T.J Mabvure (Mr.) 1 ADVANCED CORPORATE FINANCE CHINHOYI UNIVERSITY OF TECHNOLOGY SCHOOL OF BUSINESS SCIENCES & MANAGEMENT DEPARTMENT OF ACCOUNTING SCIENCE & FINANCE ADVANCED CORPORATE FINANCE (CUAC401) BCOM (HONS) ACCOUNTANCY BPFA COURSE OUTLINE 2009 COURSE LECTURER: T.J MABVURE (Mr.) General Information • Office: Room 7-16/11-08 • Phone: 0913 593 523 • E-mail: [email protected], [email protected], [email protected]1.0 Aim This course is designed to develop an understanding of finance and corporate financial analytical tools at a higher level. The course is a continuation of Corporate Finance. 2.0 Objectives By the end of the course, students should be able to: 2.1 Determine the value of Equity and Firms 2.2 Analyse Mergers and Acquisitions of Companies 2.3 Discuss Short term Financial strategies of firms 3.0 Method of instruction 3.1 Lectures 3.2 Demonstrations 3.3 Group discussions 3.4 Assignments 4.0 Assessment 4.1 Assignments 15% 4.2 Intrasessional test 15% 4.3 Final examination 70%
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ADVANCED CORPORATE FINANCE
CHINHOYI UNIVERSITY OF TECHNOLOGY SCHOOL OF BUSINESS SCIENCES & MANAGEMENT
This course is designed to develop an understanding of finance and corporate financial analytical tools at a higher level. The course is a continuation of Corporate Finance.
2.0 Objectives By the end of the course, students should be able to: 2.1 Determine the value of Equity and Firms 2.2 Analyse Mergers and Acquisitions of Companies 2.3 Discuss Short term Financial strategies of firms
3.0 Method of instruction
3.1 Lectures 3.2 Demonstrations 3.3 Group discussions 3.4 Assignments
4.0 Assessment 4.1 Assignments 15% 4.2 Intrasessional test 15% 4.3 Final examination 70%
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Total 100% 5.0 Course Content
5.1 Corporate Strategy And Financial Strategy 5.2 Introduction To Valuation
• Free cash flow to equity for Unlevered firms • Free cash flow to equity for Levered firms
5.4.2 Free cash flows to the firm (FCFF)
5.5 Valuation Of Companies 5.5.1 Valuation of Equity
• Valuation in the stable growth model • Valuation in the two stage model • Valuation in the three stage model
5.5.2 Valuation of the Firm 5.5.3 Growth rate in FCFE and Growth rate in FCFF
5.6 Relative Valuation 5.6.1 Price Earnings Ratio 5.6.2 Price To Book Value Per Share 5.6.3 Price to sales
5.7 Short Term Financial Strategy
5.7.1 Spontaneous Sources of funds 5.7.2 Internal sources 5.7.3 External Sources 5.7.4 Relationships between sales and debtors, fixed assets and current
Assets, stocks and creditors. 5.7.5 Constant ratio method 5.7.6 Formula methods
5.8 Mergers and Acquisitions
5.8.1 Horizontal, conglomerate, and vertical mergers 5.8.2 Reasons for mergers 5.8.3 Terms of mergers
Correia etal. Financial Management 3rd edition. Juta & Company, Johannesburg
Damodaran Aswath.Investment Valuation Tools and Techniques for determining the value of any asset.2nd Edition.1996.Wiley Frontiers in Finance.
Hinderling C. Capital Budgeting Kotler D. Marketing Strategy
Stickland A.J, Thompson A.A, Strategic Management: Concepts and Cases. 13th Edition.2003. McGraw Hill Higher Education. University of Alabama.
Text 1. Brigham and Gapenski; Financial Theory, Policy, and
Practice a. Financial Planning b. Restructuring,Mergers,acquisitions c. Financial Reporting
2. Correia etal, Financial Management
a. Mergers and Acquisitions 3. Companies Act 24:03
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b. Legal Provisions on the Restructuring,liquidations,arrangements
4. Aswath Damodaran; Investment Valuation: Tools and
Techniques for determining the value of any Asset. a. Main Textbook
5. Strickland; Strategic Management
a. Reference book for strategic issues 6. D. Kotler; Marketing issues
a. Reference for Strategic issues 7. Keith Ward; Corporate Financial Strategy. Functional Strategy
a) Marketing Strategy b) Human Resources Strategy c) Production Strategy d) Financial Strategy
Financial Strategy Issues to consider in crafting this strategy:
a) Sources of funds b) Uses of funds c) Capital structure(Debt/Equity structure) d) Risk return(measured by ke,P0,g,β) e) Dividend policy
Main Corporate Strategy issues: How financial strategy fits into it.
a) Market share and growth rate of the market b) Product range(Product life cycle)-At what stage of the PLC is each
product c) Strategic Business Units (SBU)-every SBU is strongly related to each
product in each product range. For e.g. Pioneer has Passenger transport, trucking, courier (removals) as its SBUs.Each SBU will follow the PLC of
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its product or product range. The PLC of the product is the PLC of the SBU.
Product Life Cycle (PLC)
Stage 1: Introduction
Profits are negative Promotion of the product(Heavy expenditure on promotional activities resulting in low profits)
Heavy expenditure on R&D Cash flow are negative
Stage 2: Growth
Profits are positive and are increasing Advertising expenditure because of new competitors Developing of Brands e.g. Buddie, Mango.Cashflows will be negative because of brand building. If positive they are still low.
Stage 3: Maturity
Market growth rate has started to decline Rebranding activities/brand transfer; Buddie to Libertie; Mazoe orange crush to raspberry, Granadilla.
Large companies who have survived Large market share Growth rate of market stabilized Cash flows now positive, now exploiting the characteristic of your brand
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Stage 4: Decline
Cash flows now negative Growth opportunities now small Divesting from Subs e.g. Harvesting SBUs like gold mining where gold has run out.Kamativi tin mine was divested long ago because of the increase in plastic.
Boston Consultant Group SBU Star
High relative market share in a high growth market
2.Growth � Dividend payments low � Listing or private placement � Option based borrowing � PE ratio high � Operating risk high � Gearing low
SBU Question Mark
Low relative market share in a high growth market
1.Introduction � Dividends nil � Equity finance-venture capital � Gearing nil � P/E ratio high � Operating risk high, financial risk low
SBU Cash Cow
High relative market share in a low growth market
3.Maturity � Dividend high because of positive
Cash flows � Net cash flows high � Rights issues � Operating risk now low � P/E ratio now low
SBU Dog
Low relative market share in a low growth market
4.Decline
Financial Strategic Issues 1. Net cash flows at each stage 2. P/E ratio at each stage 3. Dividend policy at each stage 4. Gearing ratio determined by the total risk
Introductory stage
� Net cash flows will be negative or very low because revenues are still low and there are outflows in concept development
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� Dividends are nil because profits still low and cash flows are negative. Retention ratio is 100% in order to gain market share in the growing market.
� P/E ratio will be very high. Market perception that the company will do well in the future are very high. Price per share relative to earnings per share is high.
� Total return(Dividend yield plus capital gain yield) � The investors are the promoters of the product concept and they are the
sponsors. The investors are venture capitalists using venture capital (venture capitalists have different portfolios in different SBUs, i.e invest in a controlling stake. They will be looking for capital gains and not dividends. They sell their equity holdings as soon as the company grows they pull out. Angel capitalists are an alternative to venture capitalists.
� Financing structure will be all equity finance. Therefore the gearing ratio will be Nill.The Company can not sustain loan obligations as they come due.
� Operating risk (business risk) will be very high so the required rate of return by debt holders will be high and can not be sustained. Total risk=Operating risk+Financail risk), so financial risk has to be maintained at low levels.
Growth Stage
� Still fighting competitors if the barriers to entry are very low. In the telecoms industry POTRAZ and BAZ for broadcasting have artificially raised the barriers.
� Net cash flows are still low because of the heavy expenditures incorporated in strengthening the brand, e.g netone, telecell, and econet.
� Dividends payments are very low � P/E ratio still very high � Capital gains being sought for, other than dividends � Gearing lo because at this stage the business risk is still relatively high,
that’s why there is need for reducing financial risk by reducing borrowings
� Equity financing but changed from venture because the company will be listed to facilitate a new share issue (IPO) for expansion of the company. Equity is now shareholders equity and the venture capitalists will pull out. At listing there will be a price which will determine the price at which the venture will sell their share. Private placements (approaching institutional investors such as the MIPF, PTC, NSSA, OLD MUTUAL, etc) would also be considered when the company does not want to list.
� Option based financing; financing with imbedded options such as convertible debentures, convertible bonds will be considered. This are issued at a lower cost than plain vanilla bonds. These will be converted after a period of time agreeable. The option to convert is not obligatory,
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only exercised when it’s profitable to do so. Also there can be debentures with warrants attached, i.e. the right to buy an agreed number of the company’s ordinary equity at an agreed time and at an agreed price (strike price/exercise price) .A convertible is known as a European option because it can only be exercised at an expiration date. A bond with a warrant is an American option because it can be exercised at any time before the expiration time. It gives an option within an option. With a warrant you become a shareholder and also a bond holder, the warrant can be detached from the bond, i.e it can have its own market value. It’s a highly valued instrument compared to the convertible. At this stage the company has to take advantage of financial leverage because earnings are increasing but can not borrow outright because business risk is still high and financial risk has to be minimized. To go around this problem, option based instruments have to be used. Option based bonds (sweeteners) are cheaper than plain vanilla bonds. They reduce the total cost of borrowing. Option based bonds can be issued at low coupon rates because they will gain value, that is they are participating in the growth of the company. Ordinary bondholders have a fixed return and they don’t benefit from the increase in the value of the share. After the exercise the equity base will increase and the debt will decrease, that is the capital structure will shift, for the convertible bonds. For the bond with warrants, the debt levels will remain the same and the equity will increase, also with these bonds there will be a fresh injection of funds as the shares have to be bought. With the options the company will be preparing for the restructuring of the balance sheet, i.e restructuring at the initial public offer (IPO) and then another restructuring at the exercise of the options.
