Acca F9 Formula Sheet
Marie Ota
From the September 2024 exam session onwards, the AFM formula sheet has been amended to include a rearranged version of the Modigliani and Miller (M&M) proposition 2 formula. Check out our new video to understand when you should and should not use the formula and how to use it in a spreadsheet.
A key consideration in financial management is the firm's WACC. TheWACC is derived by finding a firm's cost of equity and cost of debt andaveraging them according to the market value of each source of finance.The formula for calculating WACC is given on the exam formula sheet as:
The CAPM derives a required return for an investor by relatingreturn to the level of systematic risk faced by an investor - note thatthe CAPM is based on the assumption that all investors are welldiversified, so only systematic risk is relevant.
The CAPM model is based upon the assumption that investors are welldiversified, so will have eliminated all the unsystematic (specific)risk from their portfolios. The beta factor is a measure of the level ofsystematic risk (general, market risk) faced by a well diversifiedinvestor - see more details on beta factors below.
Beta factors are derived by statistically analysing returns from aparticular share over a period compared to the overall market returns.If the returns on the individual share are more volatile than theoverall market, the firm's beta will be greater than 1.
A proxy beta is usually found by identifying a quoted company with asimilar business risk profile and using its beta. However, whenselecting an appropriate beta from a similar company, account has to betaken of the gearing ratios involved.
The directors of Moorland Co, a company which has 75% of itsoperations in the retail sector and 25% in manufacturing, are trying toderive the firm's cost of equity. However, since the company is notlisted, it has been difficult to determine an appropriate beta factor.Instead, the following information has been researched:
The risk free rate is 3% and the equity risk premium is 6%. Tax oncorporate profits is 30%. Moorland Co has gearing of 50% debt and 50%equity by market values. Assume that the risk on corporate debt isnegligible.
Hence, if a short term growth rate is required, the ARR provides afair approximation for use in the growth model. However, if a long termgrowth rate is needed, ke should be used as the percentage return. To avoid a recursion problem, this should be derived using CAPM.
If you are given the "cost of debt", be aware that the cost of debtis normally quoted pre-tax because this is the rate at which thecompanies will pay interest on their borrowings (even though the 'true'cost to them will be net of tax because interest is payable before taxand therefore companies benefit from the 'tax shield').
However, the main technique used in Paper P4 for deriving cost of debt is based on an awareness of credit spread (sometimes referred to as the "default risk premium"), and the formula:
The credit spread is a measure of the credit risk associated with acompany. Credit spreads are generally calculated by a credit ratingagency and presented in a table like the one below: To understand howcredit spreads are derived, see the section on how lenders set theirinterest rates at the end of this chapter.
A large number of agencies can provide information on smallerfirms, but for larger firms credit assessments are usually carried outby one of the international credit rating agencies. The three largestinternational agencies are Standard and Poor's, Moodys and Fitch.
The CAPM can be used to derive a required return as long as thesystematic risk of an investment is known. Earlier in the chapter we sawhow to use an equity beta to derive a required return on equity. Wealso said that the risk on debt is usually relatively low, so the debtbeta is often zero. However, if the debt beta is not zero (for exampleif the company's credit rating shows that it has a credit spread greaterthan zero) the CAPM can also be used to derive kd as follows:
The main limitation of duration is that it assumes a linearrelationship between interest rates and bond price. In reality, therelationship is likely to be curvilinear. The extent of the deviationfrom a linear relationship is known as convexity. The more convexthe relationship between interest rates and bond price, the moreinaccurate duration is for measuring interest rate sensitivity.
The sensitivity of bond prices to changes in interest rates isdependent on their redemption dates. Bonds which are due to be redeemedat a later date are more price-sensitive to interest rate changes, andtherefore are riskier.
However, duration is only useful in assessing small changes in interest rates because of convexity.As interest rates increase, the price of a bond decreases and viceversa, but this decrease is not proportional for coupon paying bonds,the relationship is non-linear. In fact, the relationship between thechanges in bond value to changes in interest rates is in the shape of aconvex curve to origin, see below.
