Chapter 3 Impact of Financing on Investment Decisions and ...
ACCA P4
Advanced Financial Management
Education Class 2
Session 3 and 4
Chapter 3
Patrick Lui
hklui2007@.hk
| |
Chapter 3 Financing Decision
|LEARNING OBJECTIVES |
| |
|1. Identify and assess the appropriateness of the range of sources of finance available to an organisation including equity, debt, |
|hybrids, lease finance, venture capital, business angel finance, private equity, and asset securitisation. Including assessment on the|
|financial position, financial risk and the value of an organisation. |
|2. Assess an organisation’s debt exposure to interest rate changes using the simple Macaulay duration method. |
|3. Discuss the benefits and limitations of duration including the impact of convexity. |
|4. Assess the organisation’s exposure to credit risk, including: |
|(i) Explain the role of, and the risk assessment models used by the principal rating agencies. |
|(ii) Estimate the likely credit spread over risk free. |
|(iii) Estimate the organization’s current cost of debt capital using the appropriate term structure of interest rates and the credit |
|spread. |
|5. Assess the impact of a significant capital investment project upon the reported financial position and performance of the |
|organization taking into account alternative financing strategies. |
[pic]
1. Short-term Debt
1.1 Overdrafts
1.1.1 Overdrafts are one of the most important sources of short-term finance available to businesses. They can be arranged relatively quickly, and offer a level of flexibility with regard to the amount borrowed at any time, whilst interest is only paid when the account is overdrawn.
1.1.2 The bank will generally charge a commitment fee when a customer is granted an overdraft facility or an increase in his overdraft facility. This is a fee for granting an overdraft facility and agreeing to provide the customer with funds if and whenever he needs them.
1.1.3 When a business customer has an overdraft facility, and the account is always in overdraft, then it has a solid core (or hard core) overdraft. If the hard core element of the overdraft appears to be becoming a long-term feature of the business, the bank might wish, after discussions with the customer, to convert the hard core of the overdraft into a loan, thus giving formal recognition to its more permanent nature. Otherwise annual reductions in the hard core of an overdraft would typically be a requirement of the bank.
1.1.4 Advantages and disadvantages of overdrafts:
|Advantages |Disadvantages |
|Flexibility – The borrowing firm is not asked to forecast the|Bank retains the right to withdraw the facility at short |
|precise amount and duration of its borrowing at the outset |notice. |
|but has the flexibility to borrow up to a stated limited. |Bank usually take a fixed charge or a floating charge as the |
|Cheapness – Banks usually charge lower interest rate |security. |
|depending on the security offered, creditworthiness and |Bank may require a personal guarantee of the directors or |
|bargaining position of the borrower. |owners of the business. |
1.2 Short-term loans
1.2.1 A term loan is a loan for a fixed amount for a specified period. It is drawn in full at the beginning of the loan period and repaid at a specified time or in defined instalments. Term loans are offered with a variety of repayment schedules. Often, the interest and capital repayments are predetermined.
1.2.2 Advantages for the borrower
(a) The borrower knows what he will be expected to pay back at regular intervals and the bank can also predict its future income with more certainty.
(b) Once the loan is agreed, the term of the loan must be adhered to, provided that the customer does not fall behind with his payments. It is not repayable on demand by the bank.
1.3 Trade credit
1.3.1 Trade credit is one of the main sources of short-term finance for a business. Current assets such as raw materials may be purchased on credit with payment terms normally varying from between 30 to 90 days. Trade credit therefore represents an interest free short-term loan.
1.3.2 In a period of high inflation, purchasing via trade credit will be very helpful in keeping costs down. However, it is important to take into account the loss of discounts suppliers offer for early payment.
1.3.3 Unacceptable delays in payment will worsen a company’s credit rating and additional credit may become difficult to obtain.
1.4 Leasing
1.4.1 Rather than buying an asset outright, using either available cash resources or borrowed funds, a business may lease an asset. Leasing has become a popular source of finance.
1.4.2 Leasing can be defined as a contract between lessor and lessee for hire of a specific asset selected from a manufacturer or vendor of such assets by the lessee. The lessor retains ownership of the asset. The lessee has possession and use of the asset on payment of specified rentals over a period.
2. Long-term debt
2.1 Long-term finance is used for major investments and is usually more expensive and less flexible than short-term finance.
2.2 Reasons for seeking debt finance:
(a) Perhaps the current shareholders will be unwilling to contribute additional capital.
(b) Possibly the company does not wish to involve outside shareholders who will have more onerous requirements than current members;
(c) May include lesser cost and easier availability, particularly if the company has little or no existing debt finance.
(d) Debt finance provides tax relief on interest payments.
2.3 Factors influencing choice of debt finance by a company:
(a) Availability – Only listed companies will be able to make a public issue of loan notes on a stock exchange; smaller companies may only be able to obtain significant amounts of debt finance from their bank.
(b) Duration – If loan finance is sought to buy a particular asset to generate revenues for the business, the length of the loan should match the length of time that the asset will be generating revenues.
(c) Fixed or floating rate – Expectations of interest rate movements will determine whether a company chooses to borrow at a fixed or floating rate. Fixed rate finance may be more expensive, but the business runs the risk of adverse upward rate movements if it chooses floating rate finance.
(d) Security and covenants – The choice of finance may be determined by the assets that the business is willing or able to offer as security, also on the restrictions in covenants that the lenders wish to impose.
(e) Gearing and financial risk – If already too high, not suitable to raise debt finance.
(f) Target capital structure – A company should seek to minimize its WACC. In practical terms this can be achieved by having some debt in its capital structure, since debt is relatively cheaper than equity.
(g) Economic expectations – It is more easy to borrow money from bank in good economic conditions.
2.4 Factors to be considered by providers of finance:
(a) Risk and the ability to meet financial obligations –
Providers of finance will assess the ability of the company to meet its future financial obligations and the risk of the company. The previous record of the company can be used as a guide to the ability of its board of directors to manage its finances in a responsible and effective manner.
(b) Security – The amount of funds made available to a company will also depend on the availability of assets to offer as security. If security is not available or is limited, the company will have to pay a higher rate of interest in compensation for the higher level of risk.
(c) Legal restrictions on borrowing – Whether there are any legal restrictions on the amount of debt that the company can take on, for example in existing debt contracts (restrictive or negative covenants), or in the company’s articles of association.
3. Valuation of debts and preference shares
3.1 Bonds are usually redeemable. They are issued for a term of ten years or more, and perhaps 25 to 30 years. At the end of this period, they will mature and become redeemable (at par or possibly at a value above par).