Maturity
This is a stage at which the balance sheet will also be restructured.
� Rights issue/seasoned issue; New shares to existing shareholders. The rationale is to reward the shareholders for being loyal because they have made the company grow by accepting low or no dividends for capital gains. The company does not want to dilute the earnings of the shareholders.
� Exercise of options if convertibles and warrants had been issued. � Net cash flows are now high, that is positive. High turnover with low cost
of R&D. Main expenditure is advertising rather than promotional because brand is now established. Consolidating your position by tour brand. No needs to reinvest as the market opportunities for expansion are now low.
� Dividends now high because growth opportunities now reduced,i.e retentions now reduced
� Cash cow because some of the cash flows can be used to finance new SBUs.
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� The returns now dividends yields rather than capital gains � Bond holders now interested in dividends rather than capital gains and
also this holds for all the former shareholders who the company started with.
� The P/E ratio now low � The operating risk now very low � Gearing ratio low, can now afford to have plain vanilla debt because the
cash flows are there. Decline
� Divesting/harvesting � Zero opportunities � Total dividend, that is 100% payout � Not able to increase borrowings because the required rate of return will
be high. If the company increase borrowings and the company is wound up the share of the debt holders will increase in the company. Therefore the debt/equity ratio has to be decreased.
� The company will grow(g) at the same rate as the growth of the economy
APPROACHES TO VALUATION The purpose is to arrive at the value of the company using its fundamentals, which is the value of its assets. There are three approaches to valuation.
1. Discounted cash flow Valuation 1. Value of equity-specifically the price per share(P0) 2. Value of the firm
� The value of an asset is the present value of the expected future cashflows, discounted at the required rate or return that reflects the risk ness of these expected cash flows.
Value=( )∑
= +
n
tt
t
ke
CF
1 1
n=Life of the asset CFt= Cash flow in year t Ke=required rate of return given the risk
� The value of equity is found by discounting the expected cash flows to equity at the rate of return required by equity investors.
� If we assume that the firm is in a stable growth period:
Value of equity=( )∑
∞
= +1tt
t
kei
CFE
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Where t is starting from year 1 to infinity CFE=Cash flow to equity Ke= risk adjusted required rate of return [ke=RF+β (rm-
rf)] Rf= Risk free rate, ie the average money market rate, TB
rate is used as proxy .Not that it is the only risk free rate, as all the securities in the money market are risk free.
β= Beta coefficient, measure the volatility of the returns on the security relative to the returns on the market. It’s a measure of the systematic risk
rm-rf= risk premium on the market [illustrate with a diagram the risk premium]
Value of firm=( )∑
∞
= +1 1tt
t
WACC
CFF
CFF=Cash flow to the firm WACC=Weighted average cost of capital
• Value of firm is the cash flows to the firm discounted to the weighted present value of the weighted average cost of capital(WACC)
• Cash flows to the firm are the equity to the shareholders and debt to debt holders. WACC=Wd[kd(1-T)]+WeKe+WpKp kd= cost of debt adjusted for tax(T) because interest is Allowable for tax to make the debt cheaper. Ke= cost of equity Wd= weight of debt Wk= weight of equity Wp= weight of preference shares
Applicability
� Discounted cash flow valuation is based on expected future cash flows and discounts rates.
� The expected cash flows have to be estimated � Given these informational requirements the approach is easier for firms
whose cash flows can be reliably estimated for future periods. � The approach also requires the use of a proxy for risk to be applied to
the discounted rates and the proxy is the β coefficient � With other models other than CAPM the β is not a sufficient proxy
however.
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� The discounted cash flow approach may be difficult to use because of the following:
1. Firms in trouble: A distressed firm generally has negative earnings and cash flows. To estimate the future cash flows for such a firm may be difficult because of the high probability of bankruptcy.
2. Cyclical firms: This is affirm whose earnings and cash flows tend to follow the economic cycle, that is increasing during economic booms and falling during recessions.
3. Firms with unutilized assets: Discounted cash flow valuation reflects the value of all assets that produce cashflows.If a firm has assets that are not utilized and therefore didn’t produce cash flows the value of these assets would not be reflected in the total value. For example a firm with a piece of land, mining claim not exploited.
4. Firms with Patents and Product options: Firms that have unutilized patents or product options that are not currently producing Cash flows but can be exploited are not also easy to value using this approach.
5. Firms in the process of restructuring: For example the firm maybe in the process of selling some of its assets and acquiring others, e.g Delta disbanded some of its subsidiaries like the hospitality, furniture and remained with the beverages.
6. Firms involved in acquisitions: This causes the problem of synergy (expected benefits of the merger and they are not easy to quantify.).
2. Relative valuation approach
1. This approach says that the value of an asset is derived from the pricing of comparable assets standardized using a common variable such as earnings, cashflows, book values or revenues.
2. We can use the industry average P/E ratio assuming that the other firms in industry are comparable to the firm being valued.
3. We can also use the price to book value (market price/book value). A firm selling at a discount to its book value relative to other firms in the industry is considered undervalued.
4. Also price to sales multiple is used in this valuation process. 5. To use these multiples we relate the multiple to the firm’s
fundamentals such as; the growth rate in earnings, and dividend payout ratio. This allows us to explore how the multiple will change as the firms characteristics change for e.g. we would want to know the effect of changing profit margins on the P/Sales ratio or the effect of changes in the growth rates on the P/E ratio.
6. This approach is useful when there is large number of comparable firms being traded on the financial markets and the market is on average pricing these firms correctly.
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3. The contingent valuation method This approach uses option pricing models to measure the value of assets with option characteristics (warrants and convertible bonds).
� Equity investors receive a residual claim on the cash flows to the firm, is they are entitled to any cash flow that is left over after meeting all the financial obligations of the firm including debt repayments and the re-investment needs of the firm.
� The free cash flow to equity (FCFE) are the cash flows that remain after operating expenses and principal repayments and any capital expenditures that are required to maintain the growth rate in projected cash flows.
a) Free cash flows for and unleveled firm: An unleveled firm has no
debt in its capital structure, therefore there are no interest and principal Repayments, it finances all capital expenditures and working capital needs with equity therefore the free cash flow to equity will be as follows:
Gross Profit xxx Operating Expenses (xx)
EBITDA xxx Depreciation and Amortization (xx) EBIT xxx Taxes (xx) Net Income xxx Depreciation and Amortisation xxx Cash flow from operations xxx Capital Expenditure (CAPEX) (xx) Changes in Working capital (xx) Free cash flow to Equity (FCFE) xxx
• Amortization is the w/o of intangible assets e.g. goodwill, pre-operations costs.
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Assuming an increase in working capital if there was a decrease we will add. � The FCFE is the residual cash flow after meeting all the firms
financial needs; it can be negative in which case the firm must raise new equity. If it’s positive it could but is not always paid out as dividends to equity investors.
� When we reach net income the amount w eventually deduct for dividends has to take into consideration the CAPEX, and the change in working capital.
� Depreciation and amortization are treated as tax deductible expenses in the income statement but they are non-cash expenses and therefore they should be added back.
� Equity investors can not withdraw the entire cash flow from operations from the firm’s since some or all of it will have to be re-invested to maintain existing assets and to create new assets to generate future growth.
� Funds tied up in working capital cant be used elsewhere in the firm therefore increases in working capital are cash outflows and decreases are cash inflows(specifically non-cash working capital)
2009($m) 2010($m) Net Income 100 20 Depreciation 40 45 Funds from operations 140 65 CAPEX (80) (20) ∆WC (40) (10) FCFE 20 35 The drop in the CAPEX and WC in 2005 resulted in increased FCFE through the net income was much lower. b) FCFE For a levered firm
In addition to making all of the outlays that an unleveled firm must make the levered firm must also generate cash flows to cover interest expenses plus principal repayments. It can also finance some of its capital expenditures and working capital needs with debt thereby reducing the equity investments needed.
EBT xxx Taxes (xx) Net Income xxx Depreciation and Amortisation xxx Cash flow from operating Activities xxx CAPEX (xx) ∆WC (xx) Principal Repayments (debt repayments) (xx) Proceeds from new debt issues xxx FCFE xxx
The interest is tax deductible but the principal repayments are not tax deductible.
i) A levered firm at its desired level of leverage � The desired leverage is the debt ratio that is viewed as
acceptable for future financing so there is no plan to change it:
Debt Ratio=equitydebt
Debt
+
� If the debt ratio is regarded to be optimal the free cash flows to equity (FCFE) will be: Net income-(1-d) (CAPEX-Depreciation)-(1-d) (∆WC). d=Debt ratio regarded as optimal.
