ACCA paper f9 financial management study materials F9FM session10 d08

SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL OVERVIEW Objective To develop a model for the valuation of shares and bonds To use this model to estimate the cost of equity and the cost of debt To consider further practical influences on the valuation of securities SECURITY VALUATION AND THE COST OF CAPITAL EQUITY ANALYSIS DEBT ANALYSIS Dividend Valuation Model Cost of equity Irredeemable debentures Redeemable debentures Semi-annual interest Convertible debentures 1001 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL DIVIDEND VALUATION MODEL 1.1 The general model The dividend valuation model states that: “the market value of a share or other security is equal to the present value of the future expected cash flows from the security discounted at the investor’s required rate of return” A security is any traded investment e.g shares and bonds 1.2 Constant Dividend The formula for share valuation can be developed as follows: Ex-div market value at time = Present value of the future dividends discounted at the shareholders’ required rate of return Ex-div market value is the market value assuming that a dividend has just been paid Let: Po Dn ke = = = Current ex-div market value Dividend at time n Shareholders’ required rate of return/company’s cost of equity The model then becomes: Po = D1 + (1 + ke) D2 (1 + ke) + D3 (1 + ke) Dn n (1 + ke) If the dividend is assumed to be constant to infinity this becomes the present value of a perpetuity which simplifies to: Po = D ke This version of the model can be used to determine the theoretical value of a share which pays a constant dividend e.g a preference share or an ordinary share in a zero growth company 1002 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL 1.3 Constant growth in dividends If dividends are forecast to grow at a constant rate in perpetuity, where g = growth rate Po = where D0(1 + g) ke − g = D1 ke − g Do = most recent dividend D1 = dividend in one year The formula is published in the exam in the following format: PO = D O (1 + g ) (re − g ) Where re = required return of equity investors = ke 1.4 Assumptions behind the dividend valuation model rational investors all investors have the same expectations and therefore the same required rate of return perfect capital market assumptions, e.g., no transactions costs large number of buyers and sellers of shares no individual can affect the share price all investors have all available information dividends are paid just once a year and one year apart dividends are either constant or are growing at a constant rate 1.5 Uses of the dividend valuation model The model can be used to estimate the theoretical fair value of shares in unlisted companies where a quoted market price is not known However if the company is listed, and the share price is therefore known, the model can be used to estimate the required return of shareholders i.e the company’s cost of equity finance 1003 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Illustration Suppose that a share has a current ex-div market value of 80 cents and investors expect a dividend of 10 cents per share to be paid each year as has been the case for the past few years Using the dividend valuation model the required return of the investors for this share can be determined: Po = D ke 80c = 10c ke ke = 10c 80c ke = 12.5% Investors will all require this return from the share as the model assumes they all have the same information about the risk of this share and they are all rational If investors think that the dividend is due to increase to 15 cents each year then at a price of 80 cents the share is giving a higher return than 12.5% Investors will therefore buy the share and the price will increase until, according to the model, the value will be: Po = 15c 0.125 = 120 cents Alternatively suppose that the investors' perception is that the dividend will remain at 10 cents per share but that the risk of the share has increased thereby requiring a return of 15% If the share only gives a return of 12.5% (on an 80 cents share price) then investors will sell and the price will fall The fair value of the share according to the model will be: Po 1004 = 10c 0.15 = 66.7 cents SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL 1.6 Practical factors affecting share prices The dividend valuation model gives a theoretical value, under the assumptions of the model, for any security In practice there will be many factors other than the present value of cash flows from a security that play a part in its valuation These are likely to include: interest rates market sentiment expectation of future events inflation press comment speculation and rumour currency movements takeover and merger activity political issues The dividend valuation model helps us to understand how a change in these variables should affect the market value of the security Share prices change, often dramatically, on a daily basis The dividend valuation model will not predict this, but will give an estimate of the underlying fair value of the shares COST OF EQUITY 2.1 Shareholders required rate of return The basic dividend valuation model is: Po = D ke This can be rearranged to find ke: ke = D Po If ke is the return required by the shareholders in order for the share value to remain constant then ke is also the return that the company must pay to its shareholders Therefore ke also equates to the cost of equity of the company Therefore the cost of equity