Chapter 4 Valuation of Securities

SECTION A MULTIPLE CHOICE QUESTIONS Which types of assets are usually easiest to value?(a) Real assets(b) Financial assets(c) Tangible assets(d) Intangible assetsWhich of the following features of a Treasury bond never changes over the life of the bond?(a) Coupon rate(b) Term to maturity(c) Yield(d) Both (a) and (b)Which of the following is a longterm debt security?(a) Promissory note(b) Commercial paper(c) Treasury note(d) DebentureFor which of the following securities is repayment guaranteed by a third party?(a) Debenture(b) Bank bill(c) Commercial paper(d) Treasury bondWhich of the following is true if a coupon bond is trading at a discount?(a) The price is less than the yield.(b) The yield is greater than the coupon rate.(c) The price is less than the coupon rate.(d) The coupon rate is greater than the yield.Which of the following investors normally have the right to vote at a companys AGM?(a) Ordinary shareholders(b) Preference shareholders(c) Debtholders(d) Both (a) and (b)Which of the following groups of investors have a contractual claim to receive a return on their investment?(a) Ordinary shareholders(b) Preference shareholders(c) Debtholders(d) All of the aboveLa Trobe University 4SECTION B SHORT ANSWER QUESTIONSWhat does the term opportunity cost mean in finance? How is the opportunity cost used?What is the easiest approach to valuating a firm? Why is this easier than the alternative?What are the fundamental differences between debt and equity?What is meant by the term discount security? List three different shortterm discount securities, indicatingthe likely issuer of each.La Trobe University 5Rank the three discount securities from Question 11 from most credit risk to least credit risk, and explain whyyou have ranked them in this way.Distinguish between the terms bond, note, debenture and consol.Describe the relationship between the price, face value, coupon rate and yield of a bond.What must be true for bond to trade at a premium, at a discount or at par?La Trobe University 6Company ABC has ordinary shares and cumulative preference shares outstanding. The dividend payable topreference shareholders is $2 per share. The only dividends paid in 2013 were preference dividends of $1 pershare. The companys fortunes improved in 2014, and they declared a $2 per share dividend to preferenceshareholders and a $1 per share dividend to ordinary shareholders. Is the company permitted to do this?Why/why not?Why are preference shares described as hybrid securities?La Trobe University 7SECTION C ESSAY QUESTIONSExplain the differences between debt, preference shares and ordinary shares.La Trobe University 8SECTION D CALCULATION QUESTIONSWhat is the price of a promissory note with 90 days to maturity, a face value of $750 and a yield of 11% p.a.?What is the value of a 180 day $1000 bank bill that was issued 30 days ago and that is trading at a yield of 8.8%p.a.?*What is the yield of a 270 day $2000 Treasury note and which is trading at a price of $1939.04?*What is the price of a zerocoupon bond with a face value of $1000 and 3 years to maturity, if it is priced toyield 6% p.a.?*What is the value of a zerocoupon bond with a face value of $500 and 5 years to maturity, if other bonds witha similar risk are trading at a yield of 7% p.a.?*La Trobe University 9What is the yield of a zerocoupon bond with a face value of $2500, 4 years to maturity and a current price of$1858.13?*What is the value of a $1000 bond that pays an 8% annual coupon and has 9 years to maturity, if the debt costof capital is 6.5%?What is the price of a $1000 Treasury bond that pays a 5.5% coupon and has 6 years to maturity, if it is pricedto yield 6.5%?You bought a Woolworths share on 1 January 2013 for $44.50 and sold it one year later for $48.50. Duringthe year, Woolworths paid a dividend of $2.50 per share. What is the dividend yield, the capital gain yield andthe total yield?La Trobe University 10You bought a CBA share on 1 January 2013 for $67.25 and sold it one year later for $64.75. CBA paid dividendsof $1.75 per share on 1 March 2013 and $2.00 per share on September 2013. What is the dividend yield, thecapital gain yield and the total yield?A preference share pays a fixed dividend of $1.25 per share. The equity cost of capital is 11% p.a. What is thevalue of the share?An ordinary share is expected to pay dividend of $1.25 per share next year, after which it is expected to growat a constant rate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share?An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a constantrate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share?