Lecture 4 (Week 4): Equity Valuation (2):

The present value of growth opportunities Lecture 4 (Week 4): Equity Valuation (2): The value of a stock can be analysed as the sum of the value of the company without earnings reinvestment and the present value of growth opportunities (PVGO) or the value of growth. V " = $ % PVGO E = no growth earnings level r = required return on equity $ = no growth value per share % Lecture example 1: Transport Inc s shares trade at $60 with expected earnings of $5 per share and a required return of 10%. Assume the shares are properly priced, so price is equal to its fundamental value. Calculate the PVGO and the percentage of the price that is related to PVGO. 60 = @ PVGO ".B PVGO = 10 B" = 16.67% D" Lecture example 2: Firm reinvests 60% of its earnings in projects with ROE of 10%, capitalisation rate is 15%. Expected year-end dividend is $2/share, paid out of earnings of $5/share. What is the PVGO? g = 1 DPR E ROE = 1 O @ 0.1 = 6% O P " = ".B@P"."D PVGO = Price per share No growth value per share = 22.22 @ ".B@ Free cash flow model What is free cash flow? Cash flows into the company as it sells its products or provides services Cash flows out as it pays its cash operating expenses Then the firm takes the leftover cash and makes short-term net investments in working capital (e.g. inventory and receivables) and long-term net investments in PPE Remaining cash is free cash flow to the firm (FCFF) and available to pay out to the firm s investors (bondholders, shareholders) The cash that is left after the firm has met all its obligations to other investors is free cash flow to equity (FCFE) The free cash flow model is particularly useful for firms that pay no dividends, for which the dividend discount model would be difficult to implement. But FCF models can be applied to any firm and can provide useful insights about the firm beyond the DDM. Firm value= FCFF discounted at the WACC Equity value= FCFE discounted at the required return on equity Equity value-= firm value market value of debt 1

Calculate FCFF from net income FCFF = NI Interest 1 tax rate NCC FCI Y[ WCI Y[ NCC = Non cash charge- Added back to net income because they represent expenses that reduce reported net income but didn t actually result in an outflow of cash (depreciation and amortisation) FCI Y[ = Capital expenditure Proceeds from sales of long term assets WCI Y[ = Investment in net working capital Calculate FCFF rom EBIT and EBITDA FCFF = EBIT 1 tax rate Depreciation FCI Y[ WCI Y[ FCFF = EBITDA 1 tax rate Depreciation tax rate FCI Y[ WCI Y[ Calculate FCFE directly from FCFF FCFE = FCFF Interest 1 tax rate Net borrowing Net borrowing = New debt issues Debt repayments FCF valuation models Single stage constant growth model: efee g = efee k(bmj) hiffpj hiffpj Two or three stage model: efee o efee o pq%ryst [stuq vw xyq wy%r Bmhiff o Bmhiff z WACC: $ WACC = k k q } 1 tax rate ~ Firm value is the present value of the expected FCFF discounted at the WACC Replacing FCFF and WACC using FCFE and required return on equity respectively gives the equity value Also common is the statement that this valuation model gives higher valuations that the DDM because it values all cash flows and not just dividends Firm value assuming constant growth in the terminal state: e ee o efee zg (hiffpj) Bmhiff z g = reinvestment rate expected return on capital = RR E(ROC) RR = Lecture example 3: fs $ wv% qƒ Y[q xrqx = pvxst fs $ P u xsyyj fs $ fs y s[syts tq swxq% fs $ v rsyxsyyj s qx $ ˆp BPx m~q %q YsxYvPhf Šz P u xsyyj fs $ oe Ltd. had a net profit margin of 25% on revenues of $30million this year. Fixed capital investment was $3 million. Depreciation was also $3 million. Working capital investment is 7.5% of total sales. Net income, fixed capital investment, depreciation, interest expense, and sales are expected to increase at 10% per year for the next three years, after which, the growth rate will be stable at 4% per year. Tax rate is 40% and the company has 1 million shares outstanding. The company s long-term debt has market value of $30 million Interest rate is 10%. What is the firm value and the firm s equity value? Use FCFF model and assume WACC is 18% during the high growth stage and 13% during the stable stage. 2

