CAPM Risk Systematic Risk Systematic Risk Business Risk Unsystema tic Financial Risk Risk

Relative Beta BusinessSystematic Equity=geared RiskRisk=Beta beta Financial RISK Beta Asset= Ungeared beta Business Risk

However, it is not simply a case that the βasset equals the sum of the βequity and the βdebt. What also need to betaken into account is the proportions of equity and debt: βAsset =βequityFinally, we need to take into account tax relief on interest payments, (as it will affect the financial risk exposureof shareholders). This now gives rise to a very important equation for the exam: We assume βDebt is zero.Where:βEquity’s known as the equity Beta. It measures the systematic business risk and the systematic financial risk ofthe company’s shares.βAsset is known as the asset beta. It measures the systematic business risk only.β Debt is known as the debt beta. It measures the systematic risk of the company’s debt securities.

Example # 1:B plc has a gearing ratio (D: E) of 1: 2 and its shares have a beta value (βEquity) of 1.45. The corporation tax rate is 30%, debt isassumed to be risk free. Calculate beta asset ?Solution: Four Implications This analysis gives rise to four important implications: A company’s equity beta will always be greater than is asset beta. This is because the equity beta measures both business and financial risk, while the asset beta measures business risk only. βe>βa The one exception to this is where the company is all equity financed, and so only has systematic business risk, and has no financial risk. In those circumstances its equity beta and its asset beta will be the same. Then βe=βa Companies in the same area of business, (i.e. they have the same business risk), will have the same asset beta. Companies in the same area of business will not have the same equity beta, unless they also happen to have the same gearing ratios. (Means financial risk same).

IF Company is operating in more than one divisionIf the company operates on a divisional basis and each division is in a different business area.Then:-1) Find suitable proxy company for each division and find βa’s of each proxy for each division field.2) Combine βa of both divisions to calculate weighted average βa. Weighted average βa = βa 1st division x % + βa 2nd division x % % proportion will be given in exam according to revenue share, asset share or any other basis3) Re gear the calculated weighted average βa using company’s own gearing level.4) Calculate Ke using CAPM5) Calculate WACC

Example 2: ABC Ltd is operating in power sector and has a beta of 1.2 Gearing level is at 40%. After tax cost Kd = 6% Equity risk premium = 7% Rf = 5 % Tax rate = 30% ABC Ltd wants to diversify into cement business. XYZ co is in Cement business it has a beta of 1.60.It does not pay tax and D/E = 2:3 Calculate WACC of ABC Ltd .After investing in Cement business .(cement will 30% of total business and gearing will remain same) Solution: XYZ co: ungear the beta of proxy co for cement division ββaa==β1e.60 [ 3/3+2] βa = 0.96 ABC Ltd: un gear the beat of Abc company for power business βa = βe βa = 1.2 [60/60+40(1-0.3)] βa = o.82

Calculate Weighted Average beta Asset of both power and cement business βa AVg = 0.82 x 70% + 0.96 x 30% = 0.86 Regear it with current gearing of ABC Ltd. 0.86 = βe [60/60+40(1-0.3)] Be = 1.26 Calculate Ke using CAPM Ke = 5% + 1.26 x 7% Ke = 13.8% WACC = Ke + Kd (after tax)= 13.8% [60/60+40] +6%[40/60+40] WACC = 10.7%

Example 3:ABC Ltd is operating in power sector and textile sector and has a beta of 1.45. Gearing level is at 40% Kd after tax = 6% Equity risk premium = 7% Rf = 5% TAX = 30%It wants to dispose of its power business.XYZ co is in power business. It has a beta of 1.16.MV/ share = $3/ shareShares = 400 mDebt MV 108 per 100 Book value = $576mCSalcoullautetiWoAnC:C of ABC Ltd after disposal of power business. (Power business is 40% of total and gearing will remain same. • XYZ Ltd Ungear beta equity of power proxy XYZ co : βa = βe βa = 1.16 [1200/1200+622(1-0.3)] βa = 0.85

