15 VALUATION OF DEBT AND EQUITY Introduction Debt Valuation - Par Value - Long Term versus Short Term - Zero Coupon Bonds - Yield to Maturity - Investment Strategies Equity Valuation - Growth Stocks - P/E Ratios Issuers of Debt or Equity People as Gamblers Summary Introduction Buy low, sell high is what all investors in shares and bonds aim to do. The key question is when are shares or bonds high or low in their value? Placing a value on an investment can be looked at as a two step procedure. The first step is to evaluate the present value of the cash flows of the investment. The second step is to adjust this value for the riskiness of these projected flows. In this chapter we will cover the first step in the valuation process - that of placing value on investments based on expected cash flows. The second step of adjusting for risk will be covered in the next chapter. For the sake of this chapter, it is assumed that all projected cash flows are 100% certain to occur. Companies finance their holding of assets by using either debt or equity. Debt can take many forms including bonds, debentures, zero coupon bonds, some types of preferred shares and convertible debentures. These are just a few examples. The basic building block of debt is an agreement between lender and borrower of a presently specified cash flow over a future period of time. The specific terms of the contract are designed to meet the unique needs of both the lender and the borrower.
292 Financial Management and Decision Making Equity, on the other hand, makes no promises about the amount of cash flowing from the company to the investor in the future. Equity simply gives the holder a piece of the action in the company. Sometimes equity carries restrictions on voting rights or transferability. The basic understanding of equity holders is that they will reap the rewards of the actions of the company. Most equity holders owning common shares in a company also benefit by having limited liability in the company s activities. If the company is liquidated, most common equity holders only stand to lose at most the value of their equity. In this chapter the valuation of debt and equity from the point of view of the investor will be examined first. Since the role of the financial manager is to maximise shareholders wealth, the second aspect to be examined will be how (indeed if ) the financial manager can increase the value of the firm through various capital raising instruments. In this way it will be possible to compare the differences in viewpoint between investing and the issuing of debt and equity. Debt Valuation A debt agreement is a contract between the lender and the borrower. This contract can include items such as the amount of money to be repaid at a specific date in the future, the amount and timing of the payments to be made to the lender in the interim, whether or not the debt can be recalled and at what costs, whether or not the debt can be turned into equity, and any other contractual agreement to which the lender and borrower agree. Once the terms of the debt agreement are understood, determining the value of debt is a straightforward present value calculation. Most debt issues, called bonds, have the following components: 1. Maturity, or the date in the future when the debt agreement concludes. 2. Face Value, sometimes called Par Value, or the amount of money for which the bond will be redeemed at maturity. The most common face value is $1,000. 3. Coupon Rate, or a percentage of the face value which is paid to the debt holder on a regular (annual, semi-annual) basis through to maturity. A present value calculation can be made when these features of a bond are known. Remember that the market value of an asset is determined by expressing the flows of money through time in terms of present value. Since the amount and timing of the future cash flows are specified in the bond agreement, calculating the present value of the bond now becomes straightforward. Given periodic specified cash flows into the future, the present value of these flows is determined by taking the present value of these flows using a discount rate which is the presently prevailing interest rates. PV (of a bond) = PV of all future cash flows Example 1. What is the value of a bond with a $1,000 face value, 8% annual coupon rate having 7 years to the maturity date if prevailing interest rates are 10%? A time line of the flows of this arrangement shows what needs to be done to arrive at the present value of the bond.
