Models Flashcards
No tax theory of Modigliani and miller 1958
The theory developed by MM was based on the premise of a perfect capital market:
No transaction costs
No traces
All investors are rationale and risk averse
No individual dominates market
Full market efficiency
MM Argued (to do with WACC)
Investors are rational, ke is directly linked to the increase in gearing
As gearing increases, ke increases in direct proportion
The increase in ke exactly offsets the benefit of cheaper debt finance
Therefore wacc remains unchanged
Conclusion that WACC and value of firm is unaffected by changes in gearing levels and gearing is irrelevant
MM five years later with tax
Modified model to reflect the corporate tax system gives tax relief on interest payments
Debt interest is tax deductible so the kd is lower than before
The increase in ke does not offset the benefit of cheaper debt finance
= wacc falls as gearing increases
Conclusion = gearing up reduces WACC
Optimal capital structure is 99.9% gearing
Firms with high levels of gearing why they don’t like it
Increased bankruptcy risks - as hearing increasing the risk of going bankrupt increases, which will cause kd to rise and ke to rise faster
Tax exhaustion- tax shield on debt may not be achieved if the company profits are not high enough to cover the interest costs
Agency costs - directors may be more risk adverse than the shareholders as their livelihood depends on the company remaining solvent
Practical influences on gearing policy
Costs of raising finance
Asset quality
Loan covenants
Av of other sources of finance
Levels of other risks
How to calc growth rate over years
Take the end value / start value * to power of 1/number of years then -1 and this is the growth rate per year
Can also be calculated via g = b x r
Where g is growth rate
B is the earnings retained and reinvested as %
R is return on investment %
Market value of shares is
P0 = D0 (dividend) (1+ growth rate) / (ke which is cost of equity - growth rate)
If you need the value of the share then divide by amount of ordinary shares
Investment appraisal (NPV)
Contribution
Fixed costs
Net trading
Tax
Then
Relief on WDA: is the initial x reducing balance then the tax of that amount - express as positive
If doing working capital and says all is back at end then you do -big part first year then - the additional working capital and the last year is the positive of the sun of all them figures to equal 0
Then once done all thag do the dosicount of these
How to calc market value of ordinary shares
If growth over number of years then do the end figure / start figure to power of 1/number of years -1.
Then put in formula:
Ke = dividend (at end) * (1+g growth rate) / price of share now Then add g
That’s cost of equity
Mv is the price of share * amount of ordinary shares
How to calc cost of preference shares and mv of preference shares
Same formula as cost of equity but no growth used
Kp = dividend (at end) / price of share now
To calc div it’s the % of pref shares * 1
Then current price will be given
Mv of shares is the current price * number of shares
To calc cost of bank loan and mv of bank loan
Kd= I which is the interest / 1-T tax rate
No mv so use book value
Redeemable debt calc the cost of debt and mv of debt
To calc cost of debt it’s IY (1-T)
IY is is the interest yield = IRR of loan of cahs flows
In spreadsheet do:
Number of periods
Interest
Current market price
Redemption value 100
IY = RATE(all value stated above) = %
Then for KD= % (1-tax rate)
The market value is amount / redemption value - current market price
To calculate a wacc
Ke * mv of equity (this is ordinary shares)+ kp*mv of pref shares (this is pref shares) + kd *mv of debt (this is all the debt so the bank loan, redeemable debt etc)
Then all divided by mv of equity + mv of pref shares + mv of all debt
Expressed as %
How to calc net asset basis (historical cost) when comes to shares
Add the ordinary share capital + retained earnings then divide by number of orginary shares
This gives value of one share
How to calculate net asset basis (revalued) when cokes to one share
Look for adjustments
So add historic basis calc (ordinary + retained) + add / - any adjustment to land and building equipment etc
Then this figure divided by amount of ordinary shares