for a company with a constant annual dividend can be estimated as the dividend divided into the ex-div share price i.e the dividend yield The ex-div market value is the market value of the share assuming that the current dividend has just been paid A cum-div market value is one which includes the value of the dividend just about to be paid If a cum-div market value is given then this must be adjusted to an ex div market value by taking out the current dividend 1005 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Example A company’s shares have a market value of $2.20 each The company is just about to pay a dividend of 20c per share as it has every year for the last ten years What is the company’s cost of equity? Solution 2.2 Dividend with constant growth The model can also deal with a dividend that is growing at a constant annual rate of g The formula for valuing the share is as seen earlier: D (1 + g) ke − g Po = where Do = most recent dividend D1 = dividend in one year = D1 ke − g Rearranged this becomes ke = D0(1 + g) +g Po where g = growth rate (assumed constant in perpetuity) where Po = ex div market value Therefore the cost of equity = dividend yield + estimated growth rate 1006 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Illustration Do = 12c, Po (ex div) = $1.75, g = 5% What is the value of ke? ke = 0.12 (1.05) + 0.05 1.75 = 12.2% The growth rate of dividends can be estimated using either of two methods Two methods Extrapolation of past dividends 2.3 Gordon’s growth model Growth from past dividends Look at historical growth and use this to predict future growth If you have specific information about future growth, use that If dividends have grown at 5% in each of the last 20 years, predicted future growth = 5% Uneven but steady growth – take an average overall growth rate Discontinuity in growth rate – take the most recent evidence New company with very high growth rates – take care! It is unlikely to produce such high growth in perpetuity No pattern – not use this method (i.e dividends up one year, down the next) 1007 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Example A company has paid the following dividends over the last five years Cents per share 100 110 125 136 145 19X0 19X1 19X2 19X3 19X4 Estimate the growth rate and the cost of equity if the current (19X4) ex div market value is $10.50 per share Solution 2.4 Gordon’s growth model Gordon’s growth model states that growth is achieved by retention and reinvestment of profits g = bre b = proportion of profits retained re = return on equity Take an average of r and b over the preceding years to estimate future growth re = Profit after tax Shareholders' funds b = Retained profit Profit after tax = Profit after tax Net assets These figures can be obtained from the statement of financial position and income statement 1008 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Example A company has 300,000 ordinary shares in issue with an ex-div market value of $2.70 per share A dividend of $40,000 has just been paid out of post-tax profits of $100,000 Net assets at the year end were valued at $1.06m Estimate the cost of equity Solution 1009 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL 2.5 Cost of equity and project appraisal Illustration A plc is all equity financed and has 1m shares quoted at $2 each ex div It pays constant annual dividends of 30c per share It is considering adopting a project which will cost $500,000 and which is of the same risk as its existing activities The cost will be met by a rights issue The project will produce inflows of $90,000 pa in perpetuity All inflows will be distributed as dividends What is the new value of the equity in A plc and what is the gain to the shareholders? Ignore tax ke = 0.30 = 15% 2.00 New dividend Existing total dividend Dividends from the project New total dividend Value of equity = $ 300,000 90,000 390,000 390 ,000 0.15 = $2,600,000 Shareholders’ gain = $(2,600,000 – 2,000,000) – $500,000 = $100,000 Project NPV = ($500,000) + Therefore, new value of equity 90 ,000 0.15 = $100,000 = Existing value + Equity outlay + NPV = Existing value + Present value of additional dividends Therefore the NPV of a project serves to increase the value of the company’s shares i.e the NPV of a project shows the increase in shareholders’ wealth This proves that NPV is the correct method of project appraisal – it is the only method consistent with the assumed objective of maximising shareholders’ wealth 1010 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL 3.2 Irredeemable debentures Irredeemable debentures are a type of debt finance where the company will never repay the principal but will pay interest each year until infinity They are also referred to as undated debentures The market value of undated debt can be calculated using the same logic as the Dividend Valuation Model: MV (ex interest) = present value of future interest payments discounted at the debentureholder’s required rate of return For irredeemable debentures the interest is a perpetuity MV (ex int) = where r = I r I = annual interest r = return required by debenture holder I MV (ex int) = Interest yield The company gets tax relief on the debenture interest it pays, which reduces the cost of debentures to the company – known as the “tax shield” on debt Illustration Consider two companies with the same earnings before interest and tax (EBIT) The first company uses some debt finance, the second uses no debt $ 100 (10) _ $ 100 Profits before tax 90 100 