Chapter 15: Valuation of Debt and Equity 293 Year 1 2 3 4 5 6 7 Cash Flow Coupon Payment 80 80 80 80 80 80 80 Face Value 1,000 The present value is: PV = $80 x Annuity Factor 10% over 7 years + $1,000 x Discount Factor 10% over 7 years = $80 x 4.8684 + $1,000 x.5132 = $389.47 + $513.20 = $902.67 This means that if you agreed to receive $80 per year over the next 7 years as well as $1,000 at the end of the seventh year, you would be willing to pay $902.67 in today s dollars for that cash flow given that interest rates are 10%. 2. What would this bond be worth if prevailing interest rates were only 5%? PV = $80 x Annuity Factor 5% over 7 years + $1,000 x Discount Factor 5% over 7 years = $80 x 5.7864 + $1,000 x.7107 = $1,173.61 It is important to note that the value of the bond is inversely related to the level of prevailing interest rates. This relationship is not intuitively clear but when interest rates fall, the value of a bond goes up since the present value of the future cash flows is discounted by a lower percentage. There are, therefore, two sorts of income that the holder of a bond (the lender) can realise. The first and most obvious income arises from the coupon payment and the final maturity payment. The second source of income is capital gain (or loss) if the prevailing interest rates fall (or rise) and the bond is sold prior to its maturity date. Par Value Issuers of bonds often try to set the coupon rate exactly equal to the prevailing interest rates. What is the value of the bond in the previous example if the prevailing interest rate is 8%? PV = $80 x 5.2064 + $1,000 x.5835 = $1,000 In other words, when the coupon rate is equal to the prevailing interest rate the value of the bond is its face value. While companies may wish to sell their bonds at par, it is difficult to go through all of the printing and underwriting procedures prior to the issuing of the bonds and estimate exactly the level of prevailing rates on the date of issue. It is worth pointing out that bond issues are typically in the millions($) while interest rates are measured in basis points with 100 basis points equalling 1%. Therefore, a 1 basis point movement in interest rates can have a significant effect on the value of the bond issue.
294 Financial Management and Decision Making Long Term versus Short Term In the above example the value of the bond increased 30% from $902.67 to $1,173.61 (or $270.94) as interest rates decreased from 10% to 5%. However, what additional effect will the time to maturity have on the value of the bond? For example, given a bond with an 8% coupon rate, $1,000 face value, and 20 years to maturity, how much will it change in value as interest rates move from 10% to 5%? at 10%, PV = $80 x 8.5136 + $1,000 x.1486 = $829.69 at 5%, PV = $80 x 12.4622 + $1,000 x.3769 = $1,373.88 The 5% drop in interest rates resulted in a 65.6% ($544.19) increase in value of the longer term bond. In the earlier example of a 7 year bond, the same change in interest rates resulted in a 30.02% increase in value. Longer term bonds are more volatile than shorter term bonds when there is a change in interest rates. As an investor in bonds anticipates an impending decline in interest rates, bonds with longer maturities will gain more value than the shorter maturities. At the same time, longer term bonds will also result in more of a loss if interest rates rise. Zero Coupon Bonds In order to take advantage of differing tax treatment on interest income and in order to gain more leverage on moving interest rates the zero coupon bond has emerged. It is simply a bond with a 0% coupon rate. Example What is the change in value of a zero coupon bond of 20 years with a $1,000 face value as interest rates drop from 10% to 5%. at 10%, PV = $1,000 x Discount Factor 10% over 20 years = $148.60 at 5%, PV = $1,000 x Discount Factor 5% over 20 years = $376.90 This change of $228.30 represents a 153.6% increase over the original amount invested. This is more than double the volatility of the previous example of a 20 year bond with an 8% coupon rate. Realisation of interest expenses and income for taxation purposes varies by country and by the entity involved. It is common to realise interest income (expense) in each taxation period even if no money changes hands. This means that the issuers of the debt can realise tax deductible interest expense without needing to pay out any actual cash. Tax exempt holders of these bonds, or holders in countries whose tax treatment does not require tax to be paid until money changes hands, will not have to pay tax on this non cash flow until money actually does change hands.