Price earnings method for calculating shares
Pe= earnings +* P/E ratio
Earnings is profit after tax and after pref share dividends (NOT ORDINARY)
Then that * PE ratio
To calc money per share : total figure calculate above / amount of ordinary shares
To calculate dividend yield if working out mv of an share
It’s the ordinary dividends / yield
Then this figure / number of ordinary shares if the mv of one share
To calc PV of future Cash flows for one share
Do the pre tax cash flows
Takeaway tax
= net cash flows
Discount factor (1/1+r)
Then sum is pv of cahs flows
To calc value per share ite this figure / number of ordinary shares
Financial gearing formula
Debt / equity or debt / debt + equity
Operating gearing
Fixed costs / variable cost or fixed costs / tota costs
Cost of equity (Ke) formula
If the dividends are expected to grow at a rate of g%, you need to find the price of the share: (also known as mv of share)
Price = dividend (1+growth rate) / ke - g
If share price known:
Ke= dividend (1+ growth rate) / price then add growth rate
Ex div and cum div for shares
Ex div is price quoted directed following a dividend payment (don’t do anything with)
If cum div it needs to be adjusted:
Cum div price - dividend due = ex div share oeice
If says ‘About to pay’ this is cum div
Two ways of estimating growth rate of dividends:
Historic method: annual growth =
To the power of number of years square rooted (dividend at end / number of years Then -1
Or growth = dividend at end / number of years then to power of 1/n then -1
The earnings retention model (golden frowth model):
G = r x b
R = accounting rate kf return on new investment
B = earrings retention rate
You then for both if working cost of equity (Ke) jsut add the figure you calculated for g in the normal formula;
Ke = dividen at end (1+ growth rate) / price of share at end + growth rate
When working out growth of shares when there’s been new issues / right issues
Do the end dividends / number of shares
Then at start for all the rights issue / bonus so say there was a 1:2 in year 2 and 1:1 year 3, apply that to the starting shares for year 1 eg if it was 12 then it’s be 12/2 =6+12=18 then 18*2=36
Then do the dividends oaid / that figure calculated
Then the growth is the last years div per share / first years adjusted div per share All to power of 1/n for number of years. Then take away 1 is the growth (g)
Cost of preference shares (Kp)
Price is = dividend at end / cost of preference shares (Kp)
Then rearrange so Kp= dividend at end / price
Eg 50,000 8% pref shares, nom value £1, mv is 1.20 a share.
The cost of preference shares = 8/1.20=6.7%
Cost of irredeemable debt (Kd) - final part you add to wacc
So the price = interest (1-T) / Kd
So rearrange = Kd = interest (1-T) / price
Eg irredeemable debt trading at 40. Coupon rate is 5% and corp tax is 25%.
Kd = 5%(1-25%) / 40 = 9.375%
How to calc pricd of debenture (last part of WACC)
=PV (investors required return, number of time periods, interest value, redemption value) > put in formula for spreadshads
How to calculate yield on debt
Yoj do the IRR(cash flows)
Or
RATE(number of time periods, interest payment, market value, redemption value)
Then to calc of cost of the debt it’s
The yield * (1-tax)
How to calculate semi annual coupon payments (eg cross yield)
First find out number of time periods eg loan of five years but pay interest every 6 months it’s 10
The interest would be the annual figure then * 6/12
Then use same method:
Rate(number of time periods,interest payment, market value, redemption value) then multiply to get to annual figure eg every 6 months is * 2
How to calculate cost of convertible debt to company
Treat as same as redeemable debt but with adjustments to:
Compare the redemption value with the value of the conversion option
Select the higher of the two values as the amount to be received at Tn
Find the IRR of cash flows
Example:
Company issued convertible loan stock which is due to be redeemed at 5% premium in 5 years time. Coupon rate is 8% and mv is 85 per 100 par. Instead of redemption payment the investor can choose to convert the stock into 20 shares on the same date.
Company’s sharss are worth 4 and value expected to grow at rate of 7%. Corp tax is 25%.