3.2 Some bonds do not have a redemption date, and are irredeemable or undated. Undated bonds might be redeemed by a company that wishes to pay off the debt, but there is no obligation on the company to do so.
|3.3 |Formulae |
| |The formulae for the various types of finance are as follows: |
| | |
| |Types of finance |
| |Market value |
| | |
| |Irredeemable debt without tax |
| |[pic] |
| | |
| |Irredeemable debt with tax |
| |[pic] |
| | |
| |Redeemable debt |
| |MV = PV of future interest and redemption receipts, discounted at investors’ required returns |
| | |
| |Preference shares |
| |[pic] |
| | |
| | |
| |Where: |
| |P0 = ex-div market value of the debt or share |
| |i = annual interest starting in one year’s time |
| |Kd = company’s cost of debt, expressed as a decimal |
| |Kp = cost of the preference shares |
|Example 1 – Irredeemable debt |
|A company has issued irredeemable loan notes with a coupon rate of 7%. If the required return of investors is 4%, what is the current|
|market value of the debt? |
| |
|Solution: |
| |
|Market value = [pic] |
|Example 2 – Preference shares |
|A firm has in issue $100, 12% preference shares. Currently the required return of preference shareholders is 14%. |
| |
|What is the value of a preference share? |
| |
|Solution: |
| |
|Market value of preference share: |
|[pic] |
|Example 3 – Redeemable debt |
|A company has issued some 9% debentures, which are now redeemable at par in three years time. Investors now require a redemption |
|yield of 10%. What will be the current market value of each $100 of debenture? |
| |
|Solution: |
| |
|Year |
| |
|Cash flow ($) |
|DF at 10% |
|PV ($) |
| |
|1 |
|Interest |
|9 |
|0.909 |
|8.18 |
| |
|2 |
|Interest |
|9 |
|0.826 |
|7.43 |
| |
|3 |
|Interest |
|9 |
|0.751 |
|6.76 |
| |
|3 |
|Redemption value |
|100 |
|0.751 |
|75.10 |
| |
| |
| |
| |
| |
|97.47 |
| |
| |
|Each $100 of debenture will have a market value of $97.47. |
|Example 4 – Convertible debt |
|A company has in issue convertible loan notes with a coupon rate of 12%. Each $100 loan note may be converted into 20 ordinary shares|
|at any time until the date of expiry and any remaining loan notes will be redeemed at $100. |
| |
|The loan notes have five years left to run. Investors would normally require a rate of return of 8% pa on a five-year debt security. |
| |
|Should investors convert if the current share price is: |
| |
|(a) $4.00. |
|(b) $5.00. |
|(c) $6.00. |
| |
|Solution: |
| |
|Value as debt |
|If the security is not converted it will have the following value to the investor: |
| |
| |
|DF @ 8% |
|PV ($) |
| |
|Interest $12 per year for 5 years |
|3.993 |
|47.916 |
| |
|Redemption $100 in 5-years |
|0.681 |
|68.100 |
| |
| |
| |
|116.016 |
| |
| |
|Value as equity |
|Market price |
|Value as equity ($) |
| |
|4.00 |
|$80 (i.e. 20 × $4) |
| |
|5.00 |
|$100 (20 × $5) |
| |
|6.00 |
|$120 (20 × $6) |
| |
| |
|If the market price of equity rises to $6.00 the security should be converted, otherwise it is worth more as debt. The breakeven |
|conversion price is $5.80 per share ($116/20 shares). |
| |
|The value of the convertible will therefore be $116, unless the share price rises above $5.80 at which point it will be the value of |
|the equity received on conversion. |
4. The Causes of Interest Rate Fluctuations
4.1 The term structure of interest rates
4.1.1 The term structure of interest rates refers to the way in which the yield on a security varies according to the term of the borrowing, as shown by the yield curve.
4.1.2 There are several reasons why interest rates differ in different markets and market segments.
(a) Risk – Higher risk borrowers must pay higher rates on their borrowing, to compensate lenders for the greater risk involved.
(b) The need to make a profit on re-lending – Financial intermediaries make their profits from re-lending at a higher rate of interest than the cost of their borrowing.
(c) The size of the loan – Deposits above a certain amount with a bank or building society might attract higher rates of interest than smaller deposits.
(d) Different types of financial asset – Different types of financial asset attract different rates of interest. This is largely because of the competition for deposits between different types of financial institution.
(e) Government policy – The policy on interest rates might be significant too. A policy of keeping interest rates relatively high might therefore have the effect of forcing short-term interest rates higher than long-term rates.
(f) The duration of the lending – The term structure of interest rates refers to the way in which the yield on a security varies according to the term of the borrowing, that is the length of time until the debt will be repaid as shown by the yield curve. Normally, the longer the term of an asset to maturity, the higher the rate of interest paid on the asset.
4.2 Yield curve (收益率曲線)
4.2.1 The yield curve is an analysis of the relationship between the yields on debt with different periods to maturity.
4.2.2 A yield curve can have any shape, and can fluctuate up and down for different maturities.
4.2.3 There are three main types of yield curve shapes: normal, inverted and flat (humped):
(a) Normal yield curve – longer maturity bonds have a higher yield compared with shorter-term bonds due to the risks associated with time.
(b) Inverted yield curve – the short-term yields are higher than the longer-term yields, which can be a sign of upcoming recession.
(c) Flat (or humped) yield curve – the shorter- and longer-term yields are very close to each other, which is also a predictor of an economic transition.
4.2.4 The slope of the yield curve is also seen as important: the greater the slope, the greater the gap between short- and long-term rates.