Chapter 15: Valuation of Debt and Equity 295 Zero coupon bonds are suitable for the investor seeking extreme leverage on changing interest rates given that the tax implications of non cash realisable income are acceptable. Issuers of zero coupon bonds take the advantage of the non cash interest expense, but receive less up front money on the issue. Yield to Maturity Given the current price (present value) of a bond, its coupon rate, and its face value, it is possible to determine the discount rate that must be used on the future cash flows so that the present value of the future cash flows is exactly equal to the price of the bond. This discount rate is known as the bond s yield to maturity, sometimes called the internal rate of return, and is found using an iterative process using varying discount rates. A discount rate is chosen to see how close the present value of the future cash flows comes to the bond s current price. If the calculated value is higher (lower) than the current price, a higher (lower) discount rate is selected and the process repeated until the present value of the future cash flows equals the current price. Example What is the yield to maturity of a $1,000 face value bond having a 5% annual coupon rate maturing in 10 years whose price is $860? $860 = $50 x Annuity Factor y% over 10 years + $1,000 x Discount Factor y% over 10 years where y is the yield to maturity. If y of 8% is used, the right side of the equation is $50 x 6.7101 + $1,000 x.4632 = $798.71 which is less than the price of $860. To increase the right side of the equation, a lower interest rate must be tried. Using y of 6% gives $50 x 7.3601 + $1,000 x.5584 = $926.41 which is higher than the price of $860. The yield to maturity must be higher than 6% and trying 7% gives $50 x 7.0236 + $1,000 x.5083 = $859.48 Therefore, the yield to maturity of the bond is very close to 7%. Extrapolation, as described in the Capital Investment chapter, can be used to better estimate the exact discount rate but where large sums of money are involved extrapolation should be avoided. A computer should be used to calculate the yield to an acceptable degree of accuracy. Investment Strategies When making a decision to invest, a further understanding of the needs and desires of the investor is necessary. If the money invested is needed at a specific point of time in the future, then investment in bonds is essentially a trading in maturity dates
296 Financial Management and Decision Making and coupon rates in anticipation of changes in interest rates. It has been shown that bonds with lower coupon rates or with longer maturity dates change their present value more with a change in interest rates, than do bonds with higher coupon rates or shorter maturities. If bonds are bought and held to maturity - not traded, or traded only for other bonds with the same maturity date - then the yield to maturity is fixed at the time of purchase regardless of the intervening changes in interest rates. Consider the initial example of a bond which cost $902.67 when interest rates were 10% and which increased in value to $1,173.61 when interest rates dropped to 5%. What benefit is there to realising this gain of $270.94 if it is to then be reinvested into a bond with the same coupon rate and maturity date? It will cost exactly $270.94 more to buy this bond with the newly prevailing interest rates. Anticipation of changes in interest rates will cause bond investors to alter their average maturity dates. If a rise in rates is anticipated, the maturity dates will be shortened. If a decline in interest rates is anticipated, the average maturity date will be lengthened. (Transaction costs in the form of commissions to brokers must also be considered. With higher transaction costs, the amount of movement in prevailing interest rates must be higher before capital gains profits can be made). Equity Valuation The ownership of shares in a company entitles the owner to the dividend payments and other benefits the company directors might recommend, as well as giving the shareholders the right to sell the shares sometime in the future. It should be noted again that all cash flows discussed here are considered risk free. The value of a share is thus the present value of the future cash flows resulting from owning the share. Given that: P 0 = price of share in time period 0 (PV) P t = price of share at end of year t D t = dividend to be given at the end of year t r = the required rate of return on the share g = the expected growth rate of the share (also of earnings and dividends), then if the share is to be held for one year: P 0 = D + P 1 1 (1+ r) But P 1 = D + P 2 2 (1+ r) ; P 2 = D + P 3 3 (1+ r) etc
Chapter 15: Valuation of Debt and Equity 297 Therefore, substituting for P1 and P2 etc: P 0 = D 1 1 (1+ r) + D 2 2 (1+ r) + D 3 3 (1+ r) +... D n (1+ r) n +... If D 1 = D 2 =... = D n and if n approaches infinity, it has already been shown that this is the formula for a perpetuity whose value can be written as: P 0 = D r 1 If the dividend is growing at rate g where g is less than r, then this is a growing perpetuity with the value: P 0 = D 1 r g While it may seem strange to assume that the company will continue to pay out a dividend forever, it is not an unreasonable assumption since the present value of dividends paid out only 50 years hence at a required rate of return of 20% has a present value of only.0001 times the future amount of the dividend. Thus, future dividend payments have less and less impact on the present value price. However, the value of the share is independent of future values of the share and is only dependent upon the dividend amount, the dividend growth rate and the required rate of return. What does this imply about the capital gain in the value of the share? It implies that any capital gain can always be defined in terms of future dividend income and subsequent growth. Examples 1. XYZ Company is expecting to pay out a dividend of $2.50 per share at the end of the year. XYZ is of the opinion that $2.50 is a reasonable dividend payout and does not plan on increasing that amount ever even if earnings rise. If your required rate of return for investing in XYZ is 18%, how much would you be willing to pay for one share of XYZ? P0 = = 2.50.18 $13.89 2. New directors of XYZ change the payout policy and announce that they would allow the dividends to grow at 9% per year. Their announcement convinces you that they can sustain this growth rate well into the future. What would you now be willing to pay for one share of XYZ?