Cost of convertible debt =
First: compare redemption value with conversion value:
Redemption value = 100 x 1.05 = 105
Conversion value is 20 * 4 (1.07)^5 = 112.20
Then select higher of two values to be amount received at Tn so use 112.20
Then to find yield of the debt it’s:
Rate(time periods, interest value, market value, redemption value)
Rate(5,8,-85,112.20) = 14.2%
Then the cost of debt = yield * (1-t)
14.2% * (1-25%) = 10.7%
To calculate non trade bake debt
Cost = interest rate * (1-T)
When is it appropriate to use WACC as a discount rate for a project
- if proportions of debt and equity (gearing) are not going to change over life of the project. If gearing changes then the wacc itself will change and another approach is used (APV).
-if the level of risk is not going to change. The Ke (cost of equity) is dependent on current level of risk the shareholders are suffering. CAPM used to calculate Ke if level of risk may be different eg new business operations
-if the finance is not project specific. The wacc utilities several different types of finance in order to calc average. If they only use one method finance then average isn’t used (would use APV)
Assumptions when using the dividend valuation model
A perfect market is operating to ensure
That the share price is the pv of the future dividends discounted at Ke.
Dividends are paid only once a year and have just been/about to be paid. Sometimes companies pay interim dividends. Also dividend growth is expect to be reasonably constant and predictable (in practice could be erratic)
If using historic dividend to predict growth an assumption past is good diode to future (but if circumstances change in future may not be as reliable)
If using the retention model to predict growth an assumption is made on the rate of return and retention rate will remain constant over time (but circumstances may mean thsi doesn’t take place eg changes)
Other issues using wacc
Ideally only using permanent long term sources kf finance in WACC calculation but some companies use overdrafts, leasing etc these aren’t included in wacc but could affect true cost of capital
Calculating wacc for smaller unquoted trading company is difficult as no market value to obtain accruals results and Amal size usually results in more expensive finance
Main reason for swaps (hedging)
Swaps used to hedge against adverse movement in interest rates eg company has 200m floating rate lon and believe the interest rates are likely to rise over next five years then stable after. The treasurer could enter into a five year swap with counter party for fixed rate of interest for next five years, then on year six move back to floating rate of interests
A swap can be used to obtain cheaper finance (better rates)
Swaps can be run for up to 30 years - pref for long term borrowing
Transaction costs involved in swap may be cheaper than costs involved in refinancing
Disadvantages of swaps (hedging)
Counterparty risk (the risk the counter party will default)
Market risk (the risk of an adverse movement in interest or exchange rates)
Transparency risk (the risk that the accounts may be misleading)
Two types of values when purchases of an option pay a premium to the writer of the option to buy it
Intrinsic value - difference between exercise prince and current market value
Known as in the money - eg market price is 5 and call option of 4.59 would have an intrinsic value of 50p
Time value - difference between actual premium and instrinsic value
Time value of a call option increases with time to expiry, volatility of underlying share and interest rates
Forward/future vs option
Forward /future:
Eliminates risk completely
No downside risk, but no upside potential
If underlying transactions falls through, the business is re-exposed to the risk
Option:
Downside risk is eliminated
Upside potential is retained
If underlying transaction falls through there is still no risk
Therefore options more flexible than forward but are more expensive
Exchange rates
As a trader you buy low and sell high for exchange rates - this is the 1.1-1.2
As the bank will buy the foreign currency at lower rate as they get more money
As the bank will sell the foreign currency at higher rate as they give away less money
IRR
IRR is the IRR(discounted cash flows)
If exceeds cost of capital should accept as will enhance shareholder weath. If below cost of capital should decline
IRR easier to understand for employees and managers but IRR does not calculate the change in absolute shareholder weath. As a conseqnuce it may provide the wrong result when alternative projects are being ranked. Also non conventional cahs flows can create more than one IRR
Benefits of leasing to buying an asset
Tax: tax effects are different
Capital rationing: firms who can’t raise capital finance to buy an asset can effectively use the asset acquired
Cash flow: avoids large cash outlay at the outset. Also predicatble payments with leases easier for business planning
Cost of capital : implicit cost of borrowing a lease can be lower than that in a conventional bank loan
Flexibility: ease of arrangement; lower payment in earlier stages, service, insurance
Hedging with forwards - discount / premium
If discount:
You add the discount to the exhcnzge rate - so the individual get more $ per £
Currency therefore has been depreciated
If premium then less $ per £. If premium then subtract.
