THEORIES OF CHAPTER 21.Money marketFinancial Market include Money Market (short term) and Capital Market (long term)The money market = cash equivalent = cash for short: because it’s highly liquid, and relatively low – risk debt instrumentsThe money market is very short – term debt securities and highly marketable2.Treasury billsTreasury bill (T – bill) issued at a discount from face value and returning the face amount at maturityMaturities: 4, 13, 26, 52 weeks (1, 3, 6, 12 months)Characteristics:oCan purchase from Treasury or on the secondary marketoLow transaction costoLittle price riskoThe income earned on T – bills is taxable at the federal level, exempt (miễn) from all state and local taxesBid price: lower price, if you wanted to sell a bill to a dealer: giá bánAsked price: you have to pay to buy a bill: giá mua
THEORIES OF CHAPTER Money market - Financial Market include Money Market (short term) and Capital Market (long term) - The money market = cash equivalent = cash for short: because it’s highly liquid, and relatively low – risk debt instruments - The money market is very short – term debt securities and highly marketable Treasury bills - Treasury bill (T – bill) issued at a discount from face value and returning the face amount at maturity - Maturities: 4, 13, 26, 52 weeks (1, 3, 6, 12 months) - Characteristics: o Can purchase from Treasury or on the secondary market o Low transaction cost o Little price risk o The income earned on T – bills is taxable at the federal level, exempt (miễn) from all state and local taxes - Bid price: lower price, if you wanted to sell a bill to a dealer: giá bán - Asked price: you have to pay to buy a bill: giá mua Calculate: Bid price, Asked price, Yield to Maturity, the price yesterday by method: bank – discount 1: Calculate discount rate of bid price and asked price 𝑑𝑎𝑦𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒 = 𝑎𝑠𝑘 × 360 2: Calculate asked price and bid price (***Bid < Asked***) 𝐴𝑠𝑘𝑒𝑑 𝑝𝑟𝑖𝑐𝑒 = 𝐹 × (1 − 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒) 3: Calculate asked yield 𝐹 365 𝐴𝑠𝑘𝑒𝑑 𝑦𝑖𝑒𝑙𝑑 = > − 1? × 𝐴𝑠𝑘𝑒𝑑 𝑝𝑟𝑖𝑐𝑒 𝑑𝑎𝑦𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦 4: Calculate the price yesterday: 𝑃F − 𝑃G 𝐶𝐻𝐺% = × 100% 𝑃G Certificates of Deposit: higher interest saving, cannot withdrawal at any time Commercial paper: - Commercial paper is short – term unsecured debt issued by large corporation - CP is backed by a bank line of credit, which gives the borrower access to cash that can be used if needed to pay off the paper at maturity Bankers’ Acceptances: - Bankers’ Acceptances is an order to a bank by a customer to pay a sum of money at a future date - It is very safe (low risk) because the bank accept to pay it if the customer cannot Repos and reserves: Repos Reserves Short – term Short – term The dealer sell and buy back with a higher The dealer buy from the investor and resell price with a higher price LIBOR market: Premier short -term interest, reference rate for a wide range of transactions The bond market: Longer – term borrowing or debt instruments, fixed – income capital market These fomulas can result in fixed income (coupon rate) Treasury Notes and Bonds: - T – bills < year - T – notes from year to 10 years - T – bonds > 10 years 10 Federal Agency Debt: dự án quốc hội hỗ trợ vốn tư nhân không đủ 11 Municipal bonds: - Issued by state and local governments - It is exempt from federal income taxation Comparing bonds: 𝑟 × (1 − 𝑡) = 𝑟H r : taxable bonds rm: municipal bonds/ free – tax paid bonds t: tax rate Choose the higher to invest 12 Corporate bonds: - Long – term debt issued by private corporations paying semiannual coupons and returning the face value of the bond at maturity - Callable bond: công ty mua lại lúc với giá người phát hành ấn định - Convertible bonds: đối trái phiếu sang cổ phiếu với giá người phát hành ấn định 13 Common stock: - Represent owership shares in a corporation - Have voting rights and may receive dividends - characteristics of common stock: residual claim and limited liability o Residual claim: Khi phá sản công ty trả nợ theo thứ tự sau: Thuế Lương Nhà cung cấp Trái phiếu Chủ nợ Common stock o Limited liability: phá sản cổ đông phần vốn góp 14 Preferred Stock: - Fixed stream of income each year (dividend: preferred stock common stock) - Similar perpetuity: Trái phiếu không kỳ hạn - Not give the holder voting power EXERCISE What are the key differences between common stock, preferred stock, and corporate bonds? - Common stock: have voting rights and may receive dividends if the company make a profit When the company goes bankrupt, stockholder are the last in line of all those who have a claim on the assets and income of the corporation - Preferred stock: not give the holder voting power and receive a fixed stream of income each year - Corporate bond: not give the holder voting power and recerive semiannual coupon and the face value of the bond at maturity When the company goes bankrupt, corporate bond have a claim on the assets and income of the corporation among three of this Why most professionals consider the Wilshire 5000 a better index of the performance of the broad stock market than the Dow Jones Industrial Average? Because the Wilshire 5000 Index includes more than 5000 stocks, while the Dow Jones Industrial Average includes 30 large companies The Wilshire 5000 Index has more company than the Dow Jones, so the Wilshire 5000 Index can be shown a trend of the market exactly What features of money market securities distinguish them from other fixed – income securities? Money markets include short – term, highly liquid and relatively low – risk debt instruments The bond market is composed of long-term borrowing or debt Most of them promise a fixed stream of income that is determined by a specified formula What are the major components of the money market? The major components of the money market are Treasury bills, certificates of deposit, commercial paper, bankers' acceptances, Eurodollars, repos, reserves, federal funds, and brokers' calls Describe alternative ways that an investor may add positions in international equity to his or her portfolio American Depository Receipts, or ADRs, are certificates traded in U.S markets that represent ownership in shares of a foreign company Investors may also purchase shares of foreign companies on foreign exchanges Lastly, investors may use international mutual funds to own shares indirectly Why are high – tax – bracket investors more inclined to invest in municipal bonds than are low – bracket investors? Because municopal bonds except their interest income is exempt from federal income taxation What is meant by the LIBOR rate? The Federal funds rate? The LIBOR is the rate at which large banks in London are willing to lend money among themselves The Fed funds rate is the rate of interest on very short-term loans among financial institutions in the U.S How does a municipal revenue bond differ from a general obligation bond? Which would you expect to have a lower yield to maturity? General obligation bonds are backed by the “full faith and