� For such a firm the proceeds from new debt issues will be given by the following: Principal repayments+d (CAPEX-Depreciation+ ∆WC).
� Since the firm is at its desired capital structure principal repayments are made with proceeds from new debt issues. CAPEX and WC needs are financed using the desired mix of debt and equity.
E.g. In 2009 a firm had $10million of debt outstanding and $30million in market value of equity giving a debt ratio of 25%. This debt ratio is assumed to be stable (there is no attempt to change it). The following information is available: 2009(Reported) 2010(Projected) $ $ Net income 250 400 Depreciation 50 75 CAPEX 150 300 WC (2008=10) 25 - Sales 1000 1500 Question: calculate the FCFE
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Working capital in 2010 is projected to be at the same percentage of sales as in 2004
WC (2009) = %5.2100*1000
25 =
WC (2010) =2.5%*1500=$37.5million 2009 2010(Projected) Net income 250 400 - (CAPEX-Dep) (75) (168.75) (11.25) (9.38) FCFE 163.75 221.87
� The FCFE will increase as the amount of debt used by the firm increases, that is the FCFE is an increasing function of‘d’.
� Suppose we increase the debt ratio to 40%, the FCFE will be high. d=40% 2009 2010 Net income 250 400 - (Capex-Depn) (1-d) (60) (135) - (∆WC) (1-d) (9) (7.5) FCFE 181.00 257.50
� This is tying up with the financial leverage effect � This increase in FCFE however comes at the price of increased risk to
the equity holders (financial risk), that is as we increase debt there is a probability that our earnings would not be able to pay our interest and principal obligations.
� This risk will result in a higher β coefficient for the firm. The higher the β, the higher the ke, that is investors, will penalize the firm’s equity by increasing the required rate of return.
ii) A levered firm with a debt ratio below the optimal level
� A levered firm that is operating at a debt ratio below its desired level can afford to use more debt in financing its capital expenditures and working capital needs until it reaches the target debt ratio(optimal level) and the FCFE for such a firm will be as follows.
Net Income xxx Depreciation and Amortisation xxx Cash flow from operations xxx
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CAPEX (xx) ∆WC (xx) Principal Repayments (xx) Proceeds from new debt issues xxx FCFE xxx
� If the firm decides to increase its leverage towards its targeted levels then the proceeds from new debt issues would be greater than the principal repayments plus the CAPEX and WC needs.
� Can not use the short cut method because debt levels not optimal
Proceeds from new debt>Principal repayments+d (CAPEX+ ∆WC)
� During the period when the firm is financing its investment needs disproportionately with debt, the FCFE for such a firm would exceed that of a firm which does not have such financing slack. A firm with financial slack will have more FCFE than a firm with no financial slack.
� The principal repayments are still financed with new debt issues therefore don’t affect the FCFE. � Suppose the company has reported the following: 2009(Reported) 2010(Projected) $ $ Net Income 900 1500 CAPEX 400 600 Depreciation 80 100 ∆WC 50 55 Debt(mkt value) 250 - Principal repayments70 70 Equity(mkt value) 800 -
d= 100*250800
250
+=24%
� The company wants to increase this debt ratio to 40% which it
considers optimal, to achieve this target the company plans to
finance 60% of its CAPEX and WC needs with debt between 2009 and
2010.
Calculate The FCFE in 2010:
We can’t use the short cut method since the debt ratio is not
optimal.
Net Income 1500
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Depreciation 100 Cash flow from operations 1600 ∆WC (55) Principal Repayments (70) Proceeds from new debt issues 463 Capex (600) FCFE 1338
Proceeds from new debt issues=70+0.60(600+55) =463
60% should be debt and 40% equity if the company wants 100% capital
injection. Equity will not remain at $800; it will increase by 40%.
iii) A levered firm with leverage above the optimal.
� The ‘d’ is the desired level of debt
� A firm will have to use disproportionately more equity in financing its
investments needs in order to reduce its debt ratio and may also have
to generate funds from equity in order to meet some or all of its
principal repayments.
The FCFE will be as follows
Net income xxx Depreciation and Amortisation xxx Cash flows from operations xxx CAPEX (xx) Principal Repayments (xx) WC needs (xx) Proceeds from new debt xxx FCFE xxx � There is some short-term debt which needs to be refinanced as they mature, we can’t live without them. � If the company decides to reduce its leverage towards the optimal
level then proceeds from new debt issues will be less than principal repayments + WC and CAPEX.
� In the period that the company is raising disproportionately more equity to finance its investments needs and principal repayments the FCFE would be lower than the FCFE for an otherwise similar firm which is operating at its desired leverage.
� In Zimbabwe companies above leverage were (2007 and before) financing through retained earnings to reduce debt levels but in the process they were reducing FCFE.
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Question-levered firm below the optimal 2009(Reported) 2010(Projected) Net income 400 850 CAPEX 120 240 Principal Repayments 20 20 ∆WC 50 60 Depreciation 55 70 Mkt value of debt 450 Market value equity 1200 Proceeds From new debt 90
FCFE 355 740
d= %27.27100*1200450
450 =+
� The company plans to increase the debt ratio to 35% by 2012. to reach this target it plans to finance 40% of its capital expenditures and WC requirements between 2010 and 2012 with debt. Calculate the current FCFE and the projected FCFE for 2010. Proceeds from new debt issues=Principal repayments+d(CAPEX+ ∆WC) =20+0.4(240+60) =140 2009 2010 Net income 400 850 Depreciation 55 70 Cash flow from operations 455 920 CAPEX (120) (240) ∆WC (50) (60) Principal repayments (20) (20) Proceeds from new debt issues 90 140 FCFE 355 740
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Question-levered firm above the optimal 2009 2010 Net income 14000 18500 CAPEX 1750 3600 Depreciation 1900 2950 ∆WC 1400 1850 Mkt value of debt 40000 - Mkt value of equity 45000 - Principal repayments 5000 7500 New Debt issues 10000 -
d= %1.47100*4000045000
40000 =+
� The company plans to reduce its debt ratio from 47% to 25% by 2012, to achieve this only the short term debt which is currently standing at $10000 will be refinanced. All CAPEX and any increases in WC needs would be financed primarily with equity that is 90% and 10% debt. Long term debt outstanding would be repaid with cash flows from equity. Calculate the FCFE for 2009 and the projections for 2010. Proceeds from new debt issues=New debt issues+0.10(3600+1800)=10540 For 2010 the 10000 which the company had in 2009 will be refinanced and raise 10% in the proportion of CAPEX and WC. 2009 2010 Net income 14000 18500 Depreciation 1900 2950 Cash flow from operations 15900 21400 CAPEX (1750) (3600) ∆WC (1400) (1800) Principal repayments (5000) (7500) New debt issues 10000 10540 FCFE 17750 19090
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II. Free cash flows to the firm
Value of the firm=gWACC
FCFF
−1
� This is the value of the firm for a company in a stable growth model. � The firm can be valued more realistically when we use the above model than the dividend growth model as some firms don’t offer dividends. � A firm is composed of all its claim holders(claim to the cash flows Including equity investors, debt holders, and preferred stock holders). � The cash flows are the total cash flows to all these claimholders. The
cash flows to the firm are those left over after meeting operating expenses and taxes but before making any payments to any claimholders.
Free cash flows to the Firm (FCFF)=FCFE+Interest expenses(1-T)+Principal repayments+New debt issues+Preferred Dividends � Another approach will give the same result is where we start with Operating earnings. EBIT(1-T)[Pre-tax EBIT] +Depreciation -CAPEX - ∆WC =FCFF Suppose we have the following information. 2009 2010 EBIT 5000 10500 Depreciation 200 350 CAPEX 3250 4500 Tax rate 40% 40% What is the FCF to the firm? 2009 2010 EBIT(1-0.4) 3000 6300 Depreciation 200 350 CAPEX (3250) (4500) Increase in WC (1300) (2500)
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FCFF 1350 (350)
� 1-T is the tax shield � Principal repayments are added back because they are payments to debt holders. � Since cash flows to the firm are before debt payments they are not
affected by the amount of debt that the firm is using but this does not mean that the value of the firm is not affected by the amount of leverage because as the amount of debt increases the WACC will also increase because the cost of capital (ke) will increase.
� WACC=Wdkd(1-T)+Weke,as Wd increase the β will increase and the ke(cost of equity) will increase.
The difference between FCFE and Net Income FCFE different from net income for the following reasons: � Non-cash charges are added back to net income to arrive at the cash
flows from operations therefore the earnings reported by firms that take significant non-cash charges against current might be lower then cash flows. � FCFE are residual cash flows after meeting CAPEX and WC
needs,whre as these are not included in the calculation of net income, therefore high growth firms that have significant CAPEX and WC needs might report positive growing earnings but negative FCFE. Investors are however more interested in FCFE. Estimating Growth
In the formula,P0=gKe
FCFE
−1 ;we discussed about the FCFE,Ke. Now we
desire to discuss about the g.
g is the expected growth rate in earnings and dividends assuming that earnings and dividends grow at the same rate.
There are two approaches to estimating the growth rate in earnings. 1) Estimating using an average of past growth rates and assuming that
this growth rate reflects the expected growth rate. � The most common ones are the arithmetic average and the
geometric Mean. � The arithmetic average is the mean of past growth and the
geometric average takes into account the compounding effect. � The geometric mean is a more accurate measure of the growth of
the earnings especially when the year to year growth in the past has been erratic.