298 Financial Management and Decision Making 2.50 P0 = (.18.09) = $27.78 This illustrates the fact that the amount of the dividend has a large effect on the price of the share - as dividend prospects go, so goes the price of the share. Some firms pay out a fixed percentage of earnings as a dividend in which case the price of the share is affected directly by earnings of the company. It is also interesting to note that companies with high growth rates are more price sensitive to changes in the required rate of return, r, than low growth companies. Example 1. If r increases from 10% to 11%: (a) in a company with a 2% growth rate and an expected dividend of $5.00, the share value decreases by 11%. 500. P 0 = (. 10. 02) = $62. 50 compared with 500. P 0 = (. 11. 02) = $55. 56 (b) in a company with an 8% growth rate and an expected dividend of $5.00, the share value decreases by 33%. 500. P 0 = (. 10. 08) = $250. 00 compared with 500. P 0 = (. 11. 08) = $166. 67 2. Compare the effect of a 1% reduction in the expected rate of return on a share with a 9% growth rate, to the effect of the same reduction on a share with a 3% growth rate. If the required rate of return drops 1% from 18% to 17% then: 2. 50 P 0 = (. 18. 09) = $27. 78 as earlier compared with 2. 50 P 0 = (. 17. 09) = $31. 25 This is $3.47, or 12.5% higher than before the reduction in the required rate of return. If the growth rate is only 3% then before the change in the required rate of return: 2. 50 P 0 = (. 18. 03) = $16. 67 compared with 2. 50 P 0 = (. 17. 03) = $17. 86 his change of $1.19 is only a 7% change in the price of the share.
Chapter 15: Valuation of Debt and Equity 299 Therefore, it has been shown that the value of the share will change as the amount of dividends, the prevailing discount rate, and the growth rate of the dividends change. While each of these three will result in a change in share price value, it is not at all uncommon for all three of these valuation parameters to change together - making the valuation process more difficult. Growth Stocks There are some share values that grow at very fast rates. In many cases g is significantly higher than r for any reasonable level of expected return. This does not mean that these stocks have infinite value. Firstly, it is impossible for any share to grow at a high compound rate for a long period of time since the value of the company will eventually exceed the value of the total economy in which the company finds itself. Secondly, there is a limit to the total amount of available equity investment in the economy. These two finite quantities, amount of available assets and amount of available equity, create upper limits to the size a firm can achieve. While it is true that firms can and do grow at rates of 50% per year for eight or ten years, this growth simply must come back to realistic levels - less than r - over a reasonable period of time. To calculate the value of these shares, it is necessary to estimate the length of time that significant growth will continue before settling down to sustainable levels. Example ABC s earnings are currently $100 per share with a 20% payout ratio. It is anticipated that ABC will grow at 20% per year for the next three years and then continue to grow at 12% well into the future. If your expected rate of return for ABC is 25%, what is the value of one share of ABC? First calculate the cash flows: Therefore: Year 0 1 2 3 4 Earnings - $120.00 $144.00 $172.80 $193.536 Dividends - $24.00 $28.80 $34.56 $38.707 24. 00 28. 80 34. 56 P 0 = + + + ( 125. ) ( 125. ) ( 125. ) 38. 707 1 (. 25. 12) ( 125. ) = 19. 2 + 18. 432 + 17. 695 + [ 297. 746 / ( 125. ) ] = 1 2 3 3 $207. 77 per share where the far right hand term of the above equation is the present value of a growing perpetuity which begins in the fourth year. 3 The important principle which must be remembered is that the value of any share is exactly equal to the present value of the expected stream of future cash flows. If
300 Financial Management and Decision Making this stream of cash flows is expected to vary, the computations required may become more complex, but the principle remains unchanged. P/E Ratios The P/E ratio, or the ratio of price to earnings, is a measure of how many times current earnings the shareholders are willing to pay to buy one share of the company. It is possible to compare P/E ratios for different companies. Average P/E ratios have varied from a low of around 6 to a high of around 20. If average P/E ratios in the market are around 15, a share with a P/E ratio of 5 is relatively inexpensive while one with a P/E of 70 is relatively expensive. However, P/E ratios should not be used as a guide to a correct price, rather they can give clues as to relative values of firms in the same industry. The riskiness of the firm cannot be divorced from the company s share price - try though we may. High P/E shares are perceived by shareholders to be less risky