Tax @ 33% 29.70 EBIT Debt interest Therefore Effective cost of debt _ 33 $3.30 difference Debt interest Less Tax shield $ 10.00 (3.30) _ Effective cost of debt 6.70 _ 1012 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Because of tax relief, the cost to the company is not equal to the required return of the debenture holders Unless told otherwise, we assume that tax relief is instant (in practice, there will be a minimum time lag of nine months under the UK tax system) Note that if debt is irredeemable then: Cost of debt to the company (also known as the post tax cost of debt) = Return required by the debenture holders × (1–Tc) = Interest yield × (1–Tc) Where Tc = corporate tax rate as a decimal Kd can be used to denote the cost of debt – but care is needed as to whether it is stated pre-tax or post-tax Example 12% undated debentures with a nominal value of $100 are quoted at $92 cum interest The rate of corporation tax is 33% Find (a) the return required by the debenture-holders (b) the cost to the company Solution 1013 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL 3.3 Redeemable debentures/dated debentures The cash flows are not a perpetuity because the principal will be repaid However from the dividend valuation model we can derive the following rule: The cost of any source of funds is the IRR of the cash flows associated with that source If we are looking at the return from an investor’s point of view, interest payments are included gross If we are looking at the cost to the company, we take the interest payments net of corporation tax Assume instant tax relief Assume that the final redemption payment does not have any tax effects To find the cost of debt for a company find the IRR of the following cash flows: Time 1−n n Market value (ex-interest) Post-tax interest Redemption value $ x (x) (x) The IRR is found as usual using linear interpolation Example A company has in issue $200,000 7% debentures redeemable at a premium of 5% on 31 December 19X6 Interest is paid annually on the debentures on 31 December It is currently January 19X3 and the debentures are trading at $98 ex interest Corporation tax is 33% What is the cost of debt for this company? Solution 1014 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Care should be taken not to confuse the required return of the debenture holders with the cost of debt of the company Required return of the redeemable debenture holder = IRR of pre-tax cash flows from the debenture = Gross redemption yield Gross Redemption Yield is also referred to as the Yield To Maturity (YTM) The cost of debt of the company is then determined by finding the IRR of the market value, net of tax interest payments and redemption value MV (ex interest) = present value of future interest payments and redemption value discounted at the debenture-holder’s required rate of return Example A company has 8% debentures redeemable at a 5% premium in ten years Debenture-holders require a return of 10% What is the cost to the company? Corporation tax is 33% Solution 1015 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL 3.4 Semi-annual interest payments In practice debenture interest is usually paid every six months rather than annually This practical aspect can be built into our calculations for the cost of debt If interest payments are being made every months then when the IRR of the debenture cash flows is calculated it should be done on the basis of each time period being months The IRR, or cost of debt, will then be a monthly cost of debt and must be adjusted to determine the annual cost of debt Effective annual cost = (1+semi annual cost)2 -1 Example A company has in issue 6% debentures the interest on which is paid on 30 June and 31 December each year The debentures are redeemable at par on 31 December 19X9 It is now January 19X7 and the debentures are quoted at 96% ex interest What is the effective annual cost of debt for the company? Ignore corporation tax Solution 1016 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL 3.5 Convertible debentures Convertible debentures allow the investor to choose between redeeming the debentures at some future date or converting them into a pre-determined number of ordinary shares in the company To estimate the market value it is first necessary to predict whether the investor will choose redemption or conversion The redemption value will be known with certainty but the future share price can only be estimated MV (ex interest) = present value of future interest payments and the higher of (i) redemption value (ii) forecast conversion value, discounted at the debenture-holder’s required rate of return You may also be required to calculate other data for convertibles: − − Floor value = the value assuming redemption Conversion premium = market value – current conversion value Example A company has in issue 9% bonds which are redeemable at their par value of $100 in five years’ time Alternatively, each bond may be converted on that date into 20 ordinary shares The current ordinary share price is $4.45 and this is expected to grow at a rate of 6.5% per year for the foreseeable future Bondholders’ required return is 7% per year Required: Calculate the following values for each $100 convertible bond: (i) market value; (ii) floor value; (iii) conversion premium Solution 1017 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL To find the post-tax cost of convertible debt for a company find the IRR of the following cash flows: Time 1−n n Market value (ex-interest) Post-tax