[pic]
[pic]
4.2.5 The shape of the yield curve at any point in time is the result of the three following theories acting together:
(a) Liquidity preference theory (流動性偏好理論)
(b) Expectations theory
(c) Market segmentation theory (市場分割理論)
|4.2.6 |Liquidity Preference, Expectations and Market Segmentation Theories |
| |(a) Liquidity preference theory |
| |Investors have a natural preference for more liquid (shorter maturity) investments. They will need to be compensated if |
| |they are deprived of cash for a longer period. |
| | |
| |Therefore the longer the maturity period, the higher the yield required leading to an upward sloping curve, assuming that |
| |the interest rates were not expected to fall in the future. |
| | |
| |(b) Expectations theory |
| |This theory states that the shape of the yield curve varies according to investors' expectations of future interest rates.|
| |A curve that rises steeply from left to right indicates that rates of interest are expected to rise in the future. There |
| |is more demand for short-term securities than long-term securities since investors' expectation is that they will be able |
| |to secure higher interest rates in the future so there is no point in buying long-term assets now. The price of short-term|
| |assets will be bid up, the price of long-term assets will fall, so the yields on short-term and long-term assets will |
| |consequently fall and rise. |
| | |
| |(c) Market segmentation theory |
| |The market segmentation theory suggests that there are different players in the short-term end of the market and the |
| |long-term end of the market. As a result the two ends of the curve may have different shapes, as they are influenced |
| |independently by different factors. |
| | |
| |The result is separate yield curves that probably do not meet very smoothly. This introduces a ‘kink’ to the yield curve |
| |presumably determined by arbitrage between the different markets to gain risk-free return. |
[pic]
|4.2.7 |Significance of Yield Curves to Financial Managers |
| |Financial managers should inspect the current shape of the yield curve when deciding on the term of borrowings or |
| |deposits, since the curve encapsulates the market's expectations of future movements in interest rates. |
| | |
| |A corporate treasurer might analyse a yield curve to decide for how long to borrow. For example, suppose a company wants |
| |to borrow $20 million for five years and would prefer to issue bonds at a fixed rate of interest. One option would be to |
| |issue bonds with a five-year maturity. Another option might be to borrow short-term for one year, say, in the expectation |
| |that interest rates will fall, and then issue a four-year bond. When borrowing large amounts of capital, a small |
| |difference in the interest rate can have a significant effect on profit. For example, if a company borrowed $20 million, a|
| |difference of just 25 basis points (0.25% or one quarter of one per cent) would mean a difference of $50,000 each year in |
| |interest costs. So if the yield curve indicates that interest rates are expected to fall then short-term borrowing for a |
| |year, followed by a 4-year bond might be the cheapest option. |
4.3 Yield to maturity
4.3.1 The yield to maturity (or redemption yield) is the effective yield on a redeemable bond which allows for the time value of money and is effectively the IRR of the cash flows.
|Example 5 – YTM |
|A five year unsecured bond with a coupon of 5% per annum, redeemable at par and issued at a 6% discount to par will have a yield to |
|maturity of 6.47%. This is calculated by assuming a nominal value of $100 and calculating NPVs at 5% and 7% discount rates. |
| |
|Year |
| |
|Cash flow ($) |
|DF |
|5% |
|PV |
|($) |
|DF |
|7% |
|PV |
|($) |
| |
|0 |
|Market value |
|(94) |
|1.000 |
|(94.00) |
|1.000 |
|(94.00) |
| |
|1 – 5 |
|Interest |
|5 |
|4.329 |
|21.64 |
|4.100 |
|20.50 |
| |
|5 |
|Capital payment |
|100 |
|0.784 |
|78.40 |
|0.713 |
|71.30 |
| |
| |
| |
| |
| |
|6.04 |
| |
|(2.20) |
| |
| |
|YTM = [pic] |
5. Other Types of Financing
5.1 Equity finance
5.1.1 Equity finance is raised through the sale of ordinary shares to investors, either as a new issue or a rights issue.
5.1.2 The issue of equity is at the bottom of the pecking order when it comes to raising funds for investments, not only because of the cost of issue but also because equity finance is more expensive in terms of required returns.
5.1.3 Equity shareholders are the ultimate bearers of risk as they are at the bottom of the creditor hierarchy in a liquidation. This means that there is a significant risk that they will receive nothing at all after all other trade payables’ claims have been met.
5.1.4 As with long-term debt, equity finance will be used for long-term investments. Companies may choose to raise equity rather than debt finance if:
(a) their gearing ratios are approaching the maximum allowable
(b) any further increases in gearing will be perceived as a significant increase in risk by investors.
5.2 Venture capital
5.2.1 Venture capital is long-term capital that is available for around five years. It is normally offered by specialist institutions, and is aimed at small and medium-size businesses that have a fairly high level of risk.
5.2.2 Venture capitalists are prepared to provide capital to such businesses if the expected returns are commensurate with the level of risk taken. This means that venture capitalists will only be interested in a business with good profit and growth prospects. The amount of capital invested will vary according to need and may be provided in stages, subject to certain key objectives being met.
5.2.3 Venture capitalist may be interested in the following types of business:
(a) Business start-ups – This can cover a wide range of situations from businesses that are still at the concept stage through to businesses that are about to begin operations. In practice it seems that venture capitalists prefer to invest in start-ups that are fairly well advanced.
(b) Growth capital – This is designed for businesses that have passed the start-up phase and are seeking capital for further expansion. It is, therefore, a form of second-stage funding.
(c) Management acquisitions – Venture capitalists will often provide capital for managers that wish to take over an existing business. The managers may be already employed by the business or they may be outside managers that are looking for a vehicle for their ambitions. This type of financing has proved to be extremely popular among venture capitalists in recent years.
(d) Share purchases – Capital may be provided to help finance the buy out of a part-owner of a business. This may be provided to someone outside the business or to the other part-owners.
(e) Business recoveries – Capital may be provided to help turn round the fortunes of a business that is currently experiencing difficulties.
(f) Venture capitalists do not usually look for quick cash returns and are often content to wait for a cash return on realisation of the investment.
5.3 Business angels
5.3.1 Business angels are wealthy individuals who invest in start-up and growth businesses in return for an equity stake. These individuals are prepared to take high risks in the hope of high returns. As a result, business angel finance can be expensive for the business.
5.3.2 Investments made by business angels can vary but, in the UK, most investments are in the region of ₤25,000.
5.3.3 Business angels are a very useful tool to fill the gap between venture capital and debt finance, particularly for start-up businesses.
5.3.4 One of the main advantages of business angels is that they often follow up their initial investment with later rounds of financing as the business grows. New businesses benefit from their expertise in the difficult early stages of trying to establish themselves.
(The article “Being an Angel” in the Technical Articles section of the ACCA website covers Business Angels in more detail.
)
5.4 Lease finance
5.4.1 There are two types of leases:
(a) A finance lease exists when the substance of the lease is that the lessee enjoys substantially all of the risks and rewards of ownership, even though legal title to the leased asset does not pass from lessor to lessee.
(b) An operating lease is a rental agreement where several lessees are expected to use the leased asset and so the lease period is much shorter than the asset’s useful economic life.
5.4.2 Attractions to lessor – the lessor invests finance by purchasing assets from suppliers and makes a return out of the lease payments from the lessee. The lessor will get capital allowances on his purchase of the equipment.
5.4.3 Attractions to lessee under finance lease –
(a) The lessee may not have enough cash to pay for the asset, and would have difficulty obtaining a bank loan to buy it. If so the lessee has to rent the asset to obtain use of it at all.
(b) Finance leasing may be cheaper than a bank loan.
(c) The lessee may find the tax relief available advantageous.
5.4.4 Attractions to lessee under operating lease –
(a) The leased equipment does not have to be shown in the lessee’s published statement of financial position, and so the lessee’s statement of financial position shows no increase in its gearing ratio.