� The geometric mean will always be lower than the arithmetic
Estimating Issues � The first problem is that the EPS must grow at the same rate as the DPS. � The growth rate is sensitive to the starting and ending period for the estimation, for e.g. the growth rate in earnings over the past five years will be different from the growth rate over the past 6 years but the length of the estimation period is subject to the judgment of the analyst for e.g. if 1999 had EPS of $0.65 then the arithmetic average will be 13.32% and the geometric mean will be 11.81%. 2) Using the fundamentals reported in the current year: what are the
determinants of earnings growth? � The growth rate in earnings is determined by the decisions that
the firm makes with regards to product lines, profit margins,leverage,and dividend policy.
The retention ratio and the Return on Equity(ROE)
� The ROE=fEquityBookValueo
NetIncome
� 1
1
−
−−=
t
tt
NI
NINIgt
NIt =Net income for this year NIt-1 =Net income for last year gt =Growth rate in the net income
T.J Mabvure (Mr.)
23
� ROE=fEquityBookValueo
NetIncome
Therefore NI =ROE*Book value of equity NIt-1 =ROEt-1*Book value of equityt-1
� Assuming that the ROE is unchanged, that is to say ROEt =ROEt-1,
( )1
1
1
11 Re
−
−
−
−− =−
=t
t
t
ttttt NI
tainedROE
NI
BVEROEBVEROEg
gt = tt
t ROENI
RE*
1
1
−
−
gt =Retention ratio*Return on Equity gt =b*ROEt
g is the growth rate in Earnings per share
� This relationship assumes that the ROE doesn’t change over time. If it changes, that is ROEt≠ROEt-1 the growth rate in period t(now) will be given by the following relationship.
gt= ( )
tt
ttt ROEbNI
ROEROEBVE*
1
11 +−
−
−−
the first term,( )
1
11
−
−− −
t
ttt
NI
ROEROEBVEmeasures the effect of
changing the ROE on the existing equity base. Increases in the ROE make it more profitable to create a higher growth rate. The following information was reported in 2008 BVE = $15600 NI = $4200 b = 60%
ROE = %27100*15600
4200 =
g = 60*0.27 = 16.15% Suppose that in 2009 we had projected that the ROE will increase to 30% from the current 27%. The retention ratio will
T.J Mabvure (Mr.)
24
however remain at 60%. Therefore we now use the other method.
g = ( )
%2930.0*6.04200
27.030.015600 =+−
An increase in the ROE of 30% translates to an increase of:
%57.79100*5.16
15.1629 =−In the growth rate of earnings,
i.e. the higher the ROE, the higher the growth in the earnings.
The relationship between the growth rate and leverage
� In this case leverage is being measured using the D/E(gearing). � The ROE and by implication the growth rate in earnings is affected by the leverage decisions of the firm. Increasing leverage will lead to a higher return on equity if the pre-interest after tax return on assets exceeds the after tax interest rates paid on debt. This is captured in the following formulation of the ROE, i.e. expansion of ROE. Pre-interest after tax earnings = EBIT (1-T) The expanded version of the ROE: ROE = ROA+ D/E(ROA-i)(1-T) = ROA+ D/E(ROA-I)(1-T)
Where ROA=BVA
TEBIT )1( −
D/E=BVE
BVD BVD=Book value of Debt
BVE=Book value of equity
i=BVD
pensesInterestEx
T=Tax rate BVA=BVD+BVE Interest expenses are those found in the income statement.
� Using this expanded version of the ROE the growth rate in earnings:
g=b*[ROA+D/E (ROA-i)(1-T)]
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The effect of the product line analysis with respect to growth rate
� A firm with an ageing product line mix may look healthy in terms of historical growth and current profitability, but it is not likely to sustain this growth into the future. The analysis of growth for a firm can be made more complete by looking at its individual products line and examining where they stand in terms of the PLC.
� The growth rate across product lines can then be estimated using the following relationship:
gjt=b*[Mjt*Tjt-D/E(Mjt-i(1-T)]
Where gjt =growth rate in year t for product line j Mjt =Pre-interest after tax profit margin in year t for product line j
=Sales
TEBIT )1( −
Tjt =Asset turnover in year t for product line j
=sTotalAsset
Sales
D/E=gearing ratio of the firm as a whole i =interest expenses
=BVD
pensesInterestEx
T =Tax rate Now to ke
� Ke=Rf+β(Rm-Rf) CAPM Rf=Risk free rate which can be the Treasury bill rate as a proxy for the risk free rate, normally it’s the money market rate. Rm =Average return on the market index, ie Holdings Period Return (HPR) on the index.
Rm=HPR=1
12
M
MM −
M2=Index at the end of the year M1=Index at the beginning of the year
Beta coefficient(β)
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� The beta coefficient measures the risk of the asset in relation to the market. The volatility of the return on the assets in relation to return on the security.
� if an asset has a β=1.2,it means that if the return on the market increases by 10% then the expected return on the security will increase by 10*1.2=12. if the market is bullish you hold an offensive security. If the market sentiments are bearish you hold a defensive security.
� To estimate the β we regress the excess returns on the security against the excess returns on the market.
Diagram The beta coefficient for a private company � Get the average gearing ratios for similar companies that are listed as well the average β. � Suppose our market consist of 3 listed banks and we have gathered the following information about the banks.
Firm Beta D/E Barclays 1.20 0.40 CBZ 0.90 0.25 NMB 1.40 0.42 Average 1.17 0.36 What is the beta for stanbic whose debt ratio is 30% and is not listed � The beta of a levered firm βL: βL =βU[1+(1-t)(D/E)] βU=β for an unlevered firm
βU = ( )( )EDTI
L
/1−+β
Then calculate the unlevered betas of the firm’s; we want to remove the leverage effect from the company’s. Assuming that tax rate is 40%.
T.J Mabvure (Mr.)
27
βU = ( )( )36.040.01
17.1
−+I
βL =0.96[1+(0.6)(0.30)]
=1.13 � Therefore the β for stanbic is 1.13 � The formula has now taken into effect the 30% leverage of stanbic.
Valuation of companies Valuation of Equity i.Valuation using the stable growth model ii.Two stage model iii.Three stage model We are canceling out the decline stage
� In the stable phase the company is growing but the growth is stable � Opportunities for expansion are no longer there � The growth rate is now equivalent to that of the economy is identical to normal growth rate
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Stable growth Model
P0=ngKe
FCFE
−1
Where gn=stable growth rate which is expected to be maintained in perpetuity � This assumption is suitable for a firm that is large for a firm that is large In size (because it has gained relative market share in that industry) but is not likely to grow much faster than the economy in the long term because there are no more growth opportunities in that industry. � It generates large cash flows, which means that it will pay out much less
dividends than it’s generating in FCFE, because of this the financial leverage will be higher but stable.
� Free cash flows large that’s why it’s called a cash cow. � Free cash flows also used to pay dividends as well as support other SBUs. E.g. The following information was reported by ABC Limited $ EPS 3.15 CAPEX per share 3.15 Depreciation per share 2.78 ∆WC 0.50 Debt ratio 25%
1. Earnings, Capex, Depreciation and other WC are all expected to grow at 6% p.a, the β coefficient is 0.9. the TB is 7.5%, and the average return on the market(Rm) is 13%
Question Estimate the value per share.
Once a company enters into a stage (introduction, Growth, Maturity) the debt ratio in that category is considered optimal and can only change when it comes out of the stage.
Can use EPS instead of Net income but have to reduce everything to per share.
Ke= Rf+β(Rm-Rf) = 7.5+0.90(13-7.5) = 12.45 β very low because the company is now in the growth stage
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EPS-(CAPEX-Depreciation)(1-d)-( ∆WC)(1-d)
FCFE =3.15-(3.15-2.78)(1-0.25)-0.50(1-0.25)
=2.4975
P0=gKe
FCFE
−1
=gKe
gFCFE
−+ )1(
=( )
06.01245.0
06.14975.2
−
=$41 Two stage model Earlier we assumed that the firm was in stage 1 and now the firm is in stage 2. We will Have FCFE1, FCFE2, FCFE3, and then discount them to year 0 to get P0.
Pn=nn
n
gKe
FCFE
−+1
P3=nn gKe
FCFE
−4
PV of P3= ( )31
3
Ke
P
+
The Two stage model � This is designed to value a firm that is expected to grow much than a stable firm in the initial period and at a stable rate after that. The value of the FCFE per year(p.a) for the extra ordinary growth period(growth above the normal growth)plus the present value of the terminal price at the end of the period.
P0 =PV of FCFE+PV of Terminal price
=( ) ( )n
nnt
tt
t
Ke
P
Ke
FCFE
++
+∑=
= 111
n = end of the high growth period Pn =Price at the end of high growth period
=nn
n
gKe
FCFE
−+1
Ken=Ke for the stable growth period
T.J Mabvure (Mr.)