interest Higher of redemption value/forecast conversion value $ x (x) (x) Example 10 A company has in issue some 8% convertible loan stock currently quoted at $85 ex interest The loan stock is redeemable at a 5% premium in five years time, or can be converted into 40 ordinary shares at that date The current ex-div market value of the shares is $2 per share and dividend growth is expected at 7% per annum Corporation tax is 33% What is the cost to the company of the convertible loan stock? Solution 1018 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Key points If capital markets are perfect the sale/purchase of any security must be a zero NPV transaction i.e market price = present value of future cash flows discounted at investors’ required return This general rule can be specifically applied to shares to develop the dividend valuation model (DVM) and also to bond valuation If the market price of a security is already known then the model can be rearranged to find the required return of investors’ i.e the company’s cost of equity/debt finance Care must be taken with the cost of debt as interest, unlike dividends, is a tax allowable expense form the side of the company FOCUS You should now be able to: understand and use the dividend valuation model; estimate the cost of equity and cost of debt for a company; understand the practical factors that affect share prices 1019 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL EXAMPLE SOLUTIONS Solution Po (cum div) = $2.20 Po (ex div) = $2.00 Ke = D Po = 20 × 100% 200 = 10% Solution 19X0–19X4 − four changes in dividend 100 (1 + g)4 = 145 (1 + g)4 = 145 100 1+g = 145 100 = 1.097 g = 9.7% ke = = D1 +g P0 145 (1.097 ) + 0.097 1,050 = 24.8% 1020 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Solution Growth rate g = bre b = % profit retained = 60 ,000 100 ,000 = 60% = Return on equity = Profit after tax Opening net assets = 100,000 × 100% 1,060,000 − 60,000 re = 10% Note – return on average equity could be used rather than return on opening equity g = 0.6 × 0.1 = 0.06 = 6% ke = D1 +g P0 = 40 ,000 (1.06 ) + 0.06 300 ,000 × 2.70 = 11.2% Solution 12% preference shares: dividend is 12% × nominal value Ke = D Po = 12 × 100% 115 = 10.4% 1021 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Solution r = Int MV ex int = 12 × 100% 92 − 12 = 15% Return required by debenture-holders is 15% Cost to the company Kd Int (1 − Tc ) MV ex int = 12 (1 − 0.33) = 92 − 12 = 10.05% Solution Time Cash PV @ 10% flow 98 98 (7) × 0.67 = (4.69) (14.87) (105) (71.72) 1−4 _ IRR = + Kd = 6.5% 1022 5.05 × (10 − 5) 5.05 + 11.41 PV @ 5% 98 (16.63) (86.42) _ 11.41 (5.05) _ _ SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Solution To find the cost to the company, we need to know the market value of the debentures We this by discounting the future flows at the debenture-holder’s required return MV = (8 × 6.145) + (105 × 0.386) = $89.69 To find the cost to the company we an IRR calculation, bringing in the effects of tax relief DF @ 10% t0 t1–10 t10 89.69 (8) × 0.67 (105) 6.145 0.386 PV $ 89.69 (32.94) (40.53) 16.22 IRR DF @ 5% 7.722 0.614 PV $ 89.69 (41.39) (64.47) (16.17) 16.17 × (10 – 5) 16.17 + 16.22 = 5+ = 7.5% Therefore Kd = 7.5% Solution Time is January 19X7 Interest payments due 30 June X7 31 Dec X7 30 June X8 31 Dec X8 30 June X9 31 Dec X9 Time Time Time Time Time Time 1023 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Each interest payment will be just half of the coupon rate, $3 each months Time 1−6 Cash flow 96 (3) (100) PV @ 3% 96 (16.25) (83.70) PV @ 5% 96 (15.23) (74.60) IRR (3.95) 6.17 3.95 × ( − 3) 3.95 + 6.17 = 3+ = 3.78% This is the monthly cost of debt The effective annual cost of debt is (1.03782) -1 = 7.7% Solution (i) Market Value Expected share price in five years’ time = 4.45 x 1.0655 = $6.10 Forecast conversion value = 6.10 x 20 = $122 Compared with redemption at par value of $100, conversion will be preferred Today’s market value is the present value of future interest payments, plus the present value of the forecast conversion value = (9 x 4.100) + (122 x 0.713) = $123.89 (ii) Floor value Floor value is the present value of future interest payments, plus the present value of the redemption value = (9 x 4.100) + (100 x 0.713) = $108.20 (iii) Conversion premium Current conversion value = 4.45 x 20 = $89.00 Conversion premium = $123.89 – 89.00 = $34.89 This is often expressed on a per share basis, i.e 34.89/20 = $1.75 per share 1024 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL Solution 10 First we need to decide whether the loan stock will be converted or not in five years To this we compare the expected value of 40 shares in five years’ time with the cash alternative We assume that the MV of shares will grow at the same rate as the dividends MV/share in five years = 2(1.07)5 = $2.81 MV of 40 shares × $2.81 = $112.40 Cash alternative = $105 Therefore all loan stock-holders will choose the share conversion To find the cost to the company, find the IRR of the post-tax flows DF @ 5% t0 t1−5 t5 (85) (8) × 0.67 (112.4) 4.329 0.784 PV $ 85.00 (23.20) (88.12) (26.32) IRR DF @ 10% 3.791 0.621 PV $ 85.00 (20.32) (69.80) (5.12) 26.32 × (10 – 5) 26.32 − 5.12 = 5+ = 11.2% Therefore cost to the company = 11.2% 1025 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL 1026 ... Profit after tax = Profit after tax Net assets These figures can be obtained from the statement of financial position and income statement 1008 SESSION 10 – SECURITY VALUATION AND THE COST OF CAPITAL