(b) The equipment is leased for a shorter period than its expected useful life. In the case of high-technology equipment, if the equipment becomes out of date before the end of its expected life, the lessee does not have to keep on using it. The lessor will bear the risk of having to sell obsolete equipment secondhand.
5.5 Asset securitisation
(Jun 10, Jun 12, Dec 15)
5.5.1 Securitisation is the process of converting illiquid assets into marketable asset-backed securities. These securities are backed by specific assets and are normally called asset-backed securities (ABS).
5.5.2 The oldest and historically most common type of asset securitization is the mortgage-backed bond or security (MBS).
5.5.3 Very simplistically, the process is as follows:
(a) A financial entity can purchase a number of mortgage loans from banks.
(b) The entity pools the mortgage loans together.
(c) The entity issues bonds to institutional investors. The money raised from issuing bonds is used to pay for the mortgage loans.
(d) The institutional investors now have the right to receive the principal and interest payments made on the mortgage.
5.5.4 Today, virtually anything that has a cash flow (e.g. a loan, a public works project, or a receivable balance) is a candidate for securitization.
5.5.5 The tangible benefit from securitisation occurs when the pooled assets are divided into tranches and tranches are credit rated. The higher rated tranches would carry less risk and have less return, compared to lower rated tranches. If default occurs, the income of the lower tranches is reduced first, before the impact of increasing defaults move to the higher rated tranches. This allows an asset of low liquidity to be converted into securities which carry higher liquidity.
5.5.6 The main reason for securitizing a cash flow is that if allows companies with a credit rating of, for example, BB but with AAA-rated cash flows to possibly borrow at AAA rates. This will lead to greatly reduced interest payments as the difference between BB rates and AAA rates can be hundreds of basis points.
5.5.7 However, securitization is expensive due to management costs, legal fees and continuing administration fees.
[pic]
5.6 Hybrids
5.6.1 Hybrids are means of finance that combine debt and equity. Such securities pay a fixed or floating rate of return up to a certain date, after which the holder has such options as converting the securities into the underlying equity.
5.6.2 Examples of hybrids include convertible bonds, debt with attached warrants and preference shares.
5.6.3 Convertible debt has a number of attractions compared with a bank loan of similar maturity, as follows:
(a) Self-liquidating (自行收回)
(i) Provided that the conversion terms are pitched correctly and expected share price growth occurs, conversion will be an attractive choice for bond holders as it offers more wealth than redemption.
(ii) This occurs when the conversion value is greater than the redemption value, or when the conversion value is greater than the floor value on the conversion date.
(iii) If the debt is converted into ordinary shares, it will not need to be redeemed. A bank loan of a similar maturity will need to have all of the capital repaid.
(b) Lower interest rate
(i) It will be lower than the interest rate on ordinary debt such as a bank loan because of the value of the option to convert.
(ii) The returns on fixed-interest debt will not increase with corporate profitability, so debt providers will have a limited share of the benefits from the investment of the funds they have provided.
(iii) When debt has been converted, however, bond holders become shareholders and will potentially have unlimited returns, or at least returns that are higher than the returns on debt finance.
(c) Increase in debt capacity on conversion
(i) Gearing increases when convertible debt is issued, but if conversion occurs, the gearing will fall not only because the debt has been removed, but will fall even further because equity has replaced the debt.
(ii) The debt capacity of the company will therefore be enhanced by conversion, compared to redemption of a bank loan of a similar maturity.
(d) More attractive than ordinary debt
(i) It may be possible to issue convertible debt even when ordinary debt such as a bank loan is not attractive to lenders, since the option to convert offers a little extra that ordinary debt does not.
(ii) This is the option to convert in the future, which can be attractive to optimists, even when the short- and medium-term economic outlook may be poor.
6. Duration
6.1 What is duration?
(Jun 11, Pilot 13)
6.1.1 Duration (also known as Macaulay duration) is the weighted average length of time to the receipt of a bond’s benefits (coupon and redemption value), the weights being the present value of the benefits involved.
6.1.2 Duration gives each bond an overall risk weighting that allows two bonds to be compared. In simple terms, it is a composite measure of the risk expressed in years.
6.2 Calculating duration
(Jun 11, Pilot 13, Jun 14)
6.2.1 The steps of calculating duration
Step 1: Add the PV of the cash flows in each time period together.
Step 2: Multiply the PV of cash flows for each time period by the time period and add together.
Step 3: Divide the result of step 2 by the result of step 1.
|Example 6 – Calculating duration |
|ABC Co. has a bond (Bond X) in issue which has a nominal value of $1,000 and is redeemable at par. |
| |
|Bond X is a 6% bond maturing in three years’ time and has a gross redemption yield (GRY) of 3.5%. The current price of the bond is |
|$1,070.12. |
| |
|Required: |
| |
|Calculate the duration of the bond. |
| |
|Solution: |
| |
|Bond X |
| |
| |
|1 |
|2 |
|3 |
|Total |
| |
|Cash flow ($) |
|60 |
|60 |
|1,060 |
| |
| |
|Discount at 3.5% |
|0.966 |
|0.934 |
|0.902 |
| |
| |
|PV |
|57.96 |
|56.04 |
|956.12 |
|1,070.12 |
| |
|× by year |
|1 |
|2 |
|3 |
| |
| |
| |
|57.96 |
|112.08 |
|2,868.36 |
|3,038.40 |
| |
| |
|Duration = 3,038.40 / 1,070.12 = 2.84 years |
| |
|Note that the total PV of the cash flows from the bond is equal to the current market price, which is what we expect. |
6.3 Properties of duration
6.3.1 The basic features of sensitivity to interest rate risk will all be mirrored in the duration calculation.
(a) Longer-dated bonds (or longer time to maturity) will have longer durations.
Consider two bonds that each cost $1,000 and yield 5%. A bond that matures in one year would more quickly repay its true cost that a bond that matures in 10 years. As a result, the shorter-maturity bond would have a lower duration and less price risk. The longer the maturity, the higher the duration.
(b) Lower-coupon bonds will have longer duration. The ultimate low-coupon bond is a zero-coupon bond where the duration will be the maturity.
A bond’s payment is a key factor in calculating duration. If two identical bonds pay different coupons, the bond with the higher coupon will pay back its original cost quicker than the lower-yield bond. The higher the coupon, the lower the duration.
(c) Lower yields will give longer durations. In this case, the PV of cash flows in the future will rise if the yield falls, extending the point of balance, therefore lengthening the duration.