30
gn =g for the stable growth period Ke =Ke for the high growth period g =growth rate for the high growth period ABC Ltd has a history of extra ordinary growth but its growth rate is now stabilizing because it’s becoming a much larger company and its products are maturing and facing competition. The company pays very low dividends but has some FCFE. This FCFE is likely to increase as the company gets larger and the growth rate stabilizes. The financial leverage is currently considered stable. The financial report for this year has the following data. EPS 15 Revenue per share 40 Capex per share 5 Depreciation per share 1.50 The following estimates have been made for the high growth period: Length of period 4 years Return on Equity 22% Retention ratio 95% The company pays very low dividends because its shareholders are more interested in capital gains. g=b*ROE=0.95*22=20.9% the following market parameters will apply during this period: TB rate 15% Average return on the market 27% β coefficient 1.8 Ke = Rf+β(Rm-Rf) = 15+(27-15) = 36.6% � CAPEX, Depreciation and revenues are expected to grow at the same
rate as earnings � The WC is expected to be 20% of revenues. The debt ratio which is
considered to be optimum at this stage will be 5%.
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31
Inputs for the stable growth stage period:
� The ROE will increase to 30% � The retention ratio will decrease to 50% as the company pays higher
dividends � The β during the stable growth stage period will decrease to 1.1
because of reduced operating risk. � The debt ratio will increase to 20% which will be considered optimal
at this stage � Risk free rate will be 15% � Rm will be 27%
Question Estimate the value per share. The assumption is that the debt ratio is at its optimal level
Three stage model The company is still at the introduction stage and wants to move through other stages,ie to grow and then mature.
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32
P0= ( ) ( ) ( ) ( ) ( ) 1
2
12
2
22
1
21
2
1
1111111 1
nn
nnn
nn
ntnn
nn
n
tn
tt
t
KeKe
P
KeKe
FCFE
Ken
FCFE
+++
+++
+ −−
−=
∑∑
CAPEX VS Depreciation � It’s reasonable to assume that as a firm goes from high growth to stable growth the relationship between CAPEX and depreciation will change. In the high growth stage CAPEX is likely to be much higher than depreciation.
� In the high growth stage CAPEX is likely to be much higher than depreciation, because we are buying new assets and depreciation, that is wearing and tear is minimal.
� In the transition stage the difference is likely to narrow down and in the stable phase they are likely to be equal
E.g. A company is expecting a growing rate in earnings in excess of 30% per year due to the high growth rate of its markets and its market share. The firm currently pays no dividends but has a negative free cash flow to equity due to its large CAPEX and working capital requirements. The firm is using very little debt in relation to equity and does not plan to change this in the near future.
T.J Mabvure (Mr.)
33
Current financial information is as follows: $
EPS 30 CAPEX 40 Depreciation per share 10 Revenues per share 100 WC as a % of revenues 20% Inputs (Projections) for the high growth period � The high growth period will last for four years and during this period the ROE is expected to be 60%.
� The retention ratio will be 100%, therefore g will be 60 %(g=b*ROE=60%*100%).
� CAPEX, depreciation and revenues will grow at the same rate as earnings which is 60%,ie CAPEX,Depreciation will increase at 60%.
� WC will be maintained at 20% of revenues. � The debt ratio(D/E) will be 5% and the following market parameters will apply:
β coefficient 1.9 Rf 15% Rm 22% Ke=28.3% Inputs for the transition period � Length of period 3 years � The growth rate in earnings will decline from 60% in yr 4 to 15% in yr 7 linearly. � Capex will grow at 40% p.a and depreciation will continue to grow at 60%(so that they will converge).
� Working capital will remain at 20% of revenues which will now be growing at 40%. � The debt ratio will increase to 10%(because at this stage we are not borrowing much). � The other market parameters will remain the same but the β will decline to 1.5, therefore Ke=25.5%.
Inputs for the stable period � Earnings will grow at 10% in perpetuity � Capex will be exactly offset by depreciation (we are now replacing what we bought and not buying.
� Revenue will grow at10% � WC will remain at 20% of revenues
T.J Mabvure (Mr.)
34
� The debt ratio will increase to 20% � The β will decrease to 0.9 � The other parameters will remain the same, Ke=21.3% Question Calculate the value per share VALUE OF A FIRM Free cash flow to the firm (FCFF) are the sum of the cash flows to all the claimholders in the firm including debt holders, preference shareholders and equity holders. To value the firm we discount the FCFF at the required rate which is the weighted average cost of capital (WACC). FCFF=EBIT (1-T)-(Capex-Depreciation) - ∆WC. The debt ratio does apply in the determination of the FCFF. For a firm in the stable growth period the value of the firm is determined as follows.
Value of Firm=ngWACC
FCFF
−1
gn=Expected growth rate in perpetuity
� This model requires that the growth rate of the firm should be reasonable, relative to the normal growth rate of the economy.
� The relationship between Cape and depreciation must also be consistent with the assumptions of stable growth,ie a stable firm generally should not have Cape that are significantly greater than depreciation, since there are no growth opportunities there would be no need for additional capital investment.
E.g. Two stage model The valuation of a firm which is highly leveraged. The base year information $ EBIT 3800 Cape x 500 Depreciation 300 Revenues 10000 WC as a % of Revenues was 25% Tax rate 40% Tax rate 40% TB rate 15% Rm 22%
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� The firm is approaching a high growth phase which will last for 4 years after which earnings will stabilize. � Expected growth rate for operating earnings (EBIT) during the high growth phase will be 20% p.a � β will be 1.5 � The other market parameters will remain the same. � The WC as a % of revenue 25% � The pre-tax cost of debt 20% � The debt ratio(D/E) 50% � This high level of leverage is targeting the resulting of a leveraged buyout in the last 2 years. � It’s anticipated that this high debt ratio will be reduced gradually over the next 4 years to acceptable levels.
� Capex,revenues and depreciation will grow at 20%
Inputs for the stable growth phase
Expected growth rate in earnings 10% Β throughout the period 0.9 Pre-tax cost of debt 8% Debt ratio(D/E) 25%
CAPEX will be offset by depreciation WC as a % of revenue 30% Revenues will grow at 10% Q. Calculate the Value of the Firm
Three stage Firm valuation model
Current inputs (2009)
$m
EBIT 400 Capex 550 Depreciation 300 WC 10% of Revenues Tax rate 40% for all periods High Growth Period Length of period 4 years Growth rate in revenues and EBIT 40% β=1.8, Rm=22%, Rf=15% Debt ratio 30% Pre-tax cost of debt 12% Capex and Depreciation will grow at 40%
T.J Mabvure (Mr.)
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WC 10% of Revenues Transition Period Length of Period 3 years Growth rate of EBIT and Revenue will decline linearly from 40% in year 4 to 10% in year 7 Capex will grow at 20% Depreciation will grow at 15% β will drop from 1.8 in Y4 to 1.20 in Yr7 linearly WC=10% of revenue Debt ratio 10% Pre-tax cost of debt 10% Stable Period Growth rate in EBIT and Revenues 5% Pre-tax cost of debt 15% Capex and Depreciation will cancel each other Β=1.00, Debt ratio WC=10% of Revenues Qn. Calculate the value of the firm
Growth rate in FCFE vs. Growth rate in FCFF SEE ASWATH DAMODARAN
RELATIVE VALUATION Another method for evaluation is the relative valuation method. In this valuation model we use the following:
i) P/E multiple= EPS
P0 =0P Price per share
ii) PBV =BVE
P0
iii) Price to Sales=Sales
P0
Estimate the P/E ratio of the fundamentals � The P/E ratio can be related to the same fundamentals that determine the value using discounted CF models. The fundamentals are: a. The expected growth rate in earnings and dividends per share. b. Dividends payout ratios c. Risk as reflected in the cost of equity
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37
The P/E ratio for a stable firm
� A stable firm is a firm that is growing at a rate that is comparable to the normal growth rate in the economy in which it’s operating.
� For a stable firm the value of equity is given by the following:
gnKe
DP
−= 1
0 If we use the dividend growth model
Since DPS1=EPS0 (Payout ratio) (1+g) =Dividends next year, i.e. dividends at the end of this year. This means that the value of equity (P0)
( )( )gnKe
goPayoutRatiEPSP
−+
=10
0
We know that 0
0
EPS
PEP =
Therefore ( )( )( )
gnKe
goPayoutRati
gEPS
PEP
−+=
+= 1
10
0
If the EP ratio is stated in terms of expected earnings in the next period,
ie we are saying:
( ) 1
0
0
0
1 EPS
P
gEPS
P=
+ EPS1=EPS next year
EPS0=EPS this year
gnKe
oPayoutRati
EPS
P
−=
1
0
� This means that the P/E ratios an increasing function of the payout ratio and the growth rate in earnings and a decreasing function of the risk ness of the firm as reflected in the β coefficient of the firm in Ke(Required rate of return).
� Therefore in calculating P/E we are calculating.
( )( )gnKe
goPayoutRati
EPS
PEP
−+== 1
0
0 OR
( )
gnKe
oPayoutRati
EPS
P
−=
1
0
This is the P/E ratio taking into account the fundamental characteristics of the firm. These fundamentals are:
a) The expected growth rate in earnings and dividends
T.J Mabvure (Mr.)
38
b) Risk ness of the firm’s cash flows as reflected by the beta of the company in the cost of equity(Ke)
c) Dividend payout ratio. E.g. A firm had EPS of $250 in 2009 and paid out a dividend of $120. The growth rate in earnings and dividends in the long term (stable state) is expected to be 10%. The market parameters are as follows: RF=20%, Rm=25%, β=1.2 Calculate the P/E today based on these fundamentals. Ke=26%
Payout ratio= 48.0250
120 =
( )( ) ( )Times
gnKe
goPayoutRati
EPS
PEP 30.3
10.026.0
10.148.01/
0
0 =−
=−
+==
� If the actual P/E at the time of the analysis was say 10.5. the low P/E of 3.3 is an indication that the firm was not paying out what it could afford as dividends.