credit” of the issuer, while revenue bonds are issued to finance particular projects and are backed either by the revenues from that project or by the municipal agency operating the project Why are corporations more apt to hold preferred stock than are other potential investors? Preferred stocks may be moẻ apt for cổprations because of its tax treatment Because they are treated as dividends rather than interest on debt, they are not tax – deductible expenses for the firm They make desirable fixed – income investments for some corporations 10 What is meant by limited liability? Limited liability means that the most shareholders can lose in event of the failure of the corporation is their original investment 11 Which of the following correctly describes a repurchase agreement? a The sale of a security with a commitment to repurchase the same security at a specified future date and a designated price b The sale of a security with a commitment to repurchase the same security at a future date left unspecified, at a designated price c The purchase of a security with a commitment to purchase more of the same security at a specified future date 12 Why are money market securities sometimes referred to as “cash equivalent”? Money markets include short – term, highly liquid and relatively low – risk debt instruments 13 A municipal bond carries a coupon rate of 6¾% and is trading at par What would be the equivalent taxable yield of this bond to a taxpayer in a 35% tax bracket? 0% because municipal bond except their interest income is exempt from federal income taxation 14 Suppose that short – term municipal bonds currently offer yields of 4%, while comparable taxable bonds pay 5% Which gives you the higher after – tax yield if your tax bracket is: a b c d Zero 10% 20% 30% SOLVE ( ) 𝑟 − 𝑡 = 𝑟H ó 5% (1 – t) = 4% ó t = 20% 15 An investor is in a 30% combined federal plus state tax bracket If corporate bonds offer 9% yields, what must municipals offer for the investor to prefer them to corporate bonds? 𝑟 (1 − 𝑡) < 𝑟H ó 9% (1 – 30%) < rm ó rm > 6.3% So municipal bonds have the coupon rate more than 6.3% for the investor to prefer them to corporate bonds 16 Find the equivalent taxable yield of the municipal bond in Problem 14 for tax brackets of zero, 10%, 20% and 30% t = 0%: 𝑟 (1 − 𝑡) = 𝑟H ó 5% (1 – 0%) = rm ó rm = 5% t = 10%: 𝑟 (1 − 𝑡) = 𝑟H ó 5% (1 – 10%) = rm ó rm = 4.5% t = 20%: 𝑟 (1 − 𝑡) = 𝑟H ó 5% (1 – 20%) = rm ó rm = 4% t = 30%: 𝑟 (1 − 𝑡) = 𝑟H ó 5% (1 – 30%) = rm ó rm = 3.5% 17 Look at the Treasury bond maturing in November 2040 a How much would you have to pay to purchase one of these bonds? Asked price = 98.0000 x 1,000 = 980,000 b What is its coupon rate? 4.25% c What is the current yield (i.e, coupon income as a fraction of bond price) of the bond? 4.371% 18 Look at the listing for General Dynamics a What was the firm’s closing price yesterday? 75.60 J,LLL b How many shares could you buy for $5,000? = 66 MJ.OL c What would be your annual dividend income from those shares? The 1.88 value in DIV column means that the last quarterly dividend payment was $0.47 per share, which is consistent with annual dividend payments of $0.47 x = $1.88 ð 66 x $1.88 = $124.08 d What must be General Dynamics’ earnings per share? P P MJ.OL P/E = QPR EPS = P/Q = TL.UV = 6.92 19 Consider the three stocks in the following table Pt represents price at time t, and Qt represents shares outstanding at time t Stock C splits two – for – one in the last period a Calculate the rate of return on a price – weighted index of the three stocks for the first period (t = to t = 1) 95 + 45 + 110 − = 4.17% 90 + 50 + 100 b What must happen to the divisor for the price – weighted index in year 2? UJ[\J[TTL The index value before the stock plit was = 83.33 ] We must find a new divisor, d, that leaves the index unchanged after C splits and its price falls to $55 Therefore we solve for d in the following equation: 95 + 45 + 55 = 83.3 → 𝑑 = 2.34 𝑑 c Calculate the rate of return of the price – weighted index for the second period (t = to t = 2) 95 × 100 + 45 × 200 + 110 × 200 − = 0% 95 × 100 + 45 × 200 + 55 × 400 20 Using the data in the previous problem, calculate the first – period rates of return on the following indexes of the three stocks: a A market value – weighted index Price Share Price Share Inital Final Value Value A $90 100 $95 100 $9,000 $9,500 B $50 200 $45 200 $10,000 $9,000 C $100 200 $110 200 $20,000 $22,000 $39,000 $40,500 \L,JLL A market value weight index = 100 × ]U,LLL = 104 b An equally weighted index Price Share Price Share Return Return/inital value 5.56% -10% 10% A $90 100 $95 100 $500 B $50 200 $45 200 -$1,000 C $100 200 $110 200 $2,000 J.JO% aTL%[TL% A equally weighted index = 100 × = 185 ] 21 What problems would confront a mutual fund trying to create an index fund tied to an equally weighted index of a broad stock market? In an equally – weighted index (EWI) fund, each stock is given equal weight regardless of its matket capitalization So smaller cap stocks will have the same weight as larger cap stocks Contrast this with a market – weight index fund in which stocks are held in proportion to market weight - Sine more volatile small – cap stocks have the same weight as large – cap stocks, EWI tend to be more volatile than market – capitalization indices - Turnover rates tend to be higher than market – weight fund becasue as stocks that have positive returns will increase weight in the fund Stocks with negative returns will decrease weight in the fund Therefore an EWI fund must be rebalanced back to return to its original target weights Many of the transactions would be among the smaller, less – liquid stocks 22 What would happen to the divisor of the Dow Jones Industrial Average if FedEx, with a current price of around $95 per share, replaced AT&T (with a current value of about $31 per share)? The Dow Jones Industrial Average is calculated by adding the price of these 30 stocks and dividing the sum by 30 The price of AT&T is higher than the price of FedEx, so if the FedEX is replaced by AT&T, the divisor of DJ will increase because the divisor is weight sensitive and is consists of the sum of all the 30 stocks 23 A T – bill with face value $10,000 and 87 days to maturity is selling at a bank discount ask yield of 3.4% What is the price of the bill? What is its bond equivalent yield? bM Discount rateasked price = 3.4% x ]OL = 0.82% Asked price = 10,000 x (1 – 0.82%) = 9,918 TL,LLL ]OJ Equivalent yieldasked price = c U,UTb − 1d × bM = 3.48 24 Which security should sell at a greater price? a A 10 – year Treasury bond with a 9% coupon rate or a 10 – year T – bond with a 10% coupon 𝐶↑ 𝐹 𝑃 ↑= >1 − ?