Currency is appreciated
Dividend valuation model explanation
Shareholders benefit from owning a share by receiving dividend into the future and a capital gain on the value of the shares.
The pv of there benefits creates the current price of the shares. This share price is determine by expected future dividends discount at investors required rate of return (Ke)
CAPM explanation
CAPM is a specific/unsystematic risk can be diversified away by investors, so it’s assumed that investors are rational and that they have a diversified portfolio. Systematic risk cannot be diversified away - macro economic factors.
A company’s beta is calculated from the performance of its share price against the market average and is taken as a measure of the markets view of the risk attached to the securities in question.
The higher the perceived risk then the higher the beta figure and thus the higher equity return required by investors
What WACC to use scenario - what would you say
Is the gearing too high if they get a loan? Debt / equity
Systematic risk
In reality if something new like loan then new wacc should be calculated that includes the new cost of debt
To calculate APV
Calc a base Cass value at ungeared cost of equity
Calculate the pv of the tax shield arising from extra debt
Adjust for issues costs
Sum = APV, if positive accept .
Portfolio effect
Al about how much risk can be removed.
Initial diversification will bring about substantial risk reduction as additional investments are added to the portfolio
But risk reduction slows and becomes insignificant once 15-20 investments have been combined
Think gambling one 59 quid bet or 10 5 pound bets. The more diversified bets the slower risk reduction is.
Unsystematic risk vs systematic risk
Unsystematic risk is unique risk to the business
Systematic risk is market risk
Pe ads / dis
The Pe method is useful for Growth companies and reflects the industry sentiment regarding a particular sector.
May be better to use industry sector average
Is it reasonable to use the past years results as basis for valuations?
Accounting policies can be used to manipulate earnings figures
Enterprise value ads / dis
Enterprise value excludes CAPEX so allows the business to compare companies in the same industry
Method is simplistic and lots of information from many value drivers is distilled into a single number
Is it reasonable to use average of past five years
Accounting policies can be manipulated
Asset methods (historical and revalued) ads and dis
Asset methods does not take into account earnings potential of the asset and ignores goodwill
When assets are revalued it’s not guarantee they are sold at NRV
Shareholder value analysis ads/dis
Shareholder value analysis evaluates future free cash flows and is more representative of the true value of the company
Method relies upon assumptions that might be unrealistic eg estimating future frowth periods for the primary period
When valuing a company at going concern
If going concern shouldn’t value using asset method since it does not reflect their earning capacity
Predictive vs prescriptive analytics
Predictive analytics uses historical and current data to create predictons about the future
Predictive analytics could be used to forecast the impact of each alternative
Prescriptive analytics combines statistical tools utilised in predictive analytics with AI and algorithms to calculate the optimum outcome from a variety of business decisions
Rights issue to calc terp
Do the additional shares value + original share value. Add the npv of investment. Then the total shares / sum of calc is term
When calculating investors wealth after rights issue (TERP)
If takes up right then do all shares (inc of additional taken) * terp. Then less cost of extra shares. Then gain is this - current wealth
If sells rights it’s holding * terp. Less additional sells sold * terp - sale price of shares sold.
Does nothing is shares * terp. Then this - current wealth
Money market hedge
If you receive money from contract:
First calc the borrowing of the foreign currency: fee received / 1+( borrowing rate of the foreign currency * number of month contract is)
Then you sell the foreign currency at spot rate (so trader sells high spot rate): the figure calc above / high spot rate
Then you deposit £ to give total receipt: so money calc above * 1+(deposit of uk interest rate * 3/12 or 6/12) then this is the answer
Forward contact when receiving money from contract
Spot rate used is the higher one as trader sells high
If discount add if prem deduct
Then the contract value / this figure
OTC Currency Option when receiving foreign money from contract
Use PUT option to sell currency with the put option exercise price
Then work out premium if any
If interest then work it out on premium too
Then need to see whether accept the project(exercise or not): if the spot rate at date of contract ending (usually at end of question) is better than original spot rate taken then exercise.