� If the firm is paying out significantly less dividends than it can afford we can use FCFE in stead of DPS to calculate P/E.
E.g. A company has EPS of $400 and paid no dividends. The following market parameters apply, RF=20%, Rm=20%, β=0.9. The expected growth rate in earnings was 10% and the FCFE per share was 350. The P/E ratio based on these fundamentals will be: Ke=24.5%
875.0400
350 ===EPS
FCFEPayout
EPS
FCFE is the free cash flow payout ratio, as an equivalent of the dividend
payout ratio.
606810.0245.0
)10.1(88.0 =−
=EP
� The firm didn’t payout dividends,ie we are saying what will be the P/E if we use FCFlows rather than the dividends that are giving a 3.0 value.
T.J Mabvure (Mr.)
39
� If the company was selling at a P/E of $10.5, then dividends alone can’t be blamed for the low valuation.
� The low value of the firm is not sorely to do with dividends. The firm is over valued by the market yet the fundamentals are lowly valuing the firm.
E.g. a company has EPS of $40 and paid out a dividend of $12.50/share. The growth rate in earnings and dividends is expected to be 10%. The β=0.9, TB=15%, Rm=22%. Calculate the P/E ratio based on these fundamentals. Ke=21.3%
Dividend payout ratio= 3125.040
50.12 =
g=10%
TimesEP 05.310.0213.0
)10.1(315.0 =−
=
E.g. A Company is currently selling at a P/E ratio of 6.00. The company had EPS of $60 and paid out dividends of $22/share. The FCFE was $30 per share. Expected growth rate in earnings is 10%. RF=15%, Rm=22%, β=0.9. Comment on the value of the company. Ke=21.3%
Dividend payout= 036760
22 =
g=10%
( )TimesEP 57.3
10.0213.0
10.1367.0 =−
=
FCF payout= 5.060
30 =
g=10%
( )10.0213.0
10.15.0
−=EP
� The Firm is overvalued by the market. � Dividends alone, ie low dividend payout are not the only one to blame for the low value of the firm.
� The free cash flows also low according to the market expectation � The market is paying more than what the company is worth given the fundamentals of the company.
T.J Mabvure (Mr.)
40
� The company is paying out less dividends than what the market is expecting. Comment � The market is overvaluing the company because the company is paying less dividends than what the market is expecting and the market is anticipating higher cash flows than what is being generated and at the same time the market is understating the risk of the cash flows or the risk ness of the firm.
Comparing the P/E ratio with other P/E’s � P/E’s across countries(markets) � P/E’s across time � P/E’s across firms SEE ASWATH DAMODARAN
P/E Ratio for a High Growth Firm Valuation for high growth; two stage model
( ) alValuePVofTerKe
FCFEP
n
t
min11
0 ++
=∑=
alValueTergnKen
FCFEPn n min1 =
−= +
� The P/E ratio for a high growth firm can also be related to the fundamentals in the case of the two stage model.
( ) ( )( ) ( ) ( )
( )( )n
nn
n
n
KegnKe
gngoPayoutRati
gKe
Ke
ggoPayoutRati
EPS
PEP
+−++
+−
++−+
==1
111
111
0
0
EPS0 =EPS in the current year g =Growth rate in the current phase Ke =Cost of equity in the current year(phase) gn =Growth rate after the first phase(growth rate in the stable period) Payout ratio =Payout in the current phase(first) Payout ration =Payout in the second phase Ken =Cost of equity in the second phase n =Length of the current phase The P/E ratio is determined by:
T.J Mabvure (Mr.)
41
1) The payout ratio during the high growth phase and the stable period, the P/E ratio increases as the payout ratio increases.
2) The riskiness of the firm through the discount rate Ke. The higher the risk the lower the P/E.
3) The expected growth rate in earnings in both the high growth and stable periods. The higher the growth rate, the higher the P/E. If the firm is not paying dividends we use the ratio of the free cash flow to equity to EPS instead of the dividend payout ratio.
E.g. A firm is expecting a five year period of high growth after which the growth rate will normalize in line with the growth rate of the economy. � The following data pertains to the high growth period: Expected ROE 20% Expected payout ratio 25% Therefore growth rate in the high growth period will be: g=b*ROE=0.20(1-0.25) =0.15=15% β 1.5 Rm 20% Rf 15% Ke=22.5% Stable growth period Expected growth rate 5% Expected ROE 15% β 1.1 Rf 15% Rm 20% Expected Payout ratio=Payoutn(1+g)
n(1+gn) g=b*ROE b=1-payout g=ROE(1-Payout)
Therefore Payoutn= 667.015.0
05.011 =−=−
ROE
g
Ke=20.5%
T.J Mabvure (Mr.)
42
( ) ( )( ) ( ) ( )
( )( )
( )( ) ( )( ) ( )( )( )
( )( ) 35.444.0
41.1
15.0225.0
08.0
225.105.0205.0
05.105.115.1667.0
15.225.0
225.1
15.1115.125.0
1
111
111
5
55
5
=+−
=−
+−
−
=
+−++
+−
++−+
=n
nn
n
n
n
KegnKe
ggPayout
gnKe
Ke
ggPayout
EP
E.g. A firm is expected to have five years of high growth after which it will be in a steady state. Inputs for the high growth period Expected ROE 22% Expected payout ratio 25% β 1.8 Rm 22% Rf 15% Stable period Expected growth rate 6% β 0.75 Rf 15% Rm 22% Expected ROE 15% Calculate the fundamental P/E 2. Price to Book Value
� The book value of equity is the difference between the book value of assets and the book value of liabilities.
� The measurement of the BVA is largely determined by accounting conventions.
Book value VS market value
� The Market value of an asset reflects its earning power and expected cash flows since the book value of an asset reflects its original cost. It might deviate significantly from the market value if the earning power of the asset has increased or decreased significantly since its acquisition. Reasons for using book values ratios � The following are the reasons why investors use price to book value ratios. 1. Book value provides a relatively stable intuitive (easily understood)
measure of value.\
T.J Mabvure (Mr.)
43
2. Price to book value ratios can be compared across similar firms for signs of under or overvaluation, even firms with negative earnings which can’t be overvalued using the PBV ratios.
Disadvantages of using PBV ratios � Book values like earnings are affected by accounting decisions on
depreciation and other variables (accounting can manipulate the book by either increasing or decreasing depreciation).
� When accounting standards vary widely across firms(some companies may not be consolidating the earnings of their subsidiaries; stock valuation methods such as FIFO, LIFO, AVCO, straight line, and reduced balance method may be in use in different companies).
� Book values may not carry much meaning for service firms that don’t have significant fixed assets (e.g. insurance companies; most of the assets are in investments a.w.a real estate).
PBV for a stable firm
nn gKe
DPSP
−= 1
0
Substituting EPS0 (Payout) (1+g) for DPS1
( )( )
gnKen
gPayoutEPSP
−+
=1
0 0
BVE
EPSROE 0=
BVEROEEPS *0 =
This means that
( )
nn gKe
gPayoutBVEROEP
−+= 1**
0
BVE
PPBV 0=
Dividing both sides by BVE
( )
nn gKe
gPayoutROE
BVE
P
−+= 1*0
If we express the book value of equity in terms of expected BVE for next year.
( ) nn gKe
PayoutROE
gBVE
P
−=
+*
10
T.J Mabvure (Mr.)
44
nn gKe
PayoutROE
BVE
P
−= *0
1
� This indicates that the PBV ratio is on increasing function of the ROE, the payout ratio and the growth rate of earnings. It is an increasing function of the risk ness of the firm as indicated by β in Ke.
nn gKe
PayoutROEPBV
BVE
P
−== *0
11
g=b*ROE =ROE (1-Payout) Relating g to the ROE. g = ROE*b =ROE (1-Payout) =ROE-ROE (Payout) g+ROEPay=ROE ROE*Payout=ROE-g ROE*Pay is identical to ROE-g
gnKe
gROE
BVE
P
n −−=0
� This relationship is telling us that the PBV of a stable firm is determined by
the differential between the ROE and the required Rate of return on its profits.
� If the ROE exceeds the RRR (Ke) the price will exceed the BVE (because g is constant).
� This formulation can therefore be used to estimate the PBV ratios for firms that don’t pay dividend.
A firm had EPS of $600 in 2009 and paid 40% of its earnings as dividends that year, the growing rate of earnings and dividends in the long term is expected to be 10%. The ROE for the firm is 20%. The following parameters apply: β =0.9, Rm =20%, Rf =15% Therefore Ke =19.5% Qn. what is the PBV a) Today b) next year and (c) when the company is not paying dividends
T.J Mabvure (Mr.)
45
gKe
gROE
BVE
PPBV
−−==
11 0
( )PBVToday
gKe
gPayoutROEPBV
BVE
P=
−+== 1*
00
0
gKe
PayoutROEPBV
BVE
P
−== *
11
0 PBV based on expected earning next year
gKe
gROE
BVE
P
−−=
1
0 PBV based on return differential (used when we are dealing
with a firm that does no payout dividends). Therefore PBV today
( )( )93.0
10.0195.0
10.14.020.0)1(*
0
0 =−
=−
+gKe
gPayoutROE
BVE
P
( )( )
84.010.0195.0
4.020.0*1 =
−=
−=
gKe
PayoutROEPBV
05.110.0195.0
10.020.00
1
=−−=
−−=gKe
gROE
BVE
P
� The purpose of these values is to compare them with fundamental based PBV and the market PBV.