ABC Ltd the total equity beta of ABC company to calculate total weighted average beta Ungear βa of ABC Ltd βa = βe βa = 1.45 [60/60+40(1-0.3)] βa = 0.99 Calculate βa of textile Βa of total business= βa of power x 40% + βa of textile x 60% 0.99 = 0.85 x 40% + βa of textile x 60% βa of textile = 1.08 Calculate βe by regearing the calculated beta asset of textile division1.08 = βe Βe = 1.58 + Kd (after tax) Calculate Ke by using CAPM Ke = 5% + 1.58 (7%) Ke = 16% WACC = Ke = 16%[60/60+40] +6%[40/60+40]WACC = 12%

WACC and market valueFor a company with constant annual 'cash profits', there is an important connection between WACC and market value. (Note: 'Cashprofits' are cash flows generated from operations, before deducting interest costs.)If we assume that annual cash profits are a constant amount in perpetuity, the total value of a company, equity plus debt capital, iscalculated as follows: From this formula, the following conclusions can be made: The lower the WACC, the higher the total value of the company will be (equity + debt capital), for any given amount of annual profits. Similarly, the higher the WACC, the lower the total value of the company. The aim should therefore be to achieve a level of financial gearing that minimizes the WACC, in order to maximize the value of the company. Capital Structure Theories: These theories explain the impact on the cost of capital of the company due to change in the capital structure of the company. It includes the following theories: The Traditional View Modigliani-Miller (MM) Theory (without tax) Modigliani-Miller (MM) Theory (with tax)

The traditional view of gearing and WACCThe traditional view of gearing is that there is an optimum level of gearing for a company. This is the level of gearing at which theWACC is minimized.The traditional view of gearing and WACC – ContinuedThe traditional View towards cost of capital is that there is an optimal capital structure at which Optimum gearing % = minimum WACC the company’s weighted average cost of capital is at its minimum. •Under the traditional view, the cost of equity increases as the level of gearing increases because of higher financial risk but the relationship between cost of equity and WACC is non-linear. As a result, WACC decreases initially due to increased borrowing until it reaches its minimum and then it starts to increase. This lowest point represents the optimal capital structure at which WACC is at its minimum AND MV is maximum.

The Modigliani-Miller propositions: ignoring corporate Taxation Taxation MAossduigmlipantiio-Mnsiller stated that, in the absence of tax, a company’s capital structure would have no impact on its WACC. A perfect capital market exists. Debt is risk-free and freely available at the same cost to investors and companies alike. All the assumptions of Traditional View Apply as well. Explanation Kd will remain constant at all level of gearing because there is no financial distress cost. Ke will increase as gearing level increase because it will increase the financial risk and beta equity The cheaper effect of Kd will exactly cancel off the increasing effect of Ke and wacc will remain constant at every level of gearing. As wacc is not changing so there will be no change in market value. Modigliani and Miller therefore reached the conclusion that the level of gearing is irrelevant for the value of a company. There is no optimum level of gearing that a company should be trying to achieve.

The Modigliani-Miler view: allowing for corporate taxationtaxation•Modigliani-Miller stated that, with tax, a company’s capital structure is maximum debt.AssumptionsA perfect capital market exists.Debt is risk-free and is lower because of tax savings and freely available at the same cost to investors andcompanies alike.

ExplanationKd(1-T) will remain constant at all level of gearing because there is no financial distress cost.Ke will increase as gearing level increase because it will increase the financial risk and beta equity The cheaper effect of Kd will dominate the increasing effect of Ke and wacc will be declining at at every level of gearing.As wacc is is declining at every level of gearing so market value is increasing with gearing. The total value of the company is therefore higher for a geared company than for an identical all-equity company/The value of acompany will rise, for a given level of annual cash profits before interest, as its gearing increases.Modigliani and Miller therefore reached the conclusion that because of tax relief on interest, there is an optimum level of gearingthat a company should be trying to achieve. A company should be trying to make its gearing as high as possible, to the maximumpracticable level, in order to maximize its value. Modigliani-Miller formulae: allowing for taxation Cost of equity The cost of equity in a geared company is higher than the cost of equity in an ungeared company, by a factor equal to: The difference between the cost of equity in the ungeared company and the cost of debt, (KEU-Kd) Multiplied by the ratio

