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4 Bond valuations 4.1 Discounted cashflow approach Government or similar highquality bonds can be valued by discounting cashflows at rates consistent with the market spot rate yield curve. The market spot rate yield curve can be derived from the yields available on zerocoupon bonds, where they exist, or from government bond strips. In a developed economy, the risks arising due to lack of security and marketability may be negligible and so these rates may reflect a riskfree yield. Other bonds, such as corporate bonds, can be valued similarly but adjusting the yield to allow for lower security and marketability. 4.2 Valuing bonds with option features Many bonds have option features eg callable and puttable bonds. A callable bond is a bond that the borrower can choose to repay at any time. Similarly, with a puttable bond, the investor can demand repayment at any time. Such bonds should theoretically be valued using option pricing techniques, although this is not always done in practice. The value of a puttable bond to the investor and so the market price should equal that of an otherwise identical bond that does not include an option, plus the value of the choice provided by the option. The value of the option will be greater, the more likely it is that the option will be exercised. Question Explain how the value of a callable bond compares with a similar bond without the call option. Solution It is lower due to the additional uncertainty that the investor faces, being unsure of the exact date at which the capital will be repaid, and hence unsure of the future series of cashflows received. The option has a positive value to the borrower and a negative value to the investor. 5 Equity valuations In this section we look at a number of approaches for placing a value on equity market value, dividend discount model, net asset value per share, value added measures, measurable key factors. 5.1 Market value The starting point for valuation of an individual equity is the market value, if there is a suitable market. For most shares this will be a simple and objective means of valuation. 5.2 Dividend discount model A discounted cashflow calculation may be carried out to value the shares, if the investor wants to value unlisted shares, check whether they think the market value is reasonable, or under or overpriced. The dividend discount model derives the value of a share as the discounted value of the estimated future dividend stream. This approach is described in Subject CM1, so we provide a recap of that material here. We start with a general approach, and then introduce simplifying assumptions so that we end up with a very useful, simple model for valuing the shares of a company. Pay close attention to the assumptions that are used in order to appreciate the limitations of the discounted dividend model. General model The general model can be expressed as V sum from t1 to infinity of D subt v of t where V is the value of the share D subt is the gross amount of the tth dividend payment v of t is the discount factor applied between time 0 and the time of the tth dividend payment. This assumes that there are no expenses or tax, shares are held forever or would be purchased by an investor using the same valuation model. Simplified model A simplified equation can be obtained by assuming in addition that dividends are payable annually, with the next payment in one years time, g, the annual dividend growth rate, is constant over time, i, the annual required rate of return, is constant over time, i is greater than g, i and g are defined consistently eg both include inflation or are net of inflation, the dividend proceeds can be reinvested at i per annum. With these additional assumptions, the equation simplifies to become V D over i minus g Thus we now have a very simple model for assessing the value of the share. Starting with D, the dividend to be paid one year from now, gives this very neat result. In most investment textbooks, the algebra starts with the dividend just paid, which is arguably more sensible as this is known. The equation is then V D sub o times 1 g over i minus g where D sub o is the most recent dividend received. Issues to consider when applying the simplified model There are several issues to be aware of when applying the model We do not know the value of i to use in the model. Additionally, the assumption of a constant required rate of return i over time might not be appropriate during an era when the yield curve is steeply sloping upwards or downwards. In order to calculate a value it is necessary to decide on an appropriate required rate of return. This would often be calculated as the yield on longterm government bonds plus an appropriate addition for the riskiness of the income stream. Conventional investment wisdom says that we will require a higher return from equities than from government bonds to compensate for the risk of dividends being reduced or even not be paid and loss of capital on wind up, uncertainty of return and the volatility of the share price, lower marketability and higher dealing costs. We do not know what the growth rate g should be. Investors with real liabilities might start from an indexlinked government bond yield and estimate the real, rather than nominal, rate of dividend growth. The value of g used in the model will reflect the investors estimates of the future dividend growth of the company, which will in turn reflect the investors view concerning the future profitability of the company. In practice it might be felt that constant dividend growth is not a realistic assumption. An alternative approach would be to use dividends based on profit forecasts for the first few years, then apply a shortterm rate of growth for a period until the growth rate settled down to a longterm average. The results obtained are very sensitive to the assumed level of i minus g. Taxpaying investors should use the net dividends received and a suitable aftertax rate of return. The equations given above ignore tax and expenses. This model assumes annual dividend payments even though the payments might be halfyearly on individual shares. This is not a key factor there are much bigger causes of uncertainty within this model than the frequency of dividends. The model is of no use unless i g. 5.3 Net asset value per share A net asset value per share approach can be adopted for companies with significant tangible assets. A similar approach can be adopted to shares of a property investment company. For example, a property company could be valued as the sum of the value of the buildings and land that it owns less any liabilities, eg borrowing. Such an approach would not give a realistic value for companies whose value comprises of significant intangible assets, eg intellectual property rights. A net asset value per share approach might be used to value an investment trust company. Investment trusts comprise several holdings in other assets, although the investment trust itself is a company. The shares of the investment trust will trade at a price set by the market, following principles of supply and demand and shareholder perceptions of risk and the future for the company. It is also possible to determine the market price or proxy for each shareholding in the investment trust. These can be aggregated and divided by the number of shares in issue to give a net asset value per share. This is what the investors would receive, less expenses, if the investment trust was wound up, all its assets sold and the proceeds distributed to shareholders. Investment trusts are frequently quoted as the market price being at a percentage premium or discount to NAV. 5.4 Value added measures Shareholder value is an attempt to get at the intrinsic or underlying value of an investment rather than its accounting value. As an alternative, economic value added EVA looks at one years results and deducts the cost of servicing the capital that supports those results. The idea is that if the EVA is positive, then the companys activities over the year have added or created value for the shareholdersas the shareholders would want the company to do which should ultimately be reflected in the share price. Thus, a companys EVA provides an indication of its success or otherwise over a particular year and can therefore be used as a measure of performance. EVA acts as a bridge between quoted share value and accounting values to give a framework for executive compensation schemes designed to produce results that increase shareholder value. 5.5 Other equity valuation methods Where companies are not making profits and a net asset valuation is not appropriate, other methods have to be employed if a calculated valuation is required of an individual share. The methods discussed above all implicitly assume at least one of the following the company is declaring dividends, it is making profits, net asset valuation is suitable. But this will not always be the case, for example, if the company is young and yet to declare any dividends, is making losses or has few tangible assets. Other methods must then be used to assess the value of the shares in the company in question. These methods often involve determining a relevant and measurable key factor for the companys business. The relationship between this factor and the market price of other quoted companies is then used as a basis for valuation. The factor used will depend on the business of the company. It will also depend upon exactly what information is available and may be either qualitative or quantitative. In some instances, a site visit to meet the managers of the company, and discuss its aims and objectives, might be of use. Question Outline the factors that might be investigated in the case of a food retailer. Solution Large food retailers typically operate with high volumes of sales and low profit margins. Efficiency of sales and turnover is therefore likely to be a crucial determinant of success. So investigate such factors as turnover per square metre of selling space or per member of staff, the inventory turnover ratio inventory turnover times 365, the trade payables turnover ratio trade payables turnover times 365 the company may be able to increase profitability by delaying payments to suppliers as long as possible. Market share and quality of management might also be of interest.