*La Trobe University 11An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a rate of5% p.a. for the next three years, after which it is expected to grow at a constant rate of 2% p.a. in perpetuity.The equity cost of capital is 11% p.a. What is the value of the share?*An ordinary share is expected to pay a dividend of $3 per share for the next 10 years. After 10 years thedividend is expected to grow at a constant rate of 3.5% p.a. in perpetuity. The required rate of return is 14%p.a. What is the value of the share?*La Trobe University 12Hint, tips, advice and guidanceSECTION D CALCULATION QUESTIONSWhat is the value of a 180 day $1000 bank bill that was issued 30 days ago and that is trading at a yield of 8.8%p.a.?Note that the value of any security is always based on the time remaining until maturity.What is the yield of a 270 day $2000 Treasury note and which is trading at a price of $1939.04?This is based on the formula for the price of a discount security, but we know the price. You need to rearrangethe formula to solve for the yield.What is the price of a zerocoupon bond with a face value of $1000 and 3 years to maturity, if it is priced toyield 6% p.a.?The yield is the return you will get, based on the known future cash flows, if you pay the current price, so pricedto yield is just a way of telling you what the yield is.What is the value of a zerocoupon bond with a face value of $500 and 5 years to maturity, if other bonds witha similar risk are trading at a yield of 7% p.a.?Securities with the same risk should be trading at the same yield, so this is a way of telling you what the yieldwill be on this bond.What is the yield of a zerocoupon bond with a face value of $2500, 4 years to maturity and a current price of$1858.13?This is based on the formula for the price of a zerocoupon bond, but we know the price. You need to rearrangethe formula to solve for the yield.25.26.27.28.29.30.An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a constantrate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share?This similar to the previous question, except that the formula for the price of a share (based on the formula forthe present value of a growing perpetuity) requires the first dividend in the numerator, and we are not giventhe first dividend. We are given dividend that has just been paid (which is not a future cash flow and is not partof the value of the share). You need to calculate the first dividend based on the most recent dividend and thegrowth rate, before you can use the formula.La Trobe University 13An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a rate of5% p.a. for the next three years, after which it is expected to grow at a constant rate of 2% p.a. in perpetuity.The equity cost of capital is 11% p.a. What is the value of the share?You need to calculate the next three dividends, using the information provided, and then separately discounteach of them to a present value. They need to be added together and form part of the price of the share. Thenyou need to calculate the fourth dividend (note that this based on one growth rate for three years and then adifferent growth rate in the fourth year). This is the first dividend in the growing perpetuity that begins withDividend 4, so you use it in the numerator of the formula for the present value of a growing perpetuity. Theanswer you get from that formula applies one period before the first payment i.e. it applies to year 3, so itneeds to be discounted by three years and then added to the present value of the first three dividends.An ordinary share is expected to pay a dividend of $3 per share for the next 10 years. After 10 years thedividend is expected to grow at a constant rate of 3.5% p.a. in perpetuity. The required rate of return is 14%p.a. What is the value of the share?This is similar in principle to the previous question, but the easiest way to calculate it is to treat the first 10dividends as an annuity. Then treat the dividend in year 11 which you will need to calculate as the firstdividend of a growing perpetuity, the value of which must be discounted by the appropriate number of yearsto a present value.La Trobe University 14SolutionsSECTION A MULTIPLE CHOICE QUESTIONSWhich types of assets are usually easiest to value?(a) Real assets(b) Financial assets(c) Tangible assets(d) Intangible assetsWhich of the following features of a Treasury bond never changes over the life of the bond?(a) Coupon rate(b) Term to maturity(c) Yield(d) Both (a) and (b)Which of the following is a longterm debt security?(a) Promissory note(b) Commercial paper(c) Treasury note(d) DebentureFor which of the following securities is repayment guaranteed by a third party?(a) Debenture(b) Bank bill(c) Commercial paper(d) Treasury bondWhich of the following is true if a coupon bond is trading at a discount?