. 9 / 100 = 0.009
  3. 009 + 1 = 1.009
  4. 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%

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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
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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
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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

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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

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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

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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)
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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

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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

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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)

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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

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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
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13
Q

Unit Trust Buying & Selling Prices

A

Calculation:

                   NAV ------------------------------------------ = Buying & selling prices Number of units in existence
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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
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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

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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
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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
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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
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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%

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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
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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
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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
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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
  1. 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
  1. 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)
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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
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25
Q

Investment Bond - Redemption Yield

SIMPLIFIED CALCULATION

A

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%
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26
Q

Investment Bond - Redemption Yield

DESCRIPTION

A

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
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27
Q

Sharpe Ratio

CALCULATION

A

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.

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28
Q

Sharpe Ratio

DESCRIPTION

A

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
Q

Alpha

CALCULATION

A

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
Q

Alpha

DESCRIPTION

A

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
Q

Information Ratio

CALCULATION

A

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
Q

Information Ratio

DESCRIPTION

A

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
Q

Compound Interest

(Working out Future Value)

CALCULATION

A

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
Q

Compound Interest

(Working out multiple interest rates and periods)

CALCULATION

A

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
Q

Effective Annual Rate

(When interest is paid more frequently than annually)

Same as APR or AER (se below)

CALCULATION

A

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
Q

Annual Percentage Rate or Annual Equivalent Rate (APR or AER)

(When interest is paid more frequently than annually)

Same as EAR (see above)

CALCULATION

A

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
Q

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

A

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
Q

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

A

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
Q

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

A

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
Q

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

A

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
Q

Basic Formula for the Accumulation of Capital

CALCULATION

A

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
Q

Net Present Value

CALCULATION

A

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
Q

Internal Rate of Return

CALCULATION

A

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
Q

Internal Rate of Return

DESCRIPTION

A

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
Q

Annual Depreciation Charge

CALCULATION

A

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
Q

Financial Statement Calculations

CALCULATIONS & DESCRIPTIONS

A

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
Q

Operating Margin

CALCULATION & DESCRIPTION

A

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
Q

Net Margin

CALCULATION & DESCRIPTION

A

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
Q

Return on Equity (ROE)

CALCULATION & DESCRIPTION

A

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
Q

Earnings Compared to Capital Employed (ROCE)

CALCULATION & DESCRIPTION

A

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
Q

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

A

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
Q

Financial Leverage (Gearing) - CALC 1

CALCULATION & DESCRIPTION

A

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
Q

Financial Leverage (Gearing) - CALC 2

CALCULATION & DESCRIPTION

A

ALTERNATIVE METHODS TO CALCULATE GEARING

CALCULATION:

              (Long-term loans + PS + short-term loans) Gearing = ----------------------------------------------------------
                   (Total assets - current liabilities)

PS = Preference shares

54
Q

Interest Cover

CALCULATION & DESCRIPTION

A

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
Q

Working Capital (‘Current’) Ratio

CALCULATION & DESCRIPTION

A

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
Q

Liquidity Ratio

CALCULATION & DESCRIPTION

A

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
Q

Working Capital

CALCULATION & DESCRIPTION

A

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
Q

Debtor Turnover

CALCULATION & DESCRIPTION

A

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
Q

Debtor Collection Period In Days

CALCULATION & DESCRIPTION

A

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
Q

Stock Turnover

CALCULATION & DESCRIPTION

A

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
Q

Creditor Turnover

&

Creditor Payment Period in Days

CALCULATION & DESCRIPTION

A

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
Q

Earnings Per Share (EPS)

CALCULATION & DESCRIPTION

A

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
Q

Price-Earnings Ratio (PE)

CALCULATION & DESCRIPTION

A

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
Q

Dividend Yield

CALCULATION & DESCRIPTION

A

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
Q

Dividend Cover

CALCULATION & DESCRIPTION

A

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
Q

Price To Book Ratio

CALCULATION & DESCRIPTION

A

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
Q

Share Valuation

CALCULATION & DESCRIPTION

A

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
Q

Net Asset Value (NAV)

CALCULATION & DESCRIPTION

A

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

J10 - Discretionary Investment Management (15 decks)

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