6.4 Modified duration
(Jun 11, Pilot 13, Jun 14)
6.4.1 Modified duration is a measure of the sensitivity of the price of a bond to a change in interest rates.
6.4.2 Formula:
|Modified duration = |
|Macaulay duration |
| |
| |
|1 + GRY |
| |
| |
|This can be used to determine the proportionate change in bond price for a given change in yield as follows: |
| |
|ΔP = – Modified duration × ΔY × P |
| |
|Where: |
|GRY = gross redemption yield |
|ΔP = change in bond price |
|ΔY = change in yield |
|P = current market price of the bond |
| |
|Remember there is an inverse relationship between yield and bond price, therefore the modified duration figure is |
|expressed as a negative number. |
|Example 7 – Calculating modified duration |
|Same information as Example 6. |
| |
|Required: |
| |
|Calculate the modified duration of the bond. |
| |
|Solution: |
| |
|Bond X |
|Duration = 3,038.40 / 1,070.12 = 2.84 years |
|GRY = 3.5% |
|Modified duration = [pic] |
| |
| |
|If, for example, the yield increased by 0.5%, the change in price can be calculated as follows: |
| |
|ΔP = –2.74 × 0.5% × $1,070.12 = –$14.66 |
6.4.3 Properties of modified duration – as the modified duration is derived from the Macaulay duration, it shares the same properties.
(a) Longer dated bonds will have higher modified durations – that is, bonds which are due to be redeemed at a later date are more price-sensitive to changes in interest rates and are therefore more risky.
(b) Lower coupon bonds will have higher modified durations.
(c) Lower yields will give higher modified durations.
6.5 Benefits of duration:
6.5.1 Benefits:
(a) Duration allows bonds of different maturities and coupon rates to be directly compared. This makes decision-making regarding bond finance easier and more effective.
(b) If a bond portfolio is constructed based on weighted average duration, it is possible to determine portfolio value changes based on estimated changes in interest rates.
(c) Managers may be able to modify interest rate risk by changing the duration of the bond portfolio – for example, by adding shorter maturity bonds or those with higher coupons (which will reduce duration), or by adding longer maturity bonds or those with lower coupons (which will increase duration).
6.6 Limitations of duration
(Jun 11, Pilot 13, Jun 14)
6.6.1 The main limitation of duration is that it assumes a linear relationship between interest rates and price, i.e. it assumes that for a certain percentage change in interest rates there will be an equal percentage change in price.
6.6.2 However, as interest rates change the bond price is unlikely to change in a linear fashion. Rather, it will have some kind of convex relationship with interest rates.
[pic]
6.6.3 As you can see from the diagram above, the more convex the relationship the more inaccurate duration is for measuring interest rate sensitivity. Therefore duration should be treated with caution in your predictions of interest rate/price relationships.
6.6.4 Duration can only be applied to measure the approximate change in a bond price due to interest changes, only if changes in interest 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 redemption yield (yield to maturity). However, if the shape of the yield curve changes, duration can no longer be used to assess the change in bond value due to interest rate changes.
7. Credit risk
7.1 Credit risk aspects
7.1.1 Credit risk, also referred to as default risk, is the risk undertaken by the lender that the borrower will default either on interest payments or on the repayment of principal on the due date, or on both.
7.1.2 Creditors to companies such as corporate bondholders and banks are also exposed to credit risk. The credit risk of an individual loan or bond is determined by the following two factors:
(a) The probability of default – this is the probability that the borrower or counterparty will default on its contractual obligations to repay its debt.
(b) The recovery rate – this is the fraction of the face value of an obligation that can be recovered once the borrower has defaulted. When an company defaults, bond holders do not necessarily lose their entire investment. Part of the investment may be recovered depending on the recovery rate.
7.1.3 The loss given default (LGD) is the difference between the amount of money owed by the borrower less the amount of money recovered.
For example, a bond has a face value of $100 and the recovery rate is 80%. The loss given default in this case is:
Loss given default = $100 – $80 = $20
7.1.4 The expected loss (EL) from credit risk shows the amount of money the lender should expect to lose from the investment in a bond or loan with credit risk.
The expected loss (EL) is the product of the loss given default (LGD) and the probability of default (PD).
EL = PD × LGD
If the probability of default is, say, 10%, the expected loss from investing in the above bond is:
EL = 0.1 × $20 = $2
7.2 Credit risk measurement
7.2.1 The oldest and most common approach is to assess the probability of default using financial and other information on the borrowers and assign a rating that reflects the expected loss from investing in the particular bond.
7.2.2 This assignment of credit risk ratings is done by credit rating companies such as Standard & Poor, Moody’s Investor Services or Fitch. The table below shows the credit rating used by Moody’s and Standard and Poor.
|Standard & Poor |Moody’s |Description of Category |
|AAA |Aaa |Highest quality, lowest default risk |
|AA |Aa |High quality |
|A |A |Upper medium grade quality |
|BBB |Baa |Medium grade quality |
|BB |Ba |Lower medium grade quality |
|B |B |Speculative |
|CCC |Caa |Poor quality (high default risk) |
|CC |Ca |Highly speculative |
|C |C |Lowest grade quality |
7.2.3 Both credit rating agencies estimate default probabilities from the empirical performance of issued corporate bonds of each category. The table below shows the probability of default for certain credit categories over different investment horizons. The probability of default within a year for AAA or AA bonds is practically zero whereas for a CCC bond is 19.79%. However, although the probability of default for a AAA company is practically zero over a single year, it becomes 1.40% over a fifteen year period (this is consistent with the theory that, the longer the time horizon, the riskier the investment).
[pic]
7.3 Criteria for establishing credit ratings
(Pilot 13)