(a) The price is less than the yield.(b) The yield is greater than the coupon rate.(c) The price is less than the coupon rate.(d) The coupon rate is greater than the yield.Which of the following investors normally have the right to vote at a companys AGM?(a) Ordinary shareholders(b) Preference shareholders(c) Debtholders(d) Both (a) and (b)Which of the following groups of investors have a contractual claim to receive a return on their investment?(a) Ordinary shareholders(b) Preference shareholders(c) Debtholders(d) All of the aboveLa Trobe University 15SECTION B SHORT ANSWER QUESTIONSWhat does the term opportunity cost mean in finance? How is the opportunity cost used? The benefit forgone by not taking up the next best alternative investment. Any investment must earn at least the opportunity cost in order to be a worthwhile investment.What is the easiest approach to valuating a firm? Why is this easier than the alternative?It is easier to value financial securities (the righthand side of the balance sheet) because: Much of the time (in the case of publicly listed companies) these securities are frequently traded inliquid markets and their market value can be determined. Real assets are rarely traded and difficult to value. Sometimes real assets are built for a particular purpose and cannot be sold for their true value.What are the fundamental differences between debt and equity?Debt EquityUsually has a limited life Valued on the assumption they will last forever(Exception: Consols) (Exceptions: Redeemable preference shares)Usually pay a fixed return Return can be variable, and sometimes negative(Exception: Floating rate notes) (Exception: Preference shares)Contractual claim Residual claimLess risky for the investor More risky for the investorWhat is meant by the term discount security? List three different shortterm discount securities, indicatingthe likely issuer of each. A security with only one cash flow (the face value repayable on maturity). As a result, it will always be sold at a discount to its face value, because of the time value of money. Examples:o Promissory notes (commercial paper) issued by businesseso Bank bills issued by businesses, with the assistance of a bank which guarantees payment ofthe face value to the holdero Treasury notes issued by the Federal governmentRank the three discount securities from Question 11 from most credit risk to least credit risk, and explain whyyou have ranked them in this way. Promissory notes (commercial paper) there is no collateral and no guarantee of repayment.Businesses can be risky investments. Bank bills although issued by businesses, repayment is guaranteed by a bank, which is less risky thana business. Treasury notes issued by the Federal government, which is considered to be free of credit risk.La Trobe University 16Distinguish between the terms bond, note, debenture and consol.Bond strictly speaking, any debt security, but in common practice, refers to a longterm debt security.Note strictly speaking, any debt security, but in common practice (used on its own) refers to a mediumtermsecurity. Also, in combination with other words, can be used for shortterm debt securities (e.g. promissorynote, Treasury note).Debenture unsecured bonds.Consol a debt security that does not mature.Describe the relationship between the price, face value, coupon rate and yield of a bond. Price is the current value of the bond. It is a function of the yield, as described below. Face Value isthe amount that will be repaid on maturity. Coupon Rate determines the amount of interest paid via coupon payments. Yield is the rate of returnimplied by the bonds current price. It is the return the investor will get if he or she pays the currentprice and holds the bond until maturity. It represents the investors opportunity cost or required rateof return. If the yield exceeds the coupon rate, the return, as a percentage of the face, is insufficientto meet the investors required rate of return and investors wont pay the face value. The price willfall until the rate of return, as percentage of the price paid, is equal to the required rate of return.What must be true for bond to trade at a premium, at a discount or at par?Premium Price > Face value, Yield < Coupon Rate. Discount Price < Face value, Yield > Coupon Rate.Par Price = Face value, Yield = Coupon Rate.Company ABC has ordinary shares and cumulative preference shares outstanding. The dividend payable topreference shareholders is $2 per share. The only dividends paid in 2013 were preference dividends of $1 pershare. The companys fortunes improved in 2014, and they declared a $2 per share dividend to preferenceshareholders and a $1 per share dividend to ordinary shareholders. Is