� Let’s suppose the market PBV is 2.00 then the price per share is twice the Book Value of the share.
� The market is saying the market price of the share is twice the book value.
NB. What is the relationship between the PBV and the ROE? � If the ROE decreases the PBV will also decrease because g will also decrease, therefore a firm with a high ROE will sell above its book value. A firm with a mismatch between the PBV and the ROE will attract the attention of investors.
� A mismatch is a low priced book value associated with a high ROE or a high PBV associated with a low ROE.
� High Price to book value is always associated with high ROE. � The ratio between PBV and indicates whether a firm is overvalued or undervalued. A ratio of less than one indicates an undervalued firm.
T.J Mabvure (Mr.)
46
Overvalued
Correctly valued
Correctly valued
undervalued
Let’s suppose we have the following information about several companies
Price/Sales per Share This is again related to the dividend model � Unlike the price to earnings or the PBV which can become negative and therefore meaningless. The price to sales multiple is always positive even for firms in trouble (can be applied in all situations). Earnings and book values are heavily influenced by accounting decisions such as decisions on: a) Depreciation and inventory valuation, revenues are however not easy to Manipulate.
� The price to sales ratio can also be related to fundamentals such as: a) Growth rates in earnings and dividends b) Payout ratios c) Risk through Ke
Value of equity for a stable firm
nn gKe
DP
−= 1
0
But D1=EPS0 (Payout) (1+g)
Therefore nn gKe
gPayoutEPSP
−+
=)1)((0
0
In this case we are interested in the profit margin (PM)
Sales
NetIncomePM =
areSalesPerSh
EPSPM
0=
T.J Mabvure (Mr.)
47
Therefore EPS0=PM (Sales per share)
Substituting: ( )( )( )
nn gKe
gPayoutareSalesPerShPMP
−+= 1
0
But Price to Sales (PS) =Sales
P0
Therefore ( )( )
gKe
gPayoutPM
Sales
P
−+= 10
This is the fundamental relationship we want � If the profit margin is based on expected earnings next year we can re-write
this as follows: ( )( )
gKe
PayoutPM
gSales
P
−=
+10
( )
nn gKe
PayoutPM
Sales
P
−=
1
0
� The price to sales ratio is an increasing function of the profit margin, the payout ratio and the growth rate in earnings and dividends. It is a decreasing function of the risk ness of the firm as reflected in the Ke(Required rate of return).
� After calculation you have to relate your answer to these fundamentals as said above.
QN. A Company has revenues/share of $100 in 2009 and EPS of $5. It paid out 60% of its earnings as dividends. The growth rate in earnings and dividends in the long-term is expected to be 5%, β=0.9, Rf=15%, Rm=20%. Calculate the current price to sales ratio based on these fundamentals and also the Price to sales ratio based on expected earnings next year. � These must be compared to the market price to sales multiples.
� Suppose the company was trading on a price to sales of 0.3 then we would
conclude that it’s overvalued according to the fundamentals.
Relationship between the price to sales (PS) and the PM
� The key determinant of the PS ratio is the PM.
T.J Mabvure (Mr.)
48
� Firms involved in businesses that have high margins can expect to sale for
much higher PS multiples (they will be trading on higher PS than the market).
A decline in PM has two effects.
1. reduction in PS Margin
2. reduction in the growth rate of earnings
We can use the ratio between the sales per share to book value of equity to
link the profit margin to the expected growth rate.
g=b*ROE
Since ROE=BVE
Sales
Sales
NI*
ROE= overEquityTurninofitMOperating *argPr
This is the pyramid that builds up the ROE. A DuPont type of ROE.
Therefore BVE
Sales
Sales
NIbg **=
BVE
SalesPMbg **=
g=retention ratio*profit margin*equity turnover
� The higher the PM the higher the expected growth rate provided that sales
will not decrease proportionately to the increase in profit margin.
� This whole discussion related to a firm which is in a stable growth period.
PS for a high growth model (Two stage model)
In the two stage model:
P0=PV of expected dividends in the high growth period+PV of the terminal Price
=( ) ( )n
n
tt Ke
Pn
Ke
Dt
++
+∑= 111
Where nn
n
gKe
DPn
−= +1 this is the same concept with the free cash flows
The H-model is a short cut for the above
D0=EPS0 (Payout)
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49
� When the growth at the end of a high growth period is assumed to be
constant for ever, then the value of the firm(P0):
( ) ( )( ) ( ) ( )
( )( )nnn
nn
n
n
n
KegKe
ggPayoutEPS
gKe
Ke
ggPayoutEPS
P+−
+++
−
++−+
=1
11*1
111*
0
0
0
But EPS0=Sales*PM
Therefore Sales
EPSPM 0=
PS=
( ) ( )( ) ( ) ( )
( )( )
+−++
+−
++−+
=n
nn
n
n
n
KegnKen
ggPayout
gKe
Ke
ggPayout
PMSales
P
1
111
111
0
This is telling us that the PS multiple is determined by the following factors
a) The net profit margin, ie the PS multiple is an increasing function of the Net
profit margin.
b) The payout ratio i.e. to say the higher the payout ratio, the higher the PS
multiple.
c) Risk as reflected in Ke, ie to say the higher the risk the lower the PS
multiple.
d) The growth rate in earnings, the higher the expected growth rate the higher
the PS multiple.
E.g. a firm is expected to go through two growth periods,ie the high growth
period and a stable period.
Inputs for the high growth period
Expected length of period 5 years Expected growth rate 25% The Average profit margin 10% Payout ratio 5% β 1.2 Rm 30% Rf 25%
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50
Stable period During the stable period the profit margins will be maintained at 10% Expected growth rate in earnings 5% Payout ratio 60% β 1.0 Rm 30% Rf 25% Qn estimate the PS multiple Growth stage n =5 g =25% PM =10% Payout =5% Ke = 31% gn =5% Payoutn =60% Ken =30%
( ) ( )( ) ( ) ( )
( )( )
+−++
+−
++−+
=n
nn
nn
n
n
n
KegKe
ggPayout
gKe
Ke
ggPayout
PMPS1
111
111
( ) ( )( ) ( ) ( )
( )( )[ ] 2211.099339.121768.010.0
31.105.03.0
05.125.16.0
25.031.0
31.1
25.1125.105.0
10.05
55
5
=+=
−+
−
−=
Growth rate We can use the following relationship to compare difference competitive strategies which are: High margin (product differentiation), low margin high volume (cost leadership).
T.J Mabvure (Mr.)
51
g=b*PM*BVE
Sales
A firm is considering these two strategies: High Margin- low Volume Low Margin-High Volume PM 20% 8% Sales/BE 2 4
� The firm is expected to payout 20% of its earnings as dividends after that. � The growth rate in earnings after two years is expected to be 10% p.a in
perpetuity. � The book value of equity per share is currently $10,β=1.5, Rm=30%,Rf=25%.
Ke=32.5%. In the stable period the β will decrease to 1.0, and other parameters will remain the same. Ke=30%. To compare these strategies we have to look at PS multiple in each case. Typical Examination A company has sales per share of $6.50 with earnings of $125 per share. The book value of equity was $420 per share. The company paid 20% of its earnings as dividends. Based on these results calculate the profit margin. The sales to book value, the retention ratio and the growth rate in earnings. It’s envisaged that the current period is a high growth period which will last for 2 years. During this period β=1.2, Rf=25%, Rm=30%. � After the high growth period the growth rate will stabilize to 10% p.a and the
dividend payout ratio will be increased to 60%. The β will drop to 1.0 and the other parameters will remain in the same.
Second scenario Suppose that the company cuts the profit margin to 10% all other things being equal. Calculate the PS multiple. Will this be a wise move?
SHORT TERM FINANCIAL STRATEGY � This is all about planning. Planning looks at forecast (prediction of what’s
going to happen). � Forecast about sales levels in the future, WC requirements, profit, financing
mix (debt to equity); short term to long term. Forecasting � Income statement-projected income statement and balance sheet. We would
be basing on the income statement this year and then predict for the next 5 years.
� The starting point for an income statement is the sales projections e.g. by 10%.
� The projected increase in sales has to be financed. The firm needs extra WC and Fixed assets.
� The increase in WC and fixed assets must be financed � Projected assets to support the increase in sales. � The Fixed assets and WC also depends on whether we are operating at full
capacity of below capacity. The former means there is need for increase in financing and the latter means there is no need.
T.J Mabvure (Mr.)