Then do contract / original spot rate (as taken deal)
The receipt is the figure above - cost of premium
Ads and dis of the options
Pick the option with the highest net receipt (don’t forget to do the non Heding calc too which is contract / spot rate at end)
Will choose one with highest net receipt but if OTC is there can say that the OTC currency option may be preferred if the directors wish to retain the upside risk potential
Ads and dis of forward contracts
Ads of forward contract is that is tailored to the business
Dis of forward contact is there is no secondary market
Ads and dis of money market hedge
Ads of money market hedge is synthetic forward positions cns be built in currencies for which there are no forward contracts
Dis of money market hedge is more difficult to set up than a forward contact
Dis of money market hedge is they might use up credit lines
Dis is relatively expensive hedge
Dis is might not be feasible if contstaints on borrowing or lending
Ads and dis of OTC currency option
Ads of otc currency option is allows business to exploit upside risk potential
Dis of otc currency option is there is no secondary market
Options are expensive
Forward contact with Bitcoin if receiving Bitcoin
If receiving Bitcoin then it’s the Bitcoin number * higher of higher spot rate or higher month Bitcoin forward price
Bitcoin futures when receiving Bitcoin
When receiving Bitcoin:
You will sell futures at the future price
Then work out number of contracts
Then work out sale of Bitcoin on date of disp ( number of Bitcoin contracts * lower of spot rate at y/e or future price at month (remember it’s the first one in spot rates))
Then the gain is sell price - buy price * number of contracts * size of contract
Net receipt is this figure + the original sale
Why the two sterling receipts may differ
They are offered at different rates
If number of contacts is .something eg 5.2 you take 5 as contacts so future contact may not cover full transaction
Put and Call options for OTC
If the company is going to be BUYING the currency in the future, then it will be buy a CALL option eg
If the company if going to be SELLING currency in the future, then it will need to buy a PUT option eg receiving money
Traded options out and call
If company is going to be buying currency in future then it will be selling sterling - so buy PUTS. EG company owes €150k invoice in 2 months
if company is going be selling currency in the future then it will be buying sterling so buy CALLS eg receding money
If FTSE100 index risk - if ftse100 falls or rises
If FTSE 100 rises;
If company has spare cash then it should buy PUT options
Calc number of contracts
If premium workout
Should let options lapse
If ftse falls:
Then exercise option:
Gain is the value - value at sold x contracts
Then net receipt is what sold for + gain - premium
Forward contacts when you have to pay foreign invoice in future
Forward spot rate is the lower and then if discount add
Then contract / fig above
Money market hedge when paying invoice in foreign in future month
Deposit in € contract / 1+(Deposit IR for foreign x 3/12)
Then: buy € at spot: figure above / lower spot
Borrow in uk = figure above * 1+(uk borrowing * 3/12) is total
OTC currency options when paying foreign invoice in future month
So this will be the PUT option
Premium is value of contact * prem
If interest do
If spot is 1.2 and exercise is 1.3 then benefitcla (higher accept)
So exercise option: contract / higher spot = x
Then net receipt is that + premium
FTSE 100 question
First work out the value of the contract if index per point is 10 then it’s thag times the index future
Then work out number of contacts so portfolio value / fig calc aboce
Then see if portfolio increases / falls in value at end of point in tiem:
Portfolio value (ftse index price at end / ftse index at start) if less than portfolio at starts its fall and poss its gain
If loss no gain on future contracts
Future position will be closed:
Future price at March - ftse 100 price) x index point x contracts
Why hedge will not be 100% efficient
Basis risk - price not same
Contracts have to be rounded
How to mitigate economic exposure
Diversify operations worldwide
Market and promotional management
Product management
Pricing strategy
If receiving money
Use higher spot rate for forward
For money market do the borrowing on foreign and deposit on uk
For otc use the put option
For paying money
Use the lower rate for forward
For money market use the deposit for foreign and uk for borrowing (high low)
For otc use the call option
High high low call
Interest parity
Interest parity links the forward exchange rate with interest rates in an exact relationship because risk free gains are possible if the rates out of alignment. The forward rate tends to be an unbiased predictor of the future spot exchange rates
To work out it’s: middle spot rate * (1+ middle foreign interest rate) / (1+ middle uk interest rate)
Purchasing power parity
Purchasing power pair is the theory that in the long term exchange rates between currencies will tend to reflect the relative purchasing power of the currency of each country
Theory based on idea thag a basket of goods in one country will after the effect of exchange rates, cost the same no Matter where it is traded. It is sometimes called the law of one price.