+ f (1 + 𝑟 ) (1 + 𝑟 )f 𝑟 So a 10 – year T – bond with a 10% coupon have payment higher than a 10 – year Treasury bond with a 9% coupon So a 10 – year T – bond with a 10% coupon sell at a greater price b A three – month expiration call option with an exercise price of $40 or a three -month call on the same stock with an exercise price of $35 Call option: The higher exercise price, the less cost of the contract So a three month call option with an exercise price of $35 sells at a greater price c A put option on a stock selling at $50 or a put option on another stock selling at $60 (All other relevant features of the stocks and options are assumed to be identical) Put option: The higher exercise price, the higher cost of the contract So a put option with an exercise price of $60 sells at a greater price 25 Look at the furtures listings for corn: a Suppose you can buy one contract for December 2011 delivery If the contract closes in December at a price of $6.43 per bushel, what will be your profit or loss? (Each contract calls for delivery of 5,000 bushels) The exercise price is $6.37, while the market price is $6.43 So the investor will make a profit = 5,000 x ($6.43 - $6.37) = $300 b How many December 2011 maturity contracts are outstanding? Open interest is the number of outstanding contracts: 487465 26 Look at the Apple options Suppose you buy an August expiration call option with exercise price $355 a If the stock price in August is $367, will you exercise your call? What are the profit and rate of return on your position? The profit = $367 - $355 = $12 but the cost paid is $13.7 so it is loss, so I won’t exercise my call and I lose the fee of this contract If the fee is higher than ($13.7 – $12 = $1.7) $1.7, I will exercise my call b What if you had bought the August call with exercise price $360? The profit = $367 - $360 = $7 but the cost paid is $11.15 so it is loss, so I won’t exercise my call and I lose the fee of this contract If the fee is higher than ($11.15 – $7 = $4.15) $4.15, I will exercise my call c What if you had bought an August put with exercise price $355? The loss = $367 - $355 = $12, the market price is $367 while the exercise price of put option $355 So I cancel this contract and pay a fee If the fee is higher than ($12 + $11.1 = $23.1) $23.1, I will exercise my put 27 What options position is associated with: a The right to buy an asset at a specified price? Call option b The right to sell an asset at a specified price? Put option c The obligation to buy an asset at a specified price? Long postition (lệnh mua) d The obligation to sell an asset at a specified price? Short position (lệnh bán) 28 Why call options with exercise prices higher than the price of the underlying stock sell for positive prices? Because the investor can make a profit from the difference between the stock price and the exercise price 29 Both a call and a put currently are traded on stock XYZ; both have strike prices of $50 and maturities of six months What will be the profit to an investor who buys the call for $4 in the following scenarios for stock prices in six months? (a) $40; (b) $45; (c) $50; (d) $55; (e) $60 What will be the profit in each scenario to an investor who buys the put for $6? Market Call option (Mua) Put option (Bán) price (cost = $4, exercise price = $50) (cost = $6 exercise price = $50) $40 Loss = fee = $4 Profit = ($50 - $40 - $6) = $4 $45 Loss = fee = $4 Exercise put option: ($50 - $45 - $6) = -1 loss = $1 Not exercise put option: loss = fee = $6 ð Exercise put option: loss = $1 $50 Loss = fee = $4 Loss = fee = $6 $55 Profit = ($55 - $50 - $4) = $1 Loss = fee = $6 $60 Profit = ($60 - $50 - $4) = $16 Loss = fee = $6 30 What would you expect to happen to the spread between yields on commercial paper and treasury bills if the economy were to enter a steep recession? The spread will widen because commercial paper is riskier, so the rate of return will increase Deterioration of the economy increases credit risk, that is, the likelihood of default Investors will demand a greater premium on debt securities subject to default risk 31 Examine the stocks listed in Figure 2.8 For how many of these stocks is the 52 – week high price at least 50% greater than the 52 – week low price? What you conclude about the volatility of prices on individual stocks? 32 Find the after – tax return to a corporation that buys a share of preferred stock at $40, sells it at year – end at $40, and receives a $4 year – end dividend The firm is in the 30% tax bracket The after – tax return = ($40 + $4 - $40) x 30% = $1.2 33 Explain the difference between a put option and a short position in a futures contract A put option gives the holder the right (but not the obligation) to sell the underlying asset at the exercise price A short position in a futures contract carries an obligation to sell the underlying asset at the futures price 34 Explain the difference between a call option and a long position in a futures contract A call option gives the holder the right (but not the obligation) to buy the underlying asset at the exercise price A long position in a futures contract carries an obligation to buy the underlying asset at the futures price Concept check 2.1: What were the bid price, asked price, and yield to maturity of the 3.5% Febuary 2018 Treasury bond? What was its asked price the previous day? Bid price = 107.2969 % x 1,000 = 1,073 Asked price = 107.3594 % x 1,000 = 1,073.6 Yield to maturity based on asked price = 2.294 P a P T,LM].O aPh CHG = g P h ó -0.547% = Po = 1,079.5 P h h Concept check 2.2: Suppose your tax bracket is 28% Would you prefer to earn a 6% taxable return or a 4% tax – free paid? What is the equivalent taxable yield of the 4% tax – free yield? r x (1 – t) = 6% x (1 – 28%) = 4.32% > 4% So I prefer to earn a 6% taxable 𝑟 × (1 − 𝑡) = 𝑟H ⟺ 𝑟 × (1 − 28%) = 4% r = 5.56% Concept check 2.3: a If you buy 100 shares of IBM common stock, to what are you entitled? Have voting rights and may receive dividends b What is the most money you can make over the next year? Your potential gain is unlimited because IBM’s dtock price has no upper bound c If you pay $95 per share, what is the most money you could lose over the year? If the company goes bankrupt, you will lose $95 per share Concept check 2.4: Suppose XYZ’s final price increases to $110, while ABC falls to $20 Find the percentage change in the price – weighter average of these two stocks Compare that to the percentage return of a portfolio that holds one share in each company Index: Inital index value = VJ [ TLL V = 62.5 Final value = Portfolio: VL[TTL V = 65 OJ.aOV.J Percentage change in index = OV.J = 4% Inital value = ($25 + $100) = $125 Final value = ($20 + $110) = $130 T]LaTVJ Percentage change in portfolio value = TVJ = 4% It is equal Concept check 2.5: Reconsider companies XYZ and ABC from Concept Check Question 2.4 Calculate the percentage change in the market value – weighted index Compare that to the rate of return of a portfolio that holds $500 of ABC stock for every $100 of XYZ (i.e., an index portfolio) OUL The percentage change in market value – weighted index = OLL = 115% Concept check 2.6: What would be the profit or loss per share of stock to an investor who bought the July 2011 expiration Apple call option with exercise price $355, if the stock price at the expiration of the option is $365? What about a purchaser of the put option with the same exercise price and expiration? Investor who bought call option: The profit = $365 - $355 - $5.6 = $4.4 per share The purchaser of the put option: they cancel the contract because the market price is higher than the exercise price so they make a loss equally a fee = $0.9 THEORIES OF CHAPTER 10 Bond characteristics: - Bond: a security that obligates the issuer to make specified payments to the holder over a period of time - Characteristics: Face value, coupon rate, duration (time to maturity) - Payment of the bond: principal (face value, par value), interest (coupon payment) Callable bond: - Bonds that may be repurchased by the issuer at a specified call price during the call period - When the market interest rate â the company will call the bond (khi lãi suất thị trường giảm giá trái phiếu tăng giá tăng = giá thu hồi ấn định trước thu hồi) - Tại lại vậy? TOL = 5.5% x 1000 × TbV = 48.35 Invoice price = P + Accrued inmterest = 1016.93 + 48.35 = $1,065.28 26 Now suppose the bond in the previous question is selling for 102 What is the bond’s yield to maturity? What would the yield to maturity be at a price of 102 if the bond paid its coupons only once per year? The YTM for semiannually: 𝑃= 𝐶 𝐹𝑉 5.5% × 100 100 >1 − ?+ >1 − ?+ ⟺ 102 = → 𝑟 = 5.31% (1 + 𝑟)F (1 + 𝑟)F (1 + 𝑟)16 (1 + 𝑟)16 𝑟 𝑟 The YTM for annually: 𝑃= 𝐶 𝐹𝑉 5.5% × × 100 100 >1 − ?+ >1 − ?+ ⟺ 102 = → 𝑟 = 10.62% F F (1 + 𝑟) (1 + 𝑟) (1 + 𝑟) (1 + 𝑟)8 𝑟 𝑟 27 A 10 – year bond of a firm in severe financial distress has a coupon rate of 14% and sells for $900 The firm is currently renegotiating the debt, and it appears that the lenders will allow the firm to reduce coupon payments on the bond to one – half the originally contracted amount The firm can handle these lower payments What are the stated and expected yields to maturity of the bonds? The bond makes its coupon payments annually Expected YTM Stated YTM Coupon payment $140 $140 Number of annually periods 10 10 Final payment $500 $1,000 Price $900 $900 YTM 13.16% 16.07% 28 A two-year bond with par value $1,000 making annual coupon payments of $100 is priced at $1,000 What is the yield to maturity of the bond? What will be the realized compound yield to maturity if the one-year interest rate next year turns out to be (a) 8%, (b) 10%, (c) 12%? The bond sell at the price = the par value YTM = the coupon rate = 10% Năm đem tái đầu tư với lãi suất 8% (a) 8%: Vo (1 + r)2 = V1 ó 1000 (1 + r)2 = 1000 + 100 + 100 + 8% x 100 r = 9.91% Tiền coupon năm (b) 10%: Vo (1 + r)2 = V1 ó 1000(1 + r)2 = 1000 + 100 + 100 + 10% x 100 r = 10% (c) 12%: Vo (1 + r)2 = V1 ó 1000(1 + r)2 = 1000 + 100 + 100 + 12% x 100 r = 10.09% 29 Suppose that today’s date is April 15 A bond with a 10% coupon paid semiannually every January 15 and July 15 is listed in The Wall Street Journal as selling at an ask price of 101:04 If you buy the bond from a dealer today, what price will you pay for it? Quoted price = 101 4/32 percent of par = 101.125 = $1,011.25 vwxy yzu{| }wyF {G~•Gu •wxH|uF Accrued interest = Semiannual coupon payment ì vwxy y|ã|wFzuã {G~ãGu ãwxH|uFy UT = 5% x 1000 ì TbV = $25 Invoice price = Quoted price + Accrued interest = 1,011.25 + 25 = $1,036.25 30 Assume that two firms issued bonds with the following characteristics Both bonds are issued at par Ignoring credit quality, identify four features of these issues that might account for the lower coupon on the ABC debt Explain Factors that might make the ABC debt more attractive to investors, therefore justifying a lower coupon rate and yield to maturity, are: - The ABC debt is a larger issue and therefore may sell with greater liquidity - An option to extend the term from 10 years to 20 years is favorable if interest rates ten years from now are lower than today’s interest rates In contrast, if interest rates increase, the investor can present the bond for payment and reinvest the money for a higher return - In the event of trouble, the ABC debt is a more senior claim It has more underlying security in the form of a first claim against real property - The call feature on the XYZ bonds makes the ABC bonds relatively more attractive since ABC bonds cannot be called from the investor - The XYZ bond has a sinking fund requiring XYZ to retire part of the issue each year Since most sinking funds give the firm the option to retire this amount at the lower of par or market value, the sinking fund can be detrimental for bondholders 31 A large corporation issued both fixed and floating – rate notes five years ago, with terms given in the following table: a Why is the price range greater for the 9% coupon bond than the floating-rate note? The floating rate note pays a coupon that adjusts to market levels Therefore, it will not experience dramatic price changes as market yields fluctuate The fixed rate note will therefore have a greater price range b What factors could explain why the floating-rate note is not always sold at par value? - The yield spread between one-year Treasury bills and other money market instruments of comparable maturity could be wider (or narrower) than when the bond was issued - The credit standing of the firm may have eroded (or improved) relative to Treasury securities, which have no credit risk Therefore, the 2% premium would become insufficient to sustain the issue at par - The coupon increases are implemented with a lag, i.e., once every year During a period of changing interest rates, even this brief lag will be reflected in the price of the security c Why is the call price for the floating-rate note not of great importance to investors? The risk of call is low Because the bond will almost surely not sell for much above par value (given its adjustable coupon rate), it is unlikely that the bond will ever be called d Is the probability of call for the fixed-rate note high or low? The fixed-rate note currently sells at only 88% of the call price, so that yield to maturity is greater than the coupon rate Call risk is currently low, since yields would need to fall substantially for the firm to use its option to call the bond e If the firm were to issue a fixed-rate note with a 15-year maturity, callable after five years at 106, what coupon rate would it need to offer to issue the bond at par value? The 9% coupon notes currently have a remaining maturity of fifteen years and sell at a yield to maturity of 9.9% This is the coupon rate that would be needed for a newlyissued fifteen-year maturity bond to sell at par f Why is an entry for yield to maturity for the floating-rate note not appropriate? Because the floating rate note pays a variable stream of interest payments to maturity, the effective maturity for comparative purposes with other debt securities is closer to the next coupon reset date than the final maturity date Therefore, yield-to-maturity is an indeterminable calculation for a floating rate note, with “yield-to-recoupon date” a more meaningful measure of return 32 A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in five years at a call price of $1,100 The bond currently sells at a yield to maturity of 7% (3.5% per half-year) a What is the yield to call? The present value of this bond: 𝑃= 𝐶 𝐹𝑉 4% × 1000 1000 >1 − ?+ = >1 − ?