53
Sources of funds to cover the required increase a) Spontaneous sources, certain current assets will be spontaneously financed by
increase in current liabilities. Increase in sales means more debtors and stocks and it also means increase in creditors, so there is self financing.
b) Internal sources. Retained earnings; as sales increase the operating earnings also increase. Retained earnings available are influenced by the dividend policy. Retained earnings are internal equity, i.e. this is equity financing.
c) External sources: Financing gap=Financing needs-(spontaneous sources+ internal sources). The external sources are debt (long term, short term) and equity (new share issues) Financing feedbacks � Extra dividends payments resulting from new share issues. � Extra interest payments resulting from new debt. � So you will have some ‘what if’ scenarios Approaches to identifying the financing a) Constant ratio method b) Formula method Constant ratio method � Let’s suppose we have got our income statement for year. We have
projected that sales will increase by 10%. The DPS this year was $1.15 and this dividend is expected to be increased by about 8% to$1.25. There are 50 million outstanding shares which means that the projected dividend will be 1.25(50 million)=62.5,ie $63. Actual Forecast $ $ Sales 3000 3300 Operating expenses (2716) (2988) Operating earnings (EBIT) 284 312 Interest (88) (88) EBT (NI) 196 224 Tax (40%) (78) (90) Net income 118 134 Preferred dividends (4) (4) Net income to ordinary 114 130 Dividend to ordinary (58) (63) Retained earnings 56 67 � The constant ratio method assumes that all expenses will increase at the
same rate as sales.
T.J Mabvure (Mr.)
54
� The primary purpose of this part of the forecast is determined by how much income the company will generate internally through retained earnings.
� The forecast now shifts to the balance sheet. � If the company was operating at full capacity this means that any increase
in sales will also lead to an increase in assets. For e.g. more cash will be required, receivables and inventory will also increase. New plant and equipment will also be required. These additional assets will lead to additional liabilities.
Balance Sheet Actual Projected
$ $ Cash 10 11 Accounts receivables 375 412 Inventory 615 677 Current assets 1000 1100 Plant and equipment 1000 1100 2000 2200 Accounts payables 60 66 Notes payable 110 110 Accruals 140 154 Long term loan 754 754 1064 1084 Preferred equity 40 40 Ordinary share capital 130 130 Retained earnings 766 833(766+67) Equity and liabilities 2000 2088 � Debt obligations that have nothing to do with sales will not increase when sales increase.
� After calculating the projected balance sheet we would have spontaneous increase in terms of accounts payable and accruals.
Additional funds needed (AFN) =2200-2088=112. This is the financing gap which needs to be covered by external sources. � The company requires 200m of new assets to support the projected sales level which is 3300. if the existing capital structure is regarded to be optimal then the additional funds of $112 must be raised by borrowing from the bank as notes payable, issuing long term loans(bonds) and selling new ordinary shares.
Raising additional funds needed. � The financing mix will be determined by the target capital structure, conditions in the debt and equity markets as well as restrictions imposed by
T.J Mabvure (Mr.)
55
existing debt agreements (the company may have borrowed too much already).
� Assuming that the following financial mix is adopted. Type of financing % Amount Cost(%) Notes payable 25 28 8 interest Long term loans 25 28 10 interest Ordinary share 50 56 � On the notes payable we are paying 8% and on the long term 10% interest. � What this means is that there is going to be financing feedbacks which
require that we draw a new forecast, i.e. draft a new one. � The external funds raised to pay for the new assets create additional
expenses which must be reflected in the income statements. � This reduces the initially forecasted additions to retained earnings. Financing feedbacks a) Additional interest.
i) Short term debts(notes),i.e. 0.08*$28=$2.24 ii) Long-term debt 0.10*$28=2.80 $5.07m
b) Additional dividend. Assuming that current share price is $23 and new share can be issued at
this price, therefore: resmillionSham
m4.2
23$
56$ =
� The dividend payout is projected to be $1.25 per share, therefore the additional dividend payments will be: 2.4*1.25=$3m.
� This means that the dividends to ordinary shareholders will now increase to $66m(63+3).
� The net effect of these financing feedbacks income by $7 million from $68m to $61 million.
� This reduces the projected retained income to $827m (766+61). This results in a reduced financed gap of $7m that should be financed using the mix of 25%,short term debt,25% long term debt,50% equity. It becomes a vicious cycle.
After doing the feedbacks we have to now consider the restated income statement and balance sheet. Re-stated income statement Sales 3300 Costs 2988(opp cost 2878 +dep 110) EBIT 312 Less interest (88+5) (93) EBT 219
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56
Tax (40%) (88) Earnings to shareholders 131 Preferred dividends (4) Net income 127 Dividends (66) Retained income 61 Restated balance sheet Cash 11 Accounts receivables 412 Inventories 677 Total current assets 1100 Plant and equipment 1100 Total assets 2200 Accounts payable 66 Notes payable (110+28) 138 Accruals 154 Long term loans (754+28) 782 Total debt 1140 Preferred equity 40 Common stock (130+56) 186 Retained earnings (766+61) 827 Total equity and liabilities 2193 Additional funds needed are now (2200-2193) =7 � We continue doing this until the needed funds becomes insignificant. � After this we analyze the forecast. Analysis of the forecast � We must analyze the projected financial statements and compare them
with our target ratios as laid down in our long-term plans. Formula method � The following formula can be used to obtain an estimate of the financial
requirements needed to support any increase in sales: (Additional funds needed)=required increase in assets-spontaneous increases in liabilities-increases in retained income.
AFN=( ) ( )
)1(1**
divMSS
SL
S
SA −−∆
−∆
∆S=Actual changes in sales =SA* These are assets that must increase is sales are to increase expressed
as a % of sales, i.e. the required dollar increase in assets per dollar increase in sales.
= 667.030002000 =
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57
� This means that for every $1 increase in sales, assets must increase by 67 cents.
Where A=Total assets A*=assets that must increase =A if the company is operating at full capacity.
=SL * Liabilities that increase spontaneously with sales as a % of sales,
i.e. the Spontaneously generated financing per $1 in sales. = (60+140)/3000=0.0667 � This means that every $1 increase in sales generated $7 cents in
spontaneously financing. L*=the liabilities that increase spontaneously L=Total liabilities L will always be greater than L* because other liabilities like long term liabilities does not increase spontaneously. S1= Sales (Total) projected for next year =3300 Where S0=current sales=Current sales=3000 M=Profit margin (net profit margin)
= 038.03000
114 ==Sales
NI
d= 5088.0114
58 ==youtRatiodividendPa
( ) ( ) ( )( ) ( ) ( )( )( )
Million
dMSSSLSSAAFN
118
6220200
5088.013300038.03000667.0300667.0
1** 1
=−−=
−−−=−−∆−∆=
Additional funds needed (AFN) = 112 = 7 119 � If we increase sales by $300 we must increase assets by $200m to support this increase in sales level.
� The $200m of assets (new) will be financed by 20million from spontaneous increases in liabilities, 62million from retained earnings. The remaining 118m must come from external earnings sources.
� Assuming that the firm is operating at full capacity. This formula is only a rough estimate because of the assumptions that we made, which are: i) Each asset item must grow at the same rate as the sales. ii) Certain liability accounts e.g. Trade creditors (a/c payable and accruals)
also increase at the same rate as our sales.
T.J Mabvure (Mr.)
58
iii) Profit margins and dividends payout ratios are constant; we may not be necessarily true.
What is the relationship between growth and financial requirements? � The faster the growths rate in sales the greater the need for additional
financing. � If we apply the formula to differential growth rates.
� Spontaneous plus retained earnings will be sufficient to meet the financial needs. It’s like a break even point.
� The table can be converted into a financial feasibility chart. Financial feasibility chart
T.J Mabvure (Mr.)
59
Break even growth rate in sales The break even point is the growth rate that will be covered by funds generated by spontaneous increase in liabilities and retained earnings (internally generated equity). Therefore we have to solve for g in the equation in the Additional funds needed equation.
Mergers and acquisitions Two ways in which a company can expand operations 1. Internal expansion: The acquisition of long term assets over the years
gradually. 2. External expansion: Can be achieved through a takeover, which is acquiring
control of the shares and assets in another company. This is more complex because it involves legal, tax, accounting and management issues.
Types of mergers
a. Horizontal, conglomerate, vertical: � When two firms in the same industry merge, it’s called a horizontal merger,
like two banks, WMMI, and Nissan and Clover Leaf motors. � A vertical merger is where either a firm expands towards a customer or
backwards towards the supplier. The former is the supply chain and the latter is the distribution chain.
� Conglomerate is where you expand along unrelated lines of business. The purpose of this is to diversify away operating risk, like ZSR who now concentrates away from sugar to Trador, Advance, Redstar.
Reasons sighted for merger The most sighted reasons are the possibilities of synergistic benefits arising from the merger. Always expressed as 1+1=3 effect. That is Vxy>Vx+Vy,ie the value of xy is greater than the value of x and y stand alone. Reasons or other benefits are: � Economies of scale; as we increase the production the cost per unit
decreases. � Operating economies; as we increase the size of operations the benefits are
bound ti increase. � Managerial skills which are endowed with a certain company especially in
the highly technological engineering firms.
T.J Mabvure (Mr.)
60
� Tax considerations; where a company has some tax assessed losses carried over the years. The idea is to reduce the tax burden. In most of the cases the company has to convince ZIMRA that the transaction was not for that purpose.
� Excess liquidity; the targeted company may have a strong liquidity position e.g. retail organizations.
� Diversification; new products and new markets � Reduced financial costs. The merger may result in reduced cost if the
company which is being targeted has a financial slack (excess borrowing capacity).
� Technology, acquisition that takes place in order to take/acquire the technological expertise of the targeted company.
Terms of the merger
An acquirer can either pay cash for the acquisition or issue its own shares in exchange for the shares of the target firm. For an acquisition financed by cash the target company and the acquirer must agree on the price to be paid per share. Nominal value Book value Market value Intrinsic value (Real value given the fundamentals of the business). See Damodaran for more on these things