and(or) have greater future potential than low P/E shares since shareholders are willing to pay more for the expected future cash flows, thus implying confidence in the underlying strength of the company and in those future cash flows occurring. As the shareholders feel less sure of future cash flows, they are willing to pay less, thus lowering the P/E. Example You are considering selling your holding in a privately held financial services company. The problem is that your partners do not know how to put a fair value on the shares in the company. It is known that current earnings per share are $10,000 per year. From the share market it is observed that people who are buying and selling equity in companies in the same business have P/E ratios ranging from 12 to 16. What could be considered a fair range for the value of a share? If the P/E is 12, the price per share would be: 12 x $10,000, or $120,000 If the P/E is 16, the price would be $160,000. Therefore, a starting point for discussion between the partners would be a price per share of $120,000 to $160,000. P/E ratios cannot provide concrete values of companies, but they can act as guides to relative values when comparing prices of similar shares. Issuers of Debt or Equity An underlying principle followed by financial managers when financing the assets of their firms is one of financial matching. This principle holds that the money raised for assets should match in length of time the purpose for which it will be used. For example, a piece of equipment expected to last for ten years could be financed with a ten year bond. An annual need for two month money could be financed with a short term loan from the bank. A permanent investment in fixed assets or working capital would be best financed by equity capital.
Chapter 15: Valuation of Debt and Equity 301 When issuing debt or equity financing, the financial market will not pay more for the shares or bonds than they feel they are worth. If comparable financial instruments are available, then these will act as a guideline for valuing new issues. It is not possible to expect more in present value terms for the new issues than the present value of the future cash flows. Since the net present value to the purchaser will always be zero, the issuer cannot expect to increase shareholders wealth by issuing debt or equity financing instruments. If the NPV of raising funds were positive for the issuer, it means that it is negative for the provider of the funds. But since there is so much competition for raising funds, the providers of funds will not permit themselves to be in a negative NPV arrangement. Therefore, a zero NPV for the purchaser implies that any financial issue is a zero NPV transaction for the issuer. This implies that the form of financing is more an exercise in marketing and matching, than one of generating profits, since generating profits through financing issues is impossible. People as Gamblers People who invest in debt and equity do so with their own personally held views firmly in mind. Debt investors, for example, may be content to accept the market set rate of return until the date of maturity. However, it is more likely that the debt investor is taking a financial gamble on the impending changes in interest rates. If the gamble is that interest rates are bound to go down, then the investor would go long (i.e. increase their duration, or time to maturity) and/or reduce their coupon stream. Equity investors also invest with a speculative view of the future. It is a rare investor indeed who decides on the total potential cash flow stream -including the final liquidation dividend - of any company. More likely, the investor cares little about the dividend flow, and cares most about the amount that the share can be resold for to another investor. Nevertheless, without potential cash flow from the company to the investor, the share has no value. Since the market place is full of investors who are gambling on the future direction of their investments, it is often the case that group psychology has an effect on the value of debt and equity. The efficient market hypothesis, discussed in more detail in the chapter on risk and return, would describe these people as noise traders. While it is true that noise traders can influence prices, it can be shown that the influence of the gambler - i.e. noise trader - is always overcome by the influence of the investor who bases their investment decisions on firm fundamental analysis of their investment. The dilemma is this: if the market is efficient and reflects the fair value of the investment correctly, then why would anyone trade in the market? The answer is that often the market is provided with new information which alters the correct value of the asset and the market is also influenced by the gamblers. Thus, the challenge facing the investor is to sort out the noise and fundamentals so that safe investments can be made.