FCFF = NI Interest 1 tax rate NCC FCI Y[ WCI Y[ 0 1 2 3 4 NI 7.5 7.5(1.1) =8.75 7.5(1.1) 2 =9.075 7.5(1.1) 3 =9.98 7(1.1) 3 x 1.04 =10.38 I(1 tax rate) 1.8 1.98 2.178 2.396 2.49 Depreciation (NCC) 3 3.3 3.63 3.993 4.15 WCinv 2.25 2.475 2.7225 2.99475 3.294225 FCinv 3 3.3 3.63 3.993 4.15 FCF 7.05 8.225 8.5305 9.38125 9.575775 efee o Œ.OO@ Œ.@ "@ Ž Terminal value = Œ.OO@ Œ.@ "@ Ž Comparing the valuation models efee o pq%ryst [stuq vw xyq wy%r Bmhiff o Bmhiff z. ŒBO@ pq%ryst [stuq.@ D ".B P"." = 108.444. ŒBO@mB"Œ. = 84.81 In principle, the free cash flow approach is fully consistent with the dividend discount model and should provide the same estimate of intrinsic value. However, in practice, values from these models may differ, sometimes substantially. This is due to the fact that in practice, analysts are always forced to make simplifying assumptions. The problem with DCF models Most of the action in these models is in the terminal value and this value can be highly sensitive to even some small changes in some input values. Therefore, you must recognise that DCF valuation estimates are almost always going to be imprecise. Growth opportunities and future growth rates are especially hard to pin down. For this reason, many value investors employ a hierarchy of valuation. They view the most reliable components of value as the items on the balance sheet that allow for the most precise estimates of market value (real estate, plant and equipment). A somewhat less reliable component of value is the economic profit on assets already in place The least reliable components of value growth are growth opportunities, the purported ability of firms like Intel to invest in positive-npv ventures that contribute to high market valuations today. Residual income model Residual income is the net income of a firm less a charge that measures stockholders opportunity cost of capital. It recognises the cost of equity capital in the measurement of income and explicitly deducts all capital costs, unlike accounting net income which only deducts cost of debt 3

RI x = E x k q B xpb = ROE k q B xpb E x = Expected EPS for year t k q = Required return on equity B xpb = Book value of equity in year t 1 Equity value is book value of equity plus the present value of expected residual income. Residual income is the excess earnings above what would be earned if the book value of equity earned a return just equal to the cost of equity capital. Book value of equity is typically well below market value of equity, so it is usual to expect positive residual income. Longer-term, it is more reasonable to expect any growth in residual income to decline as the firm finds it harder to identify positive NPV projects in mature markets. When computing a terminal value, an assumption that new projects earn a return equal to the cost of capital is equivalent to assuming zero growth in residual income. It is not equivalent to assuming that residual income declines to zero V q = B " Lecture example 4: x ˆ = B " (Bm ) o x $ o P ošg (Bm ) o Consolidated Product has a required rate of return of 14%. The current book value is $6.5. Earnings forecasts for 2013, 2014 and 2015 are $1.1, $1 and $0.95 respectively. Dividends in 2013 and 2014 are forecasted to be $0.5 and $0.6 respectively. The dividend in 2015 is a liquidating dividend, which means that the company will pay out its entire book value in dividends and cease doing business at the end of 2015. Calculate value of Consolidated Product s stock at the beginning of 2013 using the RI model. RI x = E x k q B xpb 2013 2014 2015 B tp1 6.5 7.1 7.5 EPS 1.1 1 0.95 DPS 0.5 0.6 8.45 B t 7.1 7.5 0 k e B tp1 0.91 0.99 1.05 RI 0.19 0.01-0.1 V q = B " PV RI = 6.5 ".B "."B P".B B.B B.B Ž B.B DDM and FCF vs residual income model DDM and FCF models measure value by discounting a stream of expected cash flows The residual income model starts with a book value and adds to this the present value of the expected stream of residual income Theoretically, if the underlying assumptions used to make necessary forecasts are the same, intrinsic values for all models should be identical 4

Strength of RI model Terminal value does not dominate the intrinsic value estimate Applicable to firms that do not pay dividends or that do not have positive expected free cash flows in the short run Focus on the economic profitability rather than just on accounting profitability Weaknesses of the RI model Rely on accounting data that can be manipulated by management Clean surplus relation B x = B xpb E x D assumed to hold. Any accounting changes that directly taken to the equity account will violate this relationship Multiples based valuation: Equity Price earnings Compute the share price relative to the expected earnings per share for a set of comparable firms Apply the median or mean price earnings ratio for the comparable firm set to the forecast earnings for the firm of interest k = BP $ g P $ Price-book value of equity Similar valuation technique to the price-earnings ratio Stocks with low price book values have historically outperformed stocks with high price book ratios Price operating cash flow Operating cash flow figures are less prone to manipulation than EPS figures, but naturally are more volatile In this instance, the operating cash flow per share should be as reported in the financial statements (i.e. no adjustments for interest) because you are comparing the price of equity with cash flows available to equity holders Valuation: The impact of risk and growth Consider the constant growth dividend discount model shown below: P " = ~ g Pj à k $ g = ~ g/$ g Pj = ~ P BP~ $ $ 5