The impact of different inflation rates in different countries will cause prices to be changed at different speeds. So even if parity is achieved, disequilibrium will be created. Purchasing power parity predicted that the disequilibrium will be removed by changes in the exchange rates
If receiving money for money market
Borrow dollar so - borrowing rate x m/12 +1
Then convert at spot (higher)
Then lend at uk rate - lending rate x m/12 + 1
Currency traded option when receiving foreign income
Buy £ so it’s a call option
Work out number of contracts: contract / exercise price then that / price per contract = contracts
Cost of option is number of contracts x call option in month of rec money x contract price
Then do future spot rate (be at end of q)
Bought for (exercise price)
Profit if + and loss if neg
Then due from customer is contract
Gain on option of profit or nothing if loss
Then due from customer (add both)
Then convert due so value above / spot rate (high)
Then less cost of option
Then that’s net receipt
When assessing what hedging option to go for
go for one with highest amount - do the no hedging too (contract / high spot rate at month of contact)
If there’s a premium indicates the forward contract premium that the market is expecting the dollar to
strengthen (sterling to weaken).
The forward contact and money market hedge both give a fixed Sterling receipt
Differences between OTC and traded currency options
Otcs are typically purchased from a bank
Otcs are tailor made so lack negotiability
Traded options are for standardised amounts and can be traded and a profit/loss made
Traded options are not av for every currency
When giving advice on what to use - when the example is you are paying
Use the cheapest net receipt
If hedge is higher than rest then could assume sterling will strengthen not weaken over time
Directors attitude to risk is also important when giving advice on which strategy to pursue
How to do a traded sterling interest rate future
Call the contact size:
Amount of contract / contract size * number of months borrowing is needed/3 months
Then compare the opening and closing rate (opening is future oeice given in question and closing is given at question end part) - this gives movement
Then work out profit / loss on futures so: contract size * number of contracts * period of future (3/12 usually)
Then work out profit or loss on future by timsint value above by the movement calculated.
Then work out interest cost: contract x months you borrow
Then multiply this to the interest rates for each one
The total cost then is the interest costs + the profit /loss on futures
OTC interest rate options
Compare interest rates given vs the interest rate at the strike rate
If strike rate is less than take that, if more then don’t exercise
Then do the interest cost of contract size x number of months need to borrow loan for /12
Then multiply that by the interest rates used
Add the premium
Equals total costs
Ads and dis of using currency futures over forward contacts
Ads are lower transaction costs and the exact date of receipt or payment does not have to be know
Dis is;
The contacts cannot be tailored to the users exact requirements
Hedge inefficiencies due to needing contacts which are rounded
Only a limited number of currencies can make use of future contracts
If neither currency is in dollar needed then this will complicate matter
Intrinsic value in practice:
Option has ex price of 355 and market Price of 365
Option has ex price of 370 and market price of 365
The intrinsic value is the different between market price - exercise price
So here it’ll be 10p
For the 370 one; there is zero intrinsic value as the exercise price is in the money
Time value in practice:
Call option:
355 ex price 365 mv price
370 ex price 365 mv price
Put option:
370 ex price and 365 mv price
355 ex orixe wnd 365 mv price
For call:
The value below the mv can have intrinsic value > 365-355=10p
The 370 has a zero intrinsic value
For put:
If ex price higher than the mv then insytinsic value > 370-365=5p
If ex prince less than the mv then zero intrinsic value
Time value:
Call option:
Put option:
This is calculated by deducting the intrinsic value from the option premium
Time value of options is affected by:
Time period to expiry of options
Volatility of the market price of underlying item
General level of interest rates
Real options (NPV)