302 Financial Management and Decision Making Summary Ignoring risk for the time being, placing a value on shares and bonds is derived from NPV calculations. The bond valuation process is one of bringing into the present, the value of the future cash flows using the prevailing interest rates as the discount factor. This form of corporate indebtedness for financing operations has several aspects including the length of maturity, coupon amount, and face value amount. Nevertheless, knowing prevailing interest rates, it is a straightforward matter of converting the future cash flows into present value terms to arrive at a market price for the bond. Equity valuation can also be thought of as converting future cash flows into present value terms. It is more difficult to anticipate future cash flows of equity since there is no contractual agreement for those future flows. Anticipated dividend payouts combined with projected growth rates determine the value of the share for a given required rate of return. Growth companies are more volatile in price due to their high sensitivity to required rates of return. Privately held companies - those not traded on a share market - can be valued by considering P/E ratios of comparable shares. Knowing what a fair price is for a bond or a share can thus be reduced to a discussion of the appropriate required rate of return. Guidelines for this rate of return can be arrived at by looking at comparable issues in the market place and using their prevailing rates. This problem of an appropriate rate of return has been simplified by avoiding risk, which will be discussed in the next chapter. While this chapter discusses proper approaches to valuation, people often place their subjective judgements on their view of value. Glossary of Key Terms Face Value The amount a bond pays at maturity. Coupon Rate The percentage of face value paid to the holder of a bond. Yield to Maturity The internal rate of return for a bond. Par Value Also called face value, the amount a bond pays at maturity. Selected Readings Brealey, R. & Myers, S., Principles of Corporate Finance, Fourth Edition, McGraw-Hill, New York, 1991. Brigham, E.F., Financial Management Theory and Practice, Third Edition, The Dryden Press, 1982.
Chapter 15: Valuation of Debt and Equity 303 Brigham, E.F. and Gardenski, L.C., Financial Management Theory and Practice, Fifth Edition, The Dryden Press, 1988. Francis, J.C., Investments: Analysis and Management, Fifth Edition, McGraw-Hill, New York, 1991. Keown, A.J., Scott, D.F., Martin, J.D., and Petty, J.W., Basic Financial Management, Third Edition, Prentice-Hall, 1985. Peirson, G., and Bird, R., Business Finance, Third Edition, McGraw Hill, Sydney, 1983. Pringle, J.J. and Harris, R.S., Essentials of Managerial Finance, Scott Foresman & Co, Glenview, Illinois, 1984.
304 Financial Management and Decision Making Questions 15.1 The value of an asset depends on several factors, what are these? 15.2 Explain the relationship between the value of an asset and the investor s required rate of return. 15.3 Explain the difference between a bond s face value and its market value. 15.4 What would you expect the value of an ordinary share to be in a company that pays no dividends? 15.5 Will the market price of a ten year government bond be more or less variable than that of a five year government bond? Explain the reasoning behind your answer. 15.6 What is the main reason why knowledge of bond and share valuation is important to managerial decision makers? 15.7 Investors buy ordinary shares in expectation of future dividends and capital gains. Is the distribution between dividends and capital gains affected by a firm s decision to pay out a higher proportion of its earnings as dividends? 15.8 Do you believe that a firm operating and owned in New Zealand could grow at an annual rate of 30% indefinitely? Explain your answer. 15.9 Two investors are considering buying shares in Robert Jones Investments. Both agree on the expected value of the upcoming dividend and also on the expected dividend growth rate. One investor intends holding the shares for one year while the other investor intends holding them for eight years. Will both investors be willing to pay the same price for the shares? Explain your answer.
Chapter 15: Valuation of Debt and Equity 305 15.10 If all other factors are held constant, what would be the effect on the market value of a firm s ordinary shares if investors lowered their assessment of the firm s risk? 15.11 ABC Company bonds have a coupon rate of 10%, a face value of $10,000 and mature in 15 years time. If investors require a return of 8%, what will be the market price of the bonds? 15.12 Percy s Plastic Products has issued $1,000 bonds with a coupon rate of 15% (paid semi-annually). If the bonds mature in two years time and your required return is 10%, what price would you be willing to pay for the bonds? Assume the semiannual return compounds to 10% annually. 15.13 Elfton Company bonds are currently priced at $9,528, have a face value of $20,000 and mature in ten years time. If the market rate of return is 20%, what is the annual coupon rate? (Assume payments are made annually.) 15.14 Smart Corp bonds, maturing in two years, are selling for $1,248.52. If the coupon rate is 24% paid annually and the face value is $1,000, what is the required rate of return? 15.15 Preference shares in Ali s Aluminium Yacht Company are currently selling for $3.56. If the annual dividend on the shares is $0.72 and is expected to be paid forever, what is the required rate of return? 15.16 An investor is willing to pay $981.41 for a one year bond (face value $1,000) with a coupon rate of 10% paid quarterly. What is her expected annual rate of return? 15.17 Ordinary shares in Heady Heights Health Centre have a current market value of $3.20. The dividend expected this year (in 364 days) is $0.08 per share. You intend to purchase a share today and sell it in one year s time. By how much will the share price have to appreciate if your required rate of return is 12%? 15.18 Percy s Plastic Products Company last year (yesterday) paid a dividend of $0.09 per share. Dividends are expected to grow at the past rate of 10% per annum. If investors require a return of 15% per annum, what is the current share price?