7.3.1 The criteria for rating international organizations encompasses the following.
|Criteria |Explanation |
|Country risk |No issuer’s debt will be rated higher than the country of origin of the issuer (the |
| |‘Sovereign Ceiling’ concept) |
|Universal/Country importance |The company’s standing relative to other companies in the country of domicile and globally|
| |(measured in terms of sales, profits, relationship with government, importance of the |
| |industry to the country, etc.) |
|Industry risk |The strength of the industry within the country, measured by the impact of economic |
| |forces, cyclical nature of the industry, demand factors, etc. |
|Industry position |Issuer’s position in the relevant industry compared with competitors in terms of operating|
| |efficiency. |
|Management evaluation |The company’s planning, controls, financing policies and strategies, overall quality of |
| |management and succession, merger and acquisition performance and record of achievement in|
| |financial results. |
|Accounting quality |Auditor’s qualifications of the accounts, and accounting policies for inventory, goodwill,|
| |depreciation policies and so on. |
|Earnings protection |Earnings power including return on capital, pre-tax and net profit margins, sources of |
| |future earnings growth. |
|Financial gearing |Long-term debt and total debt in relation to capital, gearing, nature of assets, |
| |off-balance commitments, working capital, management, etc. |
|Cash flow adequacy |Relationship of cash flow to gearing and ability to finance all business cash needs. |
|Financial flexibility |Evaluation of financing needs, plans and alternatives under stress (ability to attract |
| |capital), banking relationships, debt covenants. |
|Question 1 |
|GNT Co is considering an investment in one of two corporate bonds. Both bonds have a par value of $1,000 and pay coupon interest on an|
|annual basis. The market price of the first bond is $1,079.68. Its coupon rate is 6% and it is due to be redeemed at par in five |
|years. The second bond is about to be issued with a coupon rate of 4% and will also be redeemable at par in five years. Both bonds are|
|expected to have the same gross redemption yields (yields to maturity). The yield to maturity of a company’s bond is determined by its|
|credit rating. |
| |
|GNT Co considers duration of the bond to be a key factor when making decisions on which bond to invest. |
| |
|Required: |
| |
|(a) Estimate the Macaulay duration of the two bonds GNT Co is considering for investment. (9 marks) |
|(b) Discuss how useful duration is as a measure of the sensitivity of a bond price to changes in interest rates. (8 marks) |
|(c) Among the criteria used by credit agencies for establishing a company’s credit rating are the following: industry risk, earnings |
|protection, financial flexibility and evaluation of the company’s management. |
| |
|Briefly explain each criterion and suggest factors that could be used to assess it. |
|(8 marks) |
|(Total 25 marks) |
|(ACCA P4 Advanced Financial Management Pilot Paper 2013 Q4) |
7.4 Credit migration
7.4.1 The credit rating of a borrower may change after a bond is issued. This is referred to as credit migration.
7.4.2 There is another aspect of credit risk which should be taken into account when investors are investing in corporate bonds, beyond the probability of default.
7.4.3 A borrower may not default, but due to changing economic conditions or management actions the borrower may become more or less risky than at the time the bond was issued and as a result, the bond issuer will be assigned by the credit agency a different credit rating. This is called credit migration.
7.4.4 The significance of credit migration lies in the fact that the assignment of lower credit rating will decrease the market value of the corporate bond. This is discussed in the next section in the context of credit spreads.
8. Credit Spreads and the Cost of Debt Capital
(Dec 11)
8.1 Credit spreads
8.1.1 The credit spread is the premium required by an investor in a corporate bond to compensate for the credit risk of the bond.
8.1.2 The yield to a government bond holder is the compensation to the investor for foregoing consumption today and saving. However, corporate bond holders should require compensation not only for foregoing consumption, but also for the credit risk that they are exposed to.
8.1.3 As we discussed in the previous section, this is a function of the probability of default, the recovery rate and the probability of migration.
8.1.4 Assuming that a government bond such as the one issued by the US or an EU government is free of credit risk, the yield on a corporate bond will be:
Yield on corporate bond = risk free rate + credit spread
8.1.5 Since credit spreads reflect the credit risk of a bond, they will be inversely related to the credit quality of the bond. Low credit quality bonds will be characterized by large spreads and high credit quality bonds will be characterized by low spreads.
8.1.6 An example of credit spreads by type of bond and maturity is given below.
Reuters Corporate Spreads for Industrials (in basis points)
[pic]
|Example 8 – Yield on corporate bond |
|The current return on a 10 year government bond is 4.2%. ABC Co, a company rated AA, has 10 year bonds in issue. Using the credit |
|spread table, calculate the expected yield on ABC Co.’s bonds. |
| |
|Solution: |
| |
|The credit spread on a 10 year AA bond is 52, which means that 0.52% should be added to the return on the government bond. |
| |
|Expected yield on ABC Co.’s bonds = 4.2% + 0.52% = 4.72% |
|Example 9 – Yield on corporate bond |
|A 15 year government bond has a current yield of 5%. BBC Co., a B rated company, has equivalent bonds in issue. What is the expected |
|yield on BBC Co.’s bonds? |
| |
|Solution: |
| |
|The table does not include credit spreads for 15 year bonds therefore some adjustment is required to the figures we have available. |
| |
|The credit spread on a 10 year B rated bond is 350 and a 30 year B rated bond is 450. The adjustment can be calculated as follows. |
| |
|[pic] |
| |
|This means that 3.75% must be added to the yield on government bonds. |
| |
|The expected yield on BBC Co.’s bonds = 5% + 3.75% = 8.75% |
8.2 The cost of debt capital
8.2.1 The cost debt capital for a company is determined by the following:
(a) its credit rating
(b) the maturity of the debt
(c) the risk-free rate at the appropriate maturity
(d) the corporate tax rate
Cost of debt capital = (1 – tax rate) × (risk free rate + credit spread)
|Example 10 – Cost of debt |
|Joe Co., a BBB rated company, has 5 year bonds in issue. The current yield on equivalent government bonds is 3.7% and the current |
|rate of tax is 28%. |
| |
|Required: |
| |
|Using the information in the credit spread table above, calculate: |
| |
|(a) the expected yield on Joe Co.’s bonds |
|(b) Joe Co.’s post tax cost of debt associated with these 5 year bonds |
| |
|Solution: |
| |
|(a) Expected yield on 5 year bonds = 3.7% + 1.05% = 4.75% |
|(b) Post-tax cost of debt = (1 – 0.28) × 4.75% = 3.42% |
8.3 Impact on credit spreads on bond values
8.3.1 We have already mentioned that credit risk is affected by the probability of migration of a certain debt or loan to another credit category.
8.3.2 In markets where loans or corporate bonds are traded this migration is reflected in increased spreads. Using only the probability of default and ignoring the probability of migration from one category to another may give a misleading estimate of the risk exposure.
8.3.3 Thus a company that has a very low or even zero probability of default but a high probability of being downgraded will have its credit risk significantly underestimated.
8.3.4 To explain how credit migration may impact on bond values consider a bond which is currently rated as BBB. In a year’s time the bond may still be rated BBB, or it may have a higher or lower credit rating. The probability of being at the same or a different rating in a year’s time is reproduced in the table below.
|Year-end rating |Probability of migration |
|AAA |0.02% |
|AA |0.33% |
|A |5.95% |
|BBB |86.93% |
|BB |5.30% |
|B |1.17% |
|CCC |0.12% |
|Default |0.18% |
8.3.5 As we have discussed, each credit category implies a different credit spread which in turn implies a different cost of debt capital. The table below is an example of the cost of debt capital for bonds of different credit ratings and different maturities. The cost of debt capital for a AAA bond with a maturity of one year is 3.6%, whereas the cost of debt capital for a CCC bond with a maturity of 4 years is 13.52%.