NPV analysis considers cash flows related directly to a project. This is because of real options associated with a project that outweighs the negative NPV. In other words there is extra value in a project that needs to be considered and evaluated
Sensitivity analyis
NPV of whole project / npv of cash flow affected by change
It facilitates subjective judgement
It identifies critical areas to the success of project
It is relatively straightforward
Dis:
Assumes chAnges to variables can be made inpedenelty
It ignores probability
It does not point to a correct decision
Simulation activities ads and dis
Ads = more than one variable ata. Time cns be changed
It takes probabilities into account
Dis:
Not a technique for decision making
It can be time consuming and expensive
Certain assumptions that need to be made can be unreliable
Three factors that affect time value of an option
Time to maturity - more time to maturity the more chance the option will be in the money
Risk free rate - level of risk free rate will affect interest element in option
Volatility - higher volatility will increase option value as more of chance option being in the money or deeper in the money at expiry
FTSE Index OPTIONS- if they want to sell as worried prices will fall
Requires option to sell so put option
If index rises then abandon and takeaway premium
If index falls then exercise and you sell option and buy new index. Add the gain and less the premium to portfolio
FTSE INDEX FUTURES - trying to sell
Do normal contracts etc with current portfolio
Use the new portfolio as starting block for calc:
If the portfolio is more than original it’s a loss. So the loss calc by new price - old price x 10 x contracts
Then minus this to portfolio
If portfolio decreases then there’s profit
So the original - new buy piece x 10 c number of contracts
Add this to portfolio
FTSE INDEX FUTURE IF NOT GOT PORTFOLIO
Work out number of contracts (use index future!
Do portfolio / contracts x 10
Then divide the portfolio by index (not future)
If greater than original then theres loss in index so do difference between future prices x contract x 10
If less than original portfolio this is offset by gain on fufure price so difference between two x 10 x contact size
Purchasing power parity
Is the theory that the long-term exchange rates between currencies will tend to reflect the purchasing power of the currency of each country
Theory based on idea of a good in one currency after the effect of the exchange rate will cost the same no matter where it’s traded. (Also law of one price)
Impact of different inflation rates will cause prices to change at different speeds. So even if parity achieved, disequilibrium will be created. Purchasing power of parity predicts that disequilibrium will be removed by changes in the exchange rates
Purchasing power parity formula
Current spot rate x 1+inflation foreign / 1+inflation uk = future spot rate
Interest rate parity formula
Current spot rate (add both divide by 2)
Times
1+foreign interest rate (add both divide then times by time apportion)
Divided by
1+ uk (add both divide by 2 then times by a portion)
This equals the forward rate
If there’s discounts in the question then the forward rate will be calculated as less than the current spot rate. So say that the foreign currency is depreciating against Sterling at a discount
Then add discount to forward rate and this is Tom he two forward rates
Methods by which management might fund its MBO
From managements equity
From venture capitalists - via equity and debt
Borrowing from bank - debt
SVA
Trick is last one is do normal cahs flow then discount factor then that / by the cost of capital then add this figure to pv of others
Less any debt and add any short term investments
Remember tax and depreciation is after tax
Methods of divestment
Divested means sold and companies sold for a number of reasons like raising cash, lack of fit; diseconomies or scale and cheaper than liquidation
Methods of divestment include;
Spin off - where shares in subsidiary are given to shareholders of parent
Share repurchase: company buys back shares from shareholders (helps with control, gearing)
Debt for equity swap: where creditors give up their debt (usually bank with loan) in reruns for an equity stake in company. Usually happens when company can’t pay debt
Liquidation: when company wound up and assets passed to shareholders