Therefore duration will predict a lower price than the actual priceand for large changes in interest rates this difference can besignificant. Duration can only be applied to measure the approximatechange in a bond price due to interest changes, only if changes ininterest rates do not lead to a change in the shape of the yield curve.This is because it is an average measure based on the gross redemptionyield (yield to maturity). However, if the shape of the yield curvechanges, duration can no longer be used to assess the change in bondvalue due to interest rate changes.
The table of credit spreads shown above showed the premium overrisk free rate which a company would have to pay in order to satisfy itslenders. Another way of looking at the issue of yield on a bond is tolook at it from the perspective of the lender. How lenders set theirinterest rates was the subject of an article written by Bob Ryan forStudent Accountant magazine in August 2008.
Lenders set their interest rates after assessing the likelihoodthat the borrower will default. The basic idea is that the lender willassess the likelihood (using normal distribution theory) of the firm'scash flows falling to a level which is lower than the required interestpayment in the coming year. If it looks likely that the firm will haveto default, the interest rate will be set at a high level to compensatethe lender for this risk.
Given that the annual volatility (standard deviation) of thecompany's cash flows (measured over the last 5 years) has been 25%,calculate the probability that Villa Co will default on its interestpayment within the next year (assuming that the company has no otherlines of credit available).
When evaluating a project, it is important to use a cost of capitalwhich is appropriate to the risk of the new project. The existing WACCwill therefore be appropriate as a discount rate if both:
(1) the new project has the samelevel of business risk as the existing operations. If business riskchanges, required returns of shareholders will change (to compensatethem for the new level of risk), and hence WACC will change.
(2) undertaking the new projectwill not alter the firm's gearing (financial risk). The values of equityand debt are key components in the calculation of WACC, so if thevalues change, clearly the existing WACC will no longer be applicable.
If one or both of these factors do not apply when undertaking a newproject, the existing WACC cannot be used as a discount rate. The nextchapter explores the alternative methods available in these situations.
I have seen spreadsheets which calculate stakes such that you make a decent profit should you earn the free bet but a small loss in all other eventualities. I would really like to see a spreadsheet or better still know the formulas for equalizing the profit no matter the outcome.
I do have access to such a tool in a web based software, however I would really like to incorporate it into a vb program I have written to manage all of my matched betting including results etc. It would also allow me to quickly calculate lay stakes for a leg that I might have in as many as ten or more accas at once without having to go and do them all individually.
2. If you lay less than the 50 then when the first legs wins you are down a little bit. But you have the value in the potential of a free bet to make up the small loss. But how to unlock or extract the value in the potential free bet is another thing. The work required to extract this value too would mean you would be probably laying small amounts on the acca even after it is dead.
For example of what I mean if you start with a 50 acca first leg is 5/5.1 and then next four legs are 1.2/1.25. Total bookie odds is therefore 10.37 and return would be 518. Probability it wins based on exchanges lay odds is 8% and probability only one leg loses would be 40%. The value of the actual acca is (probability it wins * payout if it wins) 41.63. The value of the free bet offer is (probability you qualify for free bet * value of free bet) 16.38. So in total its a value bet, you have about 58.01 expected value.
Can someone give an example of what the online tool says that you should lay for an acca like 5/5.1 and then four 1.2/1.25? Do you still continue to lay small amount to realise the potential of winning a free bet even after one leg loses?
mwilks. I have done the paddy power shops before, you have to take the matches on the coupon which can be limitting but at the same time they have all the popular matches like Bayern, Barca, Celtic, Chelsea, Man City, PSG etc who are usually good odds. The odds are printed in fractions but you can just convert to decimal (15/8 in fraction convert to 15/8+1 = 2.875). The free bets work by handing in your losing acca bet slip and they hand you back a coupon. You can use the free bet in any paddy power but i think its best to use it in the shop you won it as it might be suspicious if you start spreading it around.
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