306 Financial Management and Decision Making 15.19 The ordinary shares of a company are currently trading at $10.52. A growth rate of 10% per annum is expected and the dividend for the upcoming year (364 days hence) has been set at $0.12. What is the expected rate of return? 15.20 Preference shares in Anderson Company are selling for $10.50 and pay an annual dividend of $0.95 which is expected to be paid forever. Required: a. What is the expected return on the shares? b. If an investor has a required rate of return of 12% should he acquire preference shares in the company? c. At what price would the investor in (b) consider purchasing the shares? 15.21 Shares in Company A traded today at $12.60. Yesterday the company paid a dividend of $0.96. The required rate of return for a company with a risk profile such as Company A is 13%. If dividends are expected to grow at a constant rate in the future, and if the required rate of return remains at 13%, what is Company A s expected share price in six years time? 15.22 Martin s Magnificent Mushroom Company is currently experiencing a period of rapid growth. A growth rate of 20% in earnings and dividends is expected for the next three years, 18% in the fourth and fifth years, and a constant rate of 5% thereafter. Last year (yesterday) the company made a dividend payout of $0.82 and the required rate of return is 15%. Required: a. What is today s share price? b. What will the share price be in one year s time? c. Calculate the dividend yield and the capital gains yield for each of years 1, 2 and 3. 15.23 The required rate of return on shares in Company Y is 15%. What is the share price if last year s (yesterday) dividend was $0.50 and investors expect dividends to grow at a constant annual rate of: a. -7% b. 0% c. 7% d. 14%
Chapter 15: Valuation of Debt and Equity 307 15.24 Mine Corp s dividend last year (yesterday) was $1.50. For the next three years earnings and dividends are expected to grow at a rate of 15% per annum. After that the dividend growth rate is expected to slow and remain at a constant rate per annum indefinitely. If the required rate of return is 12% per annum and the current share price is $22.17, what is the expected annual growth rate after three years? 15.25 You buy shares in a company at $3.50 each. Expected dividends for the next three years are: $0.60, $0.63, $0.66. At the end of the three years you expect to sell the shares at $4.70. Required: a. Calculate the dividend growth rate (not a constant). b. Calculate the current dividend yield. c. Assuming that the growth rate is expected to continue, what is the expected total rate of return? 15.26 A sharebroker offers you shares in a company that paid a $0.87 dividend last year (yesterday). The expected growth rate in dividends is 15% per annum for the next three years and 6% thereafter. If you buy the shares you intend to hold them for three years and then sell them. Required: a. If the required rate of return is 10%, what is the present value of the dividend stream over the first three years? b. You expect the share price to be $35.00 in three years time. What is the present value of the expected share price? c. If you plan to hold the shares for three years, what is the maximum price you should pay? d. What is the present value of the shares? e. What is the present value of the shares if you decide to hold them for seven years? 15.27 A company has recently made an issue of $1,000 zero coupon bonds which are to be repaid in ten years time. If market interest rates are now 18%, what is the market value of the bonds? 15.28 A company has issued bonds that are not repayable but bear a 12% coupon rate and have a face value of $2,000. The market rate of return is 10%. Required: a. What is the current market price of the bonds? b. What would the market price be if the market return fell to 8%? c. How would the answers to (a) and (b) be different if the bonds were to be repaid in ten years time?
308 Financial Management and Decision Making 15.29 You wish to have $60,000 in eight years time in order to purchase a new car. Upon inquiring at the local sharebroker you discover that a company has recently issued a series of zero coupon bonds that are repayable in eight years time. If market interest rates are currently 15%, how much must you invest in the bonds today?