Forward rate agreement
An FRA is a commitment to an interest rate on a future loan
It is tailor made (lack of negotiability)
Workings of FRA:
If company has requirement to borrow money, to offset risk of an interest rate rise, the company enters into an FRA
So cap amount is borrowed and interest is paid on loan
If the interest is greater than the FRA the FRA contract pays the difference to the company, if the interest is less than agreed forward rate the company pays the bank the interest
Fra if borrow 8m at 5% and interest rate is 7 and 4% in three months time
So you lock into effective interest rate of 5%: 8m x 5% x 3/12 = 100,000
Then if interest rate rises to 7% then there’s a receivable from bank of 140,000 (8m x 7% x 3/12) so receivable of 40,000
A rise in interest rates causes a gain to business BUT FRA Hedges this so no gain no loss is payable
If interest falls to 4% then company pays bank: 8m x 4% x 3/12 = 80,000
So loss of 20,000
A fall in interest rates causes a loss to occur for business but FRA hedges this so no gain no loss is payable
So company is protected from rise in interest rates but is not able to benefit from a fall in interest rates. The fra hedges the company against both an adverse and favourable movement in interest rates
Interest rate futures
Standardised amount so more choice
Selling future contracts fixed the interest paid on borrowing
Buying a future contracts fixes the interest received on deposits
If your sell is higher than buy it’s a gain
Gain x number of irfs x size x apportion
Eg wants to borrow 1 mil for period of 3 months. He sells 2 500 June irfs at 95 each. What’s impact on hedge if interest rates rise to 6.5%
So wants to borrow so this is sell IRFs
Price is 95 so 5%
Needs 2
So he sells at 95
Then buys at 93.5 (6.5%)
Gain of 1.5 x 2 x 500,000 x 3/12 = 3750
Borrow at market for 6.5% so 1m x 3/12 x 6.5% = 16,250
Less profit so net cost is 12,500
Interest future if wanting to buy futures
So they want to invest 3m and are concerned interest rates will fall. If buying futures of interest fall it results in loss on future
Buy 94.5
Sell 95
Loss 0.5 c x borrow amount x apportion
Then workout number of futures bought for:
Contact size x number of contract x time a portion x
Offset by futures contract will rise in price by 0.5% so gain of 7500
Interest rate options
If lending it’s call
If borrowing it’s put
If lending:
Interst rates at exercise are 4,5 and 6
Option to invest 10m for 4 months at 5%
So exercise is 5,5,5
Spot 4,5,6
Excerckze: yes, don’t matter, no
Interest received = 10m c 4/12 x 5%,
10m x 4/12 x 5%
10m x 4/12 x 6% (not exercised)
Then add premium : 10m x 4/12 x 3%
Deducted to net cost
Traded interest rate options
If borrowing it’s purchasing put
If lending/investing it’s purchasing call
If investing so purchasing call compare the buy price to sell, if buy more then don’t exercise if less then exercise
Then gain x contract sizes x contracts x time Appleton
Interst on investment
So do contract x time x the diff Interst rates
The gain on option add if not don’t
Option premium add
Bet
Reasons for an imperfect hedge
Rounding contracts
The basis risk - if transaction occurs, future price may not exactly match spot price at date it’s closed out
View of modigliani and miller
Company’s wacc and therefore value is not affected by level of gearing other than through the effects of tax relief and that this leads to a fall in WACC and corresponding increase in value of company.
Traditional view of gearing
At lower levels of gearing a company’s wacc will decrease, this will cause the value of the company to rise.
However as gearing becomes a greater proportion of total long term funds, the cost of debt will start to increase and wacc will rise too and the value of the company will fall
Predictive analytics examples
Big data
Regression analytics (statistical tool used to understand and quantity the relationship between two variables)
Decision trees
Simulations
Enteprise value ads / dis
Excludes the affect of the way in which the company is financed
It excludes CAPEX so can compare companies in same industries that have different levels of CAPEX
Dis
Simplistic method
Lot of info from many value drivers is distilled into a single number
Asset methods ads and dis
Dis: doesn’t take into account intangible assets
Don’t always take into account the realisable values of the asset