+ = 1,124.72 (1 + 𝑟)F (1 + 𝑟)F (1 + 3.5%)OL (1 + 3.5%)OL 𝑟 3.5% Yield to call: 𝑃= 𝐶 𝐶𝑎𝑙𝑙 𝑝𝑟𝑖𝑐𝑒 4% × 1000 1100 >1 − ?+ ⟺ 1,124.72 = >1 − ?+ (1 + 𝑟)F (1 + 𝑟)F (1 + 𝑟)TL (1 + 𝑟)TL 𝑟 𝑟 → 𝑟 = 3.37% b What is the yield to call if the call price is only $1,050? 𝑃= 𝐶 𝐶𝑎𝑙𝑙 𝑝𝑟𝑖𝑐𝑒 4% × 1000 1050 >1 − ?+ ⟺ 1,124.72 = >1 − ?+ F F TL (1 + 𝑟) (1 + 𝑟) (1 + 𝑟) (1 + 𝑟)TL 𝑟 𝑟 → 𝑟 = 2.98% c What is the yield to call if the call price is $1,100 but the bond can be called in two years instead of five years? 𝑃= 𝐶 𝐶𝑎𝑙𝑙 𝑝𝑟𝑖𝑐𝑒 4% × 1000 1100 >1 − ?+ ⟺ 1,124.72 = >1 − ?+ F F \ (1 + 𝑟) (1 + 𝑟) (1 + 𝑟) (1 + 𝑟)\ 𝑟 𝑟 → 𝑟 = 3.03% 33 A newly issued 20-year maturity, zero-coupon bond is issued with a yield to maturity of 8% and face value $1,000 Find the imputed interest income in the first, second, and last year of the bond’s life The price when it’s issued: 𝐹𝑉 1000 𝑃= = = 214.55 F (1 + 𝑟 ) (1 + 8%)VL The price in the first year: 𝐹𝑉 1000 = = 231.71 F (1 + 𝑟 ) (1 + 8%)TU Imputed interest income in the first year = 231.71 – 214.55 = 17.16 The price in the second year: 𝐹𝑉 1000 𝑃= = = 250.25 (1 + 𝑟)F (1 + 8%)Tb Imputed interest income in the second year = 250.25 – 231.71 =18.54 The price in the 19th year: 𝐹𝑉 1000 𝑃= = = 925.93 F (1 + 𝑟 ) (1 + 8%)T Imputed interest income in the last year = 1000 – 925.93 = 74.07 34 A newly issued 10-year maturity, 4% coupon bond making annual coupon payments is sold to the public at a price of $800 What will be an investor’s taxable income from the bond over the coming year? The bond will not be sold at the end of the year The bond is treated as an original-issue discount bond 𝑃= 𝐶 𝐹𝑉 4% × 1000 1000 >1 − ?+ ⟺ 800 = >1 − ?+ → 𝑟 = 6.82% (1 + 𝑟)F (1 + 𝑟)F (1 + 𝑟)TL (1 + 𝑟)TL 𝑟 𝑟 𝐶 𝐹𝑉 4% × 1000 1000 𝑃T = >1 − ?+ = >1 − ?+ = 814.86 (1 + 𝑟)F (1 + 𝑟)F (1 + 6.82%)U (1 + 6.82%)U 𝑟 6.82% 𝑃= taxable income = 4% x 1000 + (814.86 – 800) = $54.86 35 Masters Corp issues two bonds with 20-year maturities Both bonds are callable at $1,050 The first bond is issued at a deep discount with a coupon rate of 4% and a price of $580 to yield 8.4% The second bond is issued at par value with a coupon rate of 8.75% a What is the yield to maturity of the par bond? Why is it higher than the yield of the discount bond? The YTM of the par bond: YTM = coupon rate = 8.75% Because the coupon rate of the par bond is higher than the discount bond b If you expect rates to fall substantially in the next two years, which bond would you prefer to hold? The 4% bond offers a greater expected return c In what sense does the discount bond offer “implicit call protection”? Implicit call protection is offered in the sense that any likely fall in yields would not be nearly enough to make the firm consider calling the bond In this case, the call feature is almost irrelevant 36 Under the expectations hypothesis, if the yield curve is upward - sloping, the market must expect an increase in short - term interest rates True/ false/ uncertain? Why? True Becasue this analysis to infer the market’s expectation of future short – term rates 37 The yield curve is upward - sloping Can you conclude that investors expect short - term interest rates to rise? Why or why not? If the yield curve is upward sloping, you cannot conclude that investors expect short – term interest rates to rise because the rising slope could be due to either exepectations of future increases in rates or the demand of investors for a risk premium on long – term bonds In fact the yield curve can be upward sloping even in the absense of expectations of future increases in rates 38 Assume you have a one-year investment horizon and are trying to choose among three bonds All have the same degree of default risk and mature in 10 years The first is a zero-coupon bond that pays $1,000 at maturity The second has an 8% coupon rate and pays the $80 coupon once per year The third has a 10% coupon rate and pays the $100 coupon once per year a If all three bonds are now priced to yield 8% to maturity, what are their prices? The zero – coupon bond: 𝑃= 𝐹𝑉 1000 = = 463.19 (1 + 𝑟)F (1 + 8%)TL The 8% coupon rate: P = par value = 1000 The 10% coupon rate: 𝑃= 𝐶 𝐹𝑉 100 1000 >1 − ?+ = >1 − ?+ = 1134.2 (1 + 𝑟)F (1 + 𝑟)F 8% (1 + 8%)TL (1 + 8%)TL 𝑟 b If you expect their yields to maturity to be 8% at the beginning of next year, what will their prices be then? What is your rate of return on each bond during the one-year holding period? The zero – coupon bond in the next year: 𝑃= 𝐹𝑉 1000 = = 500.25 (1 + 𝑟)F (1 + 8%)U JLL.VJa\O].TU Rate of return = = 8% \O].TU The 8% coupon rate in the next year: P = par value = 1000 bL Rate of return = TLLL = 8% The 10% coupon rate in the next year: 𝑃= 𝐶 𝐹𝑉 100 1000 >1 − ?+ = >1 − ?+ = 1124.94 F F U (1 + 𝑟) (1 + 𝑟) (1 + 8%) (1 + 8%)U 𝑟 8% TLL[(TTV\.U\aTT]\.V) Rate of return = = 8% TT]\.V 39 Under the liquidity preference theory, if inflation is expected to be falling over the next few years, long-term interest rates will be higher than short-term rates True/ false/ uncertain? Why? 40 The current yield curve for default – free zero – coupon bonds is as follows: a What are the implied one-year forward rates? (1 + 𝑦u )u = (1 + 𝑦uaT )uaT × (1 + 𝑓) Maturity YTM Forward rate 10% 11% 12.01% 12% 14.03% b Assume that the pure expectations hypothesis of the term structure is correct If market expectations are accurate, what will the pure yield curve (that is, the yields to maturity on one- and two-year zero-coupon bonds) be next year? Maturity Expected future Price YTM 1000 12.01% = 892.78 + 12.01% 1000 = 782.93 (1 + 12.01%) × (1 + 14.03%) 13.02% c If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a three-year zero-coupon bond? (Hint: Compute the current and expected future prices.) Ignore taxes Maturity YTM Price bUV.Mb year: bTT.OV − = 10% 10% 11% 12% 909.09 811.62 711.78 MbV.U] year: MTT.Mb − = 10% 41 The yield to maturity on one-year zero-coupon bonds is 8% The yield to maturity on two-year zero-coupon bonds is 9% a What is the forward rate of interest for the second year? Total proceeds dollar invested years will be: = $1+ (1 + 9%)2= $1.1881 Total proceeds dollar invested year will be: = $1 x (1 + 8%) x (1 + f) = $1.2321 f = 10% b If you believe in the expectations hypothesis, what is your best guess as to the expected value of the short-term interest rate next year? 𝑃= 1000 = 909.09 + 10% c If you believe in the liquidity preference theory, is your best guess as to next year’s short-term interest rate higher or lower than in (b)? 42 The following table contains spot rates and forward rates for three years However, the labels got mixed up Can you identify which row of the interest rates represents spot rates and which one the forward rates? - Line 1: Spot rates - Line 2: Forward rates 43 Consider the following $1,000 par value zero-coupon bonds: According to the expectations hypothesis, what is the market’s expectation of the one-year interest rate three years from now? (1 + 𝑦u )u = (1 + 𝑦uaT )uaT × (1 + 𝑓) Maturity YTM Forward rate 5% 6% 7.01% 6.5% 7.51% 7% 8.51% 44 A newly issued bond pays its coupons once a year Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 8% a Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 7% by the end of the year The present value: 𝑃= 𝐶 𝐹𝑉 50 1000 >1 − ?