Yields by credit category (%)
[pic]
8.3.6 The value of a bond is the present value of the coupons and the redemption value, discounted using the appropriate cost of debt capital.
|Example 11 – Impact of credit spreads on bond values |
|Suppose the bond has a face value of $100 and pays an annual coupon of 6%. Using the discount factors from the table above, we |
|calculate the value of the bond at the end of a year if it remained rated BBB using: |
| |
|[pic] |
| |
|If it is upgraded to A, it will be worth $102.64 |
|[pic] |
| |
|If it is downgraded to CCC, it will be worth $77.63 |
|[pic] |
| |
|The value of the bond when it defaults will not be zero, as the issuing firm will have some assets. The available empirical evidence |
|from credit agencies shows that about 51% of the value of a BBB bond is recovered when the issuing from defaults. |
| |
|If bondholders expect to recover in case of bankruptcy, the non-recoverable amount is $49 per $100 of face value. The Loss Given |
|Default for a BBB bond will therefore be: |
| |
|LGD = 0.49 × 100 = $49 |
| |
|The expected loss for the BBB bond in the example is: |
|EL = 0.0018 × $49 = $0.0882 |
| |
|The low probability of default reduces the credit risk of a BBB bond despite the fact that it loses nearly 50% of its value in the |
|case of a default. |
8.4 Predicting credit ratings
8.4.1 Credit rating companies use financial ratios and other information in order to arrive at the credit score of a company.
8.4.2 Many researchers have tried to guess the models that are employed by credit rating agencies and have estimated models which link the observed credit rating to financial characteristics of a company.
8.4.3 One of these models is the Kaplan Urwitz model. This model calculates a numerical value for a company based on certain characteristics which is then used to assign a credit rating to that company.
8.4.4 If a question on the Kaplan-Urwitz model comes up in an exam, the formula will be given.
A. Quoted companies
8.4.5 The Kaplan-Urwitz model for quoted companies is as follows.
|Y = 5.67 + 0.011F + 5.13π – 2.36S – 2.85L + 0.007C – 0.87β – 2.90σ |
| |
|Where: |
|Y = the score that the model produces |
|F = the size of a firm measured in total assets |
|π = net income / total assets |
|S = debt status (subordinated debt = 1, otherwise = 0) |
|L = gearing (measured as long term debt / total assets) |
|C = interest cover (PBIT / interest payment) |
|β = beta of the company estimated using CAPM |
|σ = the variance of the residuals from the CAPM regression equation (calculated as |
|[pic], where [pic] is the variance of the market) |
8.4.6 Subordinated debt (次級債務) has no priority claim as it is subordinated to other debt.
8.4.7 Unsubordinated debt is a loan or security that ranks above other loans or securities with regard to claims on assets or earnings. Also known as a senior security. In the case of default, creditors with unsubordinated debt would get paid out in full before the junior debt holders. Therefore, unsubordinated debt is less risky than subordinated debt.
8.4.8 The classification of companies into credit rating categories is done in the following way.
|Score (Y) |Rating category |
|Y > 6.76 |AAA |
|Y > 5.19 |AA |
|Y > 3.28 |A |
|Y > 1.57 |BBB |
|Y > 0 |BB |
|Example 12 – Kaplan-Urwitz model for quoted company |
|The following information is available for Kaplan Inc, a quoted company: |
| |
|Total assets = $650m |
|Net income = $250m |
|Type of debt = unsubordinated |
|Long term debt (unsubordinated) = $200m |
|Profit before interest and tax = $500m |
|Interest payments = $40m |
|In addition, the following CAPM model was estimated: |
|RKaplan = 0.045 + 0.800 × market risk premium |
|Kaplan’s volatility (σ) and the volatility of the market are 22% and 20% respectively. |
| |
|Required: |
| |
|What is the predicted credit rating for Kaplan Inc, using the Kaplan Urwitz model? |
| |
|Solution: |
| |
|The inputs to the model are as follows. |
| |
|F = $650m |
|π = $250 / $650 = 0.385 |
|S = 0 (unsubordinated debt) |
|L = $200 / $650 = 0.308 |
|C = $500 / $40 = 12.5 times |
|β = 0.800 |
|σ = [pic] |
|Y = 5.67 + (0.011 × 650) + (5.13 × 0.385) – (2.36 × 0) – (2.85 × 0.308) + (0.007 × 12.5) – (0.87 × 0.800) – (2.90 × 0.151) = 12.87 |
| |
|The credit rating for Kaplan Inc = AAA |
B. Unquoted companies
8.4.9 The second Kaplan Urwitz model was estimated using data on unquoted companies:
|Y = 4.41 + 0.014F + 6.4π – 2.56S – 2.72L + 0.006C – 0.53σ |
You will notice that there is no beta factor in the above equation – this is because we are dealing with unquoted companies.
In this case σ is the standard deviation of earnings. All the other variables remain the same.
|Question 2 |
|Levante Co is a large unlisted company which has identified a new project for which it will need to increase its long term borrowings |
|from $250 million to $400 million. This amount will cover a significant proportion of the total cost of the project and the rest of |
|the funds will come from cash held by the company. |
| |
|The current $250 million unsubordinated borrowing is in the form of a 4% bond which is trading at $98.71 per $100 and is due to be |
|redeemed at par in three years. The issued bond has a credit rating of AA. The new borrowing will also be raised in the form of a |
|traded bond with a par value of $100 per unit. It is anticipated that the new project will generate sufficient cash flows to be able |
|to redeem the new bond at $100 par value per unit in five years. It can be assumed that coupons on both bonds are paid annually. |
| |
|Both bonds would be ranked equally for payment in the event of default and the directors expect that as a result of the new issue, the|
|credit rating for both bonds will fall to A. The directors are considering the following two alternative options when issuing the new |
|bond: |
|(i) Issue the new bond at a fixed coupon of 5% but at a premium or discount, whichever is appropriate to ensure full take up of the |
|bond; or |
|(ii) Issue the new bond at a coupon rate where the issue price of the new bond will be $100 per unit and equal to its par value. |
| |
|The following extracts are provided on the current government bond yield curve and yield spreads for the sector in which Levante Co |
|operates: |
| |
|Current Government Bond Yield Curve |
| |
|Years |
|1 |
|2 |
|3 |
|4 |
|5 |
| |
| |
|3.2% |
|3.7% |
|4.2% |
|4.8% |
|5.0% |
| |
| |
|Yield spreads (in basis points) |
|Bond rating |
|1 year |
|2 years |
|3 years |
|4 years |
|5 years |
| |
|AAA |
|5 |
|9 |
|14 |
|19 |
|25 |
| |
|AA |
|16 |
|22 |
|30 |
|40 |
|47 |
| |
|A |
|65 |
|76 |
|87 |
|100 |
|112 |
| |
|BBB |
|102 |
|121 |
|142 |
|167 |
|193 |
| |
| |
|Required: |
| |
|(a) Calculate the expected percentage fall in the market value of the existing bond if Levante Co’s bond credit rating falls from AA |
|to A. (3 marks) |
|(b) Advise the directors on the financial implications of choosing each of the two options when issuing the new bond. Support the |
|advice with appropriate calculations. (8 marks) |
|(c) Among the criteria used by credit agencies for establishing a company’s credit rating are the following: industry risk, earnings |
|protection, financial flexibility and evaluation of the company’s management. Briefly explain each criterion and suggest factors that |
|could be used to assess it. (8 marks) |
|(d) The following information is available for the expected situation after the proposed bond issue. |
|Total assets = $1,050m |
|Monthly net income = $25m |
|Annual profit before interest and tax = $450m |
|Standard deviation of earnings = 8% |
|Assume the new bond is issued with a 5% coupon. |
|Use the Kaplan-Urwitz model for unquoted companies to predict whether the credit rating will be AAA, AA or A. (6 marks) |
| |
|Note: The model is Y = 4.41 + 0.014F + 6.4π – 2.56S – 2.72L + 0.006C – 0.53σ |
|(Amended ACCA P4 Advanced Financial Management December 2011 Q3) |
9. Effect of Alternative Financing Strategies on Financial Reporting
9.1 Impact of gearing on EPS, EBIT and return on equity
(Jun 12)
9.1.1 To appreciate the impact of financial gearing we shall explain and calculate the effects of changes in EBIT on EPS for a company with differing amounts of debt financing.