Example: 1An ABC co is currently in trading business and wants to diversify into new business.Haizum Co, a listed company is in same business in which abc co wants to diversify Haizum Co’s cost of equity is estimated to be14% and it pays tax at 28%. Haizum Co has 15 million shares in issue trading at $2·53 each and $40 million bonds trading at $94·88per $100. The five-year government debt yield is currently estimated at 4·5% and the market risk premium at 4%Abc co has market value of equity of $60 million. It borrows $20 million of debt finance, costing 5%.The rate of taxation oncompany profits is 25%.According to Modigliani and Miller:a) Identify the suitable proxy co and ungear its cost of equity

Relevance for capital investment appraisalThe Modigliani and Miler formulae can be used to re-calculate the cost of equity and the WACC in a companywhere the level of gearing changes, provided there is no change in the overall business risk and the company istherefore similar in all respects except for its gearing.When a company plans a new capital investment that will alter its gearing, without affecting its business riskprofile, the MM formulae can be used to calculate the cost of equity and WACC at the new level of gearing. Thenew WACC can then be used as the discount rate for calculating the NPV of the proposed project.Assumptions of WACCExisting WACC can only be used as a cost of capital for new investment appraisal project if the followingconditions are met:Business risk of the project should be same as the existing business risk of the company and by business risk wemean the nature of the business or the type of industry should remain same.Financial risk of the project should be same as the existing financial risk of the company, where financial risk isthe level of gearing.(gearing should remain same)Size of the project should be smaller or comparable to the existing size of the company.Required return of investors should remain same.

DETERMINATION OF ‘DISCOUNT RATE’ FOR APPRAISAL OF PROJECT Undertaking the project will alter the company’s capital structure No Yes Regardless of whether the project have same orif new project is in same line of existing different systematic business risk use APVbusiness methodYes= the project in same area NO= project is in a different areaof business of businessCo’s existing WACC is suitable Risk adjusted WACC

STEPS FOR THE DETERMINATION RISK ADJUSTED WACC in (c) i) or ii) above to find the Riska) Find a suitable proxy company having same level of operations.b)Ungear βe to find the asset βeta.c)Re-gear βa to find the project equity βeta. Use either:- i. The company’s existing gearing level or ii. The specified gearing level post projectd)Use the calculated beta equity , calculate Ke CAPM .e)Find the relevant Kd(1-t)f)Use WACC Formula, project Ke, Kd(1-t) and gearing level statedAdjusted WACC-a nominal cost of capital.:

Example # 1:SKANS is an education services provider with a debt: equity ratio of 1:3. It wishes to diversifyinto the professional publications of ACCA & CA students, using an NPV analysis. The companydoes not intend to change its capital structure.Suppose that BPP is a typical professional book publisher. It has an equity beta of 1.25 and adebt: equity ratio of 1: 2. Because BPP is in the same area of business as the project, it is knownas the pure-play company.If Rf = 6%, Rm = 14% and Tc = 30% - and it is assumed that the debt is risk free.Required:Calculate risk adjusted WACC for the project.

SolutionStage One - The asset beta of BPP – the pure-play comparison company – is calculated and then used as anestimate of the asset beta of SKANS publishing project.Using This asset beta reflects the systematic business risk of publishing books Stage Two - Having estimated an asset beta for the publishing project, we can now estimate an equity beta for the project; to reflect both the systematic business risk of professional publication and the systematic financial risk of SKANS capital structure.

Stage Three: - Using CAPM calculate KeKe Publication Project = Rf + [Rm - Rf] βEquityKe Publication Project = 6% + [14% - 6%] X 1.142 = 15.14%Therefore the cost of equity capital for the project is 15.14% Stage four : - Using the following formulaIf a cost of debt capital is needed but no cost of debt is given, we can make use of the fact thatthe question allows use to assume the debt beta is zero. In these circumstances;Kd = RfAnd KdAT = Rf X (1 – TC)Therefore, KdAt = 6 X (1 – 0.30) = 4.2%

# AFM--Investment-Appraisal-(1)-CAPM

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**Description: ** AFM--Investment-Appraisal-(1)-54-74

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