+ = >1 − ?+ = 705.46 (1 + 𝑟)F (1 + 𝑟)F 8% (1 + 8%)VL (1 + 8%)VL 𝑟 The value after year 𝑃= 𝐶 𝐹𝑉 50 1000 >1 − ?+ = >1 − ?+ = 793.29 (1 + 𝑟)F (1 + 𝑟)F 7% (1 + 7%)TU (1 + 7%)TU 𝑟 → 𝐻𝑃𝑅 = 50 + (793.29 − 705.46) = 19.54% 705.46 b If you sell the bond after one year when its yield is 7%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to original-issue discount (OID) tax treatment Using OID tax rules so the constant yield method are obtained YTM = 8%: Po = 705.46 P1 = 711.89 Interest in year: = $50 + ($711.89 - $705.46) = $56.43 Tax on interest income = 40% x 56.43 = $22.57 Capital gain in first year = Actual price at 7% YTM – constant yield price = 793.29 – 711.89 = $81.40 Tax on capital gain = 30% x 81.40 = $24.42 Total taxes = 22.57 + 24.42 = $46.99 c What is the after-tax holding-period return on the bond? 𝐴𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝐻𝑃𝑅 = 50 + (793.29 − 705.46) − 46.99 = 12.88% 705.46 d Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 7% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3% interest rate The value after year 𝑃= 𝐶 𝐹𝑉 50 1000 >1 − ?+ = >1 − ?+ = 798.82 (1 + 𝑟)F (1 + 𝑟)F 7% (1 + 7%)Tb (1 + 7%)Tb 𝑟 The coupon can be reinvested for one year at a 3% interest rate: $50 x 3% = $1.5 Total income after year = Value after year + x coupon payment + reinvested = 798.82 + x 50 + 1.5 = 900.32 Realized compound yield before taxes: 900.32 = 705.46 × (1 + 𝑟)V r = 12.97% e Use the tax rates in part (b) to compute the after-tax two-year realized compound yield Remember to take account of OID tax rules Using OID tax rules so the constant yield method are obtained YTM = 8%: Coupon interest received in first year: $50.00 Less: tax on coupon interest 40%: – 20.00 Less: tax on imputed interest (0.40*$6.43): – 2.57 Net cash flow in first year: $27.43 The year-1 cash flow can be invested at an after-tax rate of: 3%x(1 - 40%) = 1.8% By year 2, this investment will grow to: $27.43 × (1+ 1.8%) = $27.92 In two years, sell the bond for: $798.82 Less: tax on imputed interest in second year: – 2.78 [0.40 × $6.95] Add: after-tax coupon interest received in year 2: + 30.00 [$50 × (1 – 0.40)] Less: Capital gains tax on – 23.99 (sales price – constant yield value): [0.30 × (798.82 – 718.84)] Add: CF from first year's coupon (reinvested): + 27.92 [from above] Total $829.97 THEORIES OF CHAPTER 13: EQUITY VALUATION Book value: The net worth of common equity according to a firm’s balance sheet (giá trị sổ sách lúc phát hành giá trị ghi vào sổ sách kế toán) (Giá trị giao dịch market value giá giao dịch) Limitations of Book Value: - Liquidation value: net amount that can be realized by selling the assets of a firm and paying off the debt - Replacement cost (chi phí bán tài sản cơng ty): cost to replace a firm’s assets Hw€Ž|F •w}~| - Tobin’s q = €|•}w{|H|uF {GyF Analyse a financial highlight: Số lượng CP lưu hành Giá trị vốn hoá thị trường = price per share x common shares outstanding (giá trị có phát hành cổ phiếu thị trường) 𝐸𝑃𝑆 = 𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 𝐶𝑜𝑚𝑚𝑜𝑛 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 Hầu tỷ lệ Microsoft nhỏ ngành CP định giá thấp Intrinsic value (giá trị thực/giá trị nội tại): - CAPM: Risk – return Tỷ suất sinh lời GTCG free – risk (T – bill) Risk 𝑘 = 𝑟 = 𝑟• + 𝛽[𝐸(𝑟H ) − 𝑟• ] Exected rate of return on the market portfolio Market risk premium (Lợi nhuận kỳ vọng cổ phiếu này) Required return: lợi nhuận yêu cầu: k, r Expected return: E(rm) - Tỷ suất sinh lời kỳ vọng: Dividend kỳ vọng Capital gain = P1 – Po 𝐸 (𝐷T ) + [𝐸(𝑃T ) − 𝑃G ] 𝑃G 𝐸 (𝐷T ) 𝐸 (𝑃T ) − 𝑃G = + 𝑃G 𝑃G 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐻𝑃𝑅 = 𝐸 (𝑟) = Expected dividend yield Expected rate of price appreciation ð If a stock is priced “correctly”, it will offer investors a “fair” return, that is, its expected return will equal its required return An underpriced stock will privide an expected return greater than the required return (nhà đầu tư nên đầu tư vào underpriced stock) - Intrinsic value: the present value / of a firms expected future net cash flows / discounted / by the required rate of return (Giá trị dòng tiền kỳ vọng tương lai chiết tỷ suất sinh lời yêu cầu) Không cố định (khác với Trái phiếu coupon payment cố định cịn cổ phiếu biến động) 𝐼𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐 𝑣𝑎𝑙𝑢𝑒 = 𝑉G = 𝐸 (𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 ) + 𝐸(𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒) 1+𝑘 K: market capitalization rate (trường hợp năm) o Nếu Vo > Po: cổ phiếu định giá thấp NĐT nên mua o Nếu Vo < Po: cổ phiếu định giá cao NĐT nên mua Dividend discount models: - năm: 𝐷T + 𝑃T 𝑉G = 1+𝑘 - năm: 𝐷T 𝐷V + 𝑃V 𝑉G = + + 𝑘 (1 + 𝑘 )V - H năm: 𝐷T 𝐷V 𝐷— + 𝑃— 𝑉G = + +⋯+ V (1 + 𝑘 )— + 𝑘 (1 + 𝑘 ) - Dividend discount models: a formila for the intrinsic value of a firm euqal to the present value of all expected future dividends (Giá trị nội = Tồn dịng tiền cổ tức kỳ vọng tương lai chiết khấu tại) 𝐷T 𝐷V 𝐷] 𝑉G = + + +⋯ + 𝑘 (1 + 𝑘 )V (1 + 𝑘 )] The Constant – Growth DDM: 𝐷T = 𝐷G (1 + 𝑔) 𝐷V = 𝐷G (1 + 𝑔)V 𝐷] = 𝐷G (1 + 𝑔)] 𝐷G (1 + 𝑔) 𝐷G (1 + 𝑔)V 𝐷G (1 + 𝑔)] 𝐷T 𝑉G = + + +⋯ = V ] (1 + 𝑘 ) (1 + 𝑘 ) 1+𝑘 𝑘−𝑔 The constant – growth rate DDM implies that a stock’s value will be greater: - The larger its expected dividend per share (D công ty làm dự án tốt V á) - The lower the market capitalization rate (K â rủi ro cổ phiếu giảm V á) - The higher the expected growth rate of dividends (g dividend lợi nhuận tạo nhiều V á) 𝐷T 𝑃G = 𝑘−𝑔 Nếu cổ tức tăng trường g P tăng theo tốc độ tăng trưởng g: 𝑃T = 𝑃G (1 + 𝑔) Vậy: 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐻𝑃𝑅 = 𝐸 (𝑟) = 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑 + 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛 𝐷T 𝑃T − 𝑃G 𝐷T = + = +𝑔 𝑃G 𝑃G 𝑃G Stock prices and Investment Opportunities: - Dividend payout ratio (tỷ lệ chia cổ tức): percentage of earnings paid out as dividends - Plowback ratio or earnings retention ratio (tỷ lệ lợi nhuận giữ lại): the prportion of the firm’s earnings that is reinvested in the business (and not paid out as dividends) Tỷ lệ chia cổ tức thấp Tỷ lệ chia cổ tức cao Giữ lại để đầu tư (do rate of return dự án cao) sau D cao Present value of growth opportunities (PVGO): Net present value of a firm’s future investments (giá trị đầu tư tương lai công ty) 𝑃𝑟𝑖𝑐𝑒 = 𝑁𝑜 − 𝑔𝑟𝑜𝑤𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 + 𝑃𝑉𝐺𝑂 𝐸T 𝑃G = + 𝑃𝑉𝐺𝑂 𝑘 E1: paid out earnings per share (khoản tiền công ty dự định chi trả) Tỷ lệ tăng trưởng g: 𝑟𝑒𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑟𝑒𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑡𝑜𝑡𝑎𝑙 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑔 = = × = 𝑏 × 𝑅𝑂𝐸 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑇𝑜𝑡𝑎𝑙 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 Plowback ratio EXERCISE In what circumstances is it most important to use multistage dividend discount models rather than constant-growth models? It is most important to use multi-stage