|Example 13 – Financial gearing on EPS |
|Assume that a company has the following statement of financial position structure. |
| |
| |
|Current |
|Proposed |
| |
|Asset |
|500 |
|500 |
| |
|Debt |
|- |
|300 |
| |
|Equity |
|500 |
|200 |
| |
| |
|The company currently has 100 shares in issue with a price of $5. It is proposing to buy back 60 shares for a total cost of $300, |
|financing this by issuing debt at a cost of 10%. This will leave 40 shares in issue. |
| |
|The EPS for the company when it has no debt = EPS (U) = EBIT / 100 |
| |
|Whereas the EPS for the company under the proposed borrowing = EPS (G) = EBIT / 40 |
| |
|The values of the ungeared EPS for different values of EBIT are shown in the table below: |
| |
| |
|Scenario |
|Scenario |
|Scenario |
|Scenario |
|Scenario |
|Scenario |
|Scenario |
| |
| |
|1 |
|2 |
|3 |
|4 |
|5 |
|6 |
|7 |
| |
|EBIT |
|0 |
|10 |
|30 |
|50 |
|70 |
|90 |
|110 |
| |
|Interest payments |
|0 |
|0 |
|0 |
|0 |
|0 |
|0 |
|0 |
| |
|Net income |
|0 |
|10 |
|30 |
|50 |
|70 |
|90 |
|110 |
| |
|EPS (U) |
|0 |
|0.1 |
|0.3 |
|0.5 |
|0.7 |
|0.9 |
|1.1 |
| |
| |
|Similarly, the values of the geared EPS for different values of EBIT are shown in the table below: |
| |
| |
| |
| |
| |
|Scenario |
|Scenario |
|Scenario |
|Scenario |
|Scenario |
|Scenario |
|Scenario |
| |
| |
|1 |
|2 |
|3 |
|4 |
|5 |
|6 |
|7 |
| |
|EBIT |
|0 |
|10 |
|30 |
|50 |
|70 |
|90 |
|110 |
| |
|Interest payments |
|30 |
|30 |
|30 |
|30 |
|30 |
|30 |
|30 |
| |
|Net income |
|-30 |
|-20 |
|0 |
|20 |
|40 |
|60 |
|80 |
| |
|EPS (G) |
|-0.75 |
|-0.5 |
|0 |
|0.5 |
|1 |
|1.5 |
|2 |
| |
| |
|As it can seen from the two tables, the earnings for the geared company are more volatile. When the values of EPS are plotted against|
|the values of EBIT, this is reflected in the gradient of the line showing the values of the geared EPS, which will be steeper than |
|the line plotting showing the values of unleveraged EPS. |
| |
|The breakeven level of EBIT where the two alternative financing schemes give the same EPS, i.e. when: |
| |
|EPS (U) = EPS (G) |
| |
|EBIT = $50. This can be seem from the fact that: |
| |
|[pic] |
|Implies EBIT = $50 |
| |
|This breakeven point can be checked as follows: |
|Original all equity structure = 50 / 100 = $0.50 |
| |
|Revised structure = (50 – 30) / 40 = $0.50 |
| |
|Above an EBIT of $50, the geared structure gives a higher EPS. In addition, the company’s ROE will exceed the interest cost of 10%. |
|Below $50, it gives a lower EPS and the ROE is less than the cost of debt of 10%. |
| |
|At the breakeven point, the ROE is equal to the interest rate on the debt, i.e.: |
|ROE = EBIT / 500 = 50 / 500 = 10% |
| |
|At an EBIT of zero, the original ungeared EPS will also be zero. However, with debt, there will be a loss per share of -30 / 40 = |
|-$0.75. |
| |
|[pic] |
| |
|Note that, although the EPS and ROE are more volatile for the geared company, the mean return is higher. This can be demonstrated by |
|calculating the mean returns for the above two capital structures, assuming that each scenario has an equal likelihood of arising. |
| |
|Ungeared company |
| |
|Mean net income for ungeared company = [pic] |
|EPS = [pic] |
|ROE = [pic] |
| |
|Geared company |
| |
|Mean net income for geared company = [pic] |
|EPS = [pic] |
|ROE = [pic] |
9.2 Degree of financial gearing
9.2.1 The degree of financial gearing measures the sensitivity of EPS to changes in EBIT.
9.2.2 The degree of financial gearing (DFG) is defined as the change in EPS over the change in EBIT or
|% change in EPS |
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|% change in EBIT |
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| |
|The degree of financial gearing can be calculated from the formula: |
| |
|EBIT |
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|EBIT – Interest |
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|Example 14 – Degree of financial gearing |
|For the ungeared company in the Example 13 above, the degree of financial gearing can be calculated as follows, for a particular |
|value of EBIT, say EBIT = $75. For the ungeared company, we have: |
| |
|[pic] |
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|Whereas for the geared company, we have: |
|[pic] |
| |
|The degree of gearing confirms our earlier finding that the geared EPS is more sensitive to changes in EBIT. |
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ACCA June 2016 Dec 2014
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