the company permitted to do this?Why/why not?No, this in not permissible. Because the preference shares are cumulative, the $1 per share that was missedin 2013 accumulate and must be repaid, along with all future dividends, before ordinary shareholders canreceive a dividend. If there is $3 available for dividends in 2014, it must all be paid as preference dividends.Why are preference shares described as hybrid securities?Equity securities with some of the features of debt securities usually fixed dividend and rank ahead ofordinary shareholders in payment of dividends and distribution of the firms assets if the company is woundup.La Trobe University 17SECTION D CALCULATION QUESTIONSWhat is the price of a promissory note with 90 days to maturity, a face value of $750 and a yield of 11% p.a.?750 $730.191 1 0.11 90365 365P FVy d What is the value of a 180 day $1000 bank bill that was issued 30 days ago and that is trading at a yield of 8.8%p.a.? 1000 $965.101 1 0.088 150365 365P FVy dWhat is the yield of a 270 day $2000 Treasury note and which is trading at a price of $1939.04?1 365 2000 1 365 4.25%1939.04 270y FVP d What is the price of a zerocoupon bond with a face value of $1000 and 3 years to maturity, if it is priced toyield 6% p.a.? 31000 $839.621 1.06 nP FVy What is the value of a zerocoupon bond with a face value of $500 and 5 years to maturity, if other bonds witha similar risk are trading at a yield of 7% p.a.? 5500 $356.491 1.07 nP FVy What is the yield of a zerocoupon bond with a face value of $2500, 4 years to maturity and a current price of$1858.13?1/ 1/4 1 2500 1 7.7%1858.13n YTM FVP What is the value of a $1000 bond that pays an 8% annual coupon and has 9 years to maturity, if the debt costof capital is 6.5%? 9 91 1 1 80 1 1 1 1000 $1099.841 1 0.065 1.065 1.065 n nP CPN FVy y y La Trobe University 18What is the price of a $1000 Treasury bond that pays a 5.5% coupon and has 6 years to maturity, if it is pricedto yield 6.5%? 12 121 1 11 127.50 1 1 1 1000 $950.960.0325 1.0325 1.0325n nP CPN FVy y y You bought a Woolworths share on 1 January 2013 for $44.50 and sold it one year later for $48.50. During theyear, Woolworths paid a dividend of $2.50 per share. What is the dividend yield, the capital gain yield and thetotal yield?10Dividend yield 2.50 5.62%44.50DivP 1 00Capital gain yield 48.50 44.50 8.99%44.50P PP 1 1 00Total yield 2.50 48.50 44.50 14.61%44.50Dividend yield Capital gain yield 5.62% 8.99% 14.61%Div P PP You bought a CBA share on 1 January 2013 for $67.25 and sold it one year later for $64.75. CBA paid dividendsof $1.75 per share on 1 March 2013 and $2.00 per share on September 2013. What is the dividend yield, thecapital gain yield and the total yield?10Dividend yield 1.75 2.00 5.58%67.25DivP 1 00Capital gain yield 64.75 67.25 3.72%67.25P PP 1 1 00Total yield 1.75 2.00 64.75 67.25 1.86%67.25Dividend yield Capital gain yield 5.58% 3.72% 1.86%Div P PP A preference share pays a fixed dividend of $1.25 per share. The equity cost of capital is 11% p.a. What is thevalue of the share?01.25 $11.360.11 EP Divr An ordinary share is expected to pay dividend of $1.25 per share next year, after which it is expected to growat a constant rate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share?101.25 $20.830.11 0.05 EP Divr g La Trobe University 19An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a constantrate of 5% p.a. The equity cost of capital is 11% p.a. What is the value of the share? 001 1.25 1.05$21.880.11 0.05 EDiv gPr g An ordinary share has just paid a dividend of $1.25 per share. This dividend is expected to grow at a rate of5% p.a. for the next three years, after which it is expected to grow at a constant rate of 2% p.a. in perpetuity.The equity cost of capital is 11% p.a. What is the value of the share? 1 0 12 22 0 13 33 0 14 34 0 1 21 1.25 1.05 $1.31251 1.25 1.05 $1.37811 1.25 1.05 $1.44701 1 1.25 1.05 1.02 $1.4760Div Div gDiv Div gDiv Div gDiv Div g g 1 2 3 40 2 3 32 3 311 1 1 11.3125 1.3781 1.4470 1.4760 1 $15.351.11 1.11 1.11 0.11 0.02 1.11E E E E EP Div Div Div Divr r r r g r Note: When answering a question like this, you may find it necessary to write down and reenter the individualdividends. If so, it is recommended that these be recorded to 4 decimal places to minimise rounding errors.An ordinary share is expected to pay a dividend of $3 per share for the next 10 years. After 10 years thedividend is expected to grow at a constant rate of 3.5% p.a. in perpetuity. The required rate of return is 14%p.a. What is the value of the share? 10110 101101 to10 10 1010 101 11 1 1 1 11 11 1 3.00 1.035 1 3.00 1 $23.630.14 1.14 0.14 0.035 1.14ttt E EE E E EP Div Divr rDiv gDivr r r g r

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