dividend discount models when valuing companies with temporarily high growth rates These companies tend to be companies in the early phases of their life cycles, when they have numerous opportunities for reinvestment, resulting in relatively rapid growth and relatively low dividends (or, in many cases, no dividends at all) As these firms mature, attractive investment opportunities are less numerous so that growth rates slow If a security is underpriced (i.e., intrinsic value price), then what is the relationship between its market capitalization rate and its expected rate of return? The intrinsic value of a share of stock is the individual investor’s assessment of the true worth of the stock The market capitalization rate is the market consensus for the required rate of return for the stock If the intrinsic value of the stock is equal to its price, then the market capitalization rate is equal to the expected rate of return On the other hand, if the individual investor believes the stock is underpriced (i.e., intrinsic value > price), then that investor’s expected rate of return is greater than the market capitalization rate Deployment Specialists pays a current (annual) dividend of $1 and is expected to grow at 20% for two years and then at 4% thereafter If the required return for Deployment Specialists is 8.5%, what is the intrinsic value of Deployment Specialists stock? Jand, Inc., currently pays a dividend of $1.22, which is expected to grow indefinitely at 5% If the current value of Jand’s shares based on the constantgrowth dividend discount model is $32.03, what is the required rate of return? A firm pays a current dividend of $1, which is expected to grow at a rate of 5% indefinitely If the current value of the firm’s shares is $35, what is the required return applicable to the investment based on the constant-growth dividend discount model (DDM)? Tri-coat Paints has a current market value of $41 per share with earnings of $3.64 What is the present value of its growth opportunities (PVGO) if the required return is 9%? A firm has current assets that could be sold for their book value of $10 million The book value of its fixed assets is $60 million, but they could be sold for $90 million today The firm has total debt with a book value of $40 million, but interest rate declines have caused the market value of the debt to increase to $50 million What is this firm’s market-to-book ratio? The market capitalization rate for Admiral Motors Company is 8% Its expected ROE is 10% and its expected EPS is $5 If the firm’s plowback ratio is 60%, what will be its P/E ratio? Miltmar Corporation will pay a year-end dividend of $4, and dividends thereafter are expected to grow at the constant rate of 4% per year The risk-free rate is 4%, and the expected return on the market portfolio is 12% The stock has a beta of 75 What is the intrinsic value of the stock? 10 Sisters Corp expects to earn $6 per share next year The firm’s ROE is 15% and its plowback ratio is 60% If the firm’s market capitalization rate is 10%, what is the present value of its growth opportunities? 11 A common stock pays an annual dividend per share of $2.10 The risk-free rate is 7% and the risk premium for this stock is 4% If the annual dividend is expected to remain at $2.10, what is the value of the stock? 12 The risk-free rate of return is 5%, the required rate of return on the market is 10%, and High-Flyer stock has a beta coefficient of 1.5 If the dividend per share expected during the coming year, D1, is $2.50 and g 4%, at what price should a share sell? 13 Explain why the following statements are true/false/uncertain a With all else held constant, a firm will have a higher P/E if its beta is higher b P/E will tend to be higher when ROE is higher (assuming plowback is positive) c P/E will tend to be higher when the plowback rate is higher 14 a Computer stocks currently provide an expected rate of return of 16% MBI, a large computer company, will pay a year-end dividend of $2 per share If the stock is selling at $50 per share, what must be the market’s expectation of the growth rate of MBI dividends? b If dividend growth forecasts for MBI are revised downward to 5% per year, what will happen to the price of MBI stock? What (qualitatively) will happen to the company’s price–earnings ratio? 15 Even Better Products has come out with a new and improved product As a result, the firm projects an ROE of 20%, and it will maintain a plowback ratio of 30 Its earnings this year will be $2 per share Investors expect a 12% rate of return on the stock a At what price and P/E ratio would you expect the firm to sell? b What is the present value of growth opportunities? c What would be the P/E ratio and the present value of growth opportunities if the firm planned to reinvest only 20% of its earnings? 16 a MF Corp has an ROE of 16% and a plowback ratio of 50% If the coming year’s earnings are expected to be $2 per share, at what price will the stock sell? The market capitalization rate is 12% b What price you expect MF shares to sell for in three years? 17 The market consensus is that Analog Electronic Corporation has an ROE 9% and a beta of 1.25 It plans to maintain indefinitely its traditional plowback ratio of 2/3 This year’s earnings were $3 per share The annual dividend was just paid The consensus estimate of the coming year’s market return is 14%, and T-bills currently offer a 6% return a Find the price at which Analog stock should sell b Calculate the P/E ratio c Calculate the present value of growth opportunities d Suppose your research convinces you Analog will announce momentarily that it will immediately reduce its plowback ratio to 1/3 Find the intrinsic value of the stock The market is still unaware of this decision Explain why V0 no longer equals P0 and why V0 is greater or less than P0 18 The FI Corporation’s dividends per share are expected to grow indefinitely by 5% per year a If this year’s year-end dividend is $8 and the market capitalization rate is 10% per year, what must the current stock price be according to the DDM? b If the expected earnings per share are $12, what is the implied value of the ROE on future investment opportunities? c How much is the market paying per share for growth opportunities (that is, for an ROE on future investments that exceeds the market capitalization rate)? 19 The stock of Nogro Corporation is currently selling for $10 per share Earnings per share in the coming year are expected to be $2 The company has a policy of paying out 50% of its earnings each year in dividends The rest is retained and invested in projects that earn a 20% rate of return per year This situation is expected to continue indefi- nitely a Assuming the current market price of the stock reflects its intrinsic value as computed using the constant-growth DDM, what rate of return Nogro’s investors require? b By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested? c If Nogro were to cut its dividend payout ratio to 25%, what would happen to its stock price? What if Nogro eliminated the dividend? 20 The risk-free rate of return is 8%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 1.2 Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $10 per share Dividends were just paid and are expected to be paid annually You expect that Xyrong will earn an ROE of 20% per year on all reinvested earnings forever a What is the intrinsic value of a share of Xyrong stock? b If the market price of a share is currently $100, and you expect the market price to be equal to the intrinsic value one year from now, what is your expected one-year holding-period return on Xyrong stock? THEORIES OF CHAPTER 15 - KEY TERMS Certificate of deposit: a bank time deposit Commercial paper: short – term unsecured debt issued by large corporations Common stock: Ownership shares in a publicly held corporation Shareholders have voting rights and may receive dividends Coporate bond: Long-term debt issued by private corporations typically paying semiannual coupons and returning the face value of the bond at maturity Federal funds: Funds in the accounts of commercial banks at the Federal Reserve Bank Money market: include short – term, highly liquid, and relatively low – risk debt instruments Municipal bond: tax – exempt bonds issued by state and local goverments Preferred stock: Nonvoting shares in a corporation, usually paying a fixed stream of dividends Repurchase agreement: short – term sales of government securities with an agreement to repurchase the securities at a higher price Bond: A security that obligates the issuer to make specified payments to the holder over a period of time Zero – coupon bond: A bond paying no coupons that sells at a discount and provides only a payment of par value at maturity Callable bond: Bonds that may be repurchased by the issuer at a specified call price during the call period Convertible bond: A bond with an option allowing the bondholder to exchange the bond for a specified number of shares of common stock in the firm Put bond: A bond that the holder may choose either to exchange for par value at some date or to extend for a given number of years Floating – rate bond: Bonds with coupon rates periodically reset according to a specified market rate YTM: The discount rate that makes the present value of a bond’s payments equal to its price - Current yield: Annual coupon divided by bond price Premium bond: Bonds selling above par value Discount bond: Bonds selling below par value Realized compound return: Compound rate of return on a bond with all coupons reinvested until maturity Reinvestment rate risk: Uncertainty surrounding the cumulative future value of reinvested bond coupon payments Investment grade bond: A bond rated BBB and above by Standard & Poor’s or Baa and above by Moody’s Speculative grade/ junk bond: A bond rated BB or lower by Standard & Poor’s, or Ba or lower by Moody’s, or an unrated bond Yield curve: A graph of yield to maturity as a function of term to maturity Expectations hypothesis: The theory that yields to maturity are determined solely by expectations of future short-term interest rates Forward rate: The inferred short-term rate of interest for a future period that makes the expected total return of a long-term bond equal to that of rolling over short-term bonds Liquidity preference theory: The theory that investors demand a risk premium on longterm bonds Liquidity premium: The extra expected return demanded by investors as compensation for the greater risk of longer-term bonds Exchange rate: The rate at which domestic currency can be converted into foreign currency GDP: The market value of goods and services produced over a period of time Unemployment rate: The ratio of the number of people classified as unemployed to the total labor force Inflation: The rate at which the general level of prices for goods and services is rising Demand shock: An event that affects the demand for goods and services in the economy Supply shock: An event that influences production capacity and costs in the economy Monetary policy: Actions taken by the Board of Governors of the Federal Reserve System to influence the money supply or interest rates Business cycles: Recurring cycles of recession and recovery Peak: The transition from the end of an expansion to the start of a contraction Trough: The transition point between recession and recovery Cyclical industries: Industries with above-average sensitivity to the state of the economy Defensive industries: Industries with below-average sensitivity to the state of the economy Leading economic indicators: Economic series that tend to rise or fall in advance of the rest of the economy Book value: The net worth of common equity according to a firm’s balance sheet Liquidation value: Net amount that can be realized by selling the assets of a firm and paying off the debt Intrinsic value: The present value of a firm’s expected future net cash flows discounted by the required rate of return Market capotalization: The market-consensus estimate of the appropriate discount rate for a firm’s cash flows Dividend discount model DDM: A formula for the intrinsic value of a firm equal to the present value of all expected future dividends Dividend payout raito: Percentage of earnings paid out as dividends - Plowback ratio/ earnings retention ratio: The proportion of the firm’s earnings that is reinvested in the business (and not paid out as dividends) Present value of growth opportunities PVGO: Net present value of a firm’s future investments Call option: The right to buy an asset at a specified exercise price on or before a specified expiration date Exercise price/ strike price: Price set for calling (buying) an asset or putting (selling) an asset Premium: purchase price of an option Put option: The right to sell an asset at a specified exercise price on or before a specified expiration date In the money: An option where exercise would generate a positive cash flow Out of the money: An option which, if exercised, would produce a negative cash flow Out-of-the-money options are therefore never exercised At the money: An option where the exercise price equals the asset price Protective put: An asset combined with a put option that guarantees minimum proceeds equal to the put’s exercise price Covered call: Writing a call on an asset together with buying the asset Straddle: A combination of a call and a put, each with the same exercise price and expiration date Spread: A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration Collar: An options strategy that brackets the value of a portfolio between two bounds ... tức cao Giữ lại để đầu tư (do rate of return dự án cao) sau D cao Present value of growth opportunities (PVGO): Net present value of a firm’s future investments (giá trị đầu tư tương lai công ty)... underpriced stock will privide an expected return greater than the required return (nhà đầu tư nên đầu tư vào underpriced stock) - Intrinsic value: the present value / of a firms expected future... bond with all coupons reinvestment until maturity (Lấy tiền coupon đầu tư thêm với lãi suất = lãi suất thị trường) Giá trị ban đầu (present value) Realized compound return