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1 . Which of the followig $,000 face-value securities has the lowest yield to maturity? A) a 5 percet coupo bod sellig for $,000 B) a 0 percet coupo bod sellig for $,000 C) a 5 percet coupo bod sellig for $,000 D) a 5 percet coupo bod sellig for $900. Aswer: A Sice yield to maturity (YTM) is defied as the iterest rate that equates the PV from a debt istrumet with its value today, coupo bod (A) s YTM would be FaceValue $,000 For simplicity, let ' s say ; PV,000 Coupo ( Iterest Paymet) Face Value Curret Yield, ,000 50,000, i i i i i YTM i 0.05 (B): likewise, FaceValue $,000 For simplicity, let ' s say ; PV, 000 Coupo ( Iterest Paymet) Face Value Curret Yield, ,000 00,000,00, i i i i i i YTM i 0. (C) Likewise, FaceValue $,000 For simplicity, let ' s say ; PV, 000 Coupo ( Iterest Paymet) Face Value Curret Yield, ,000 50,000,50, i i i i i i YTM i 0.5 Page / 7

2 (D) FaceValue $,000 For simplicity, let ' s say ; PV, 000 Coupo ( Iterest Paymet) Face Value Curret Yield, ,050, YTM i 0.05 i i i i i i 2. Explai ad show all your work for each part. ) If the iterest rate is 5%, what is the preset value of a security that pays you $, 050 ext year ad $,02.50 two years from ow? 2) If this security sold for $2200, is the yield to maturity greater or less tha 5%? 3) Why? 2. Aswer: ) PV = $,050/( +.05) + $,02.50/( + 0.5) 2 = $2,000 2) ad 3) If this security sold for $2200, the yield to maturity is less tha 5%. The lower the iterest rate the higher the preset value. 3. What is the retur o a 5 percet coupo bod that iitially sells for $,000 ad sells for $900 ext year? 3. Aswer: -5% , Rate of returs %,000,000,000 Page 2 / 7

3 4. Suppose you are holdig a 5 percet coupo bod maturig i oe year with a yield to maturity of 5 percet. If the iterest rate o oe-year bods rises from 5 percet to 20 percet over the course of the year, what is the yearly retur o the bod you are holdig? 4. Aswer: Suppose FaceValue be $,000 Coupo ( Iterest Paymet) Face Value Curret Yield, PV PV,000, $93.5 i i ,000, $, i i Rate of returs Thus the aswer is 5%. 5. Would it make sese to buy a house whe mortgage rates are 4% ad expected iflatio is 5%? Explai your aswer. 5. Aswer: Eve though the omial rate for the mortgage appears high, the real cost of borrowig the fuds is -%. Yes, uder this circumstace it would be reasoable to make this purchase. 6. Duratio is A) a asset's term to maturity. B) the time util the ext iterest paymet for a coupo bod. C) the average lifetime of a debt security's stream of paymets. D) the time betwee iterest paymets for a coupo bod. 6. Aswer: C Duratio is expressed i terms of years, but it is ot the same thig as a bod s maturity date. That said, the maturity date of a bod is oe of the key compoets i figurig duratio, as is the bod s coupo rate. I the case of a zero-coupo bod, the bod s remaiig time to its maturity date is equal to its duratio. Whe a coupo is added to the bod, however, the bod s duratio umber will always be less tha the maturity date. The larger the coupo, the shorter the duratio umber becomes. 7. All else equal, the the coupo rate o a bod, the the bod's duratio. A) higher; loger B) higher; shorter Page 3 / 7

4 C) lower; shorter D) greater; loger 7. Aswer: B Geerally, bods with log maturities ad low coupos have the logest duratios. These bods are more sesitive to a chage i market iterest rates ad thus are more volatile i a chagig rate eviromet. Coversely, bods with shorter maturity dates or higher coupos will have shorter duratios. Bods with shorter duratios are less sesitive to chagig rates ad thus are less volatile i a chagig rate eviromet. For example, if rates were to rise %, a bod or bod fud with a five-year average duratio would likely lose approximately 5% of its value. 8. Joh speds $4,000 o a perpetuity that pays $50 each year. The yield to maturity of this perpetuity is 8. Aswer: 3.75% ,000 i % i 4, O September, 202, Al buys a bod for $5,000 that makes coupo paymets of $750 after each of the followig three years ad returs its pricipal of $5,000 at the ed of the three years. I other words, it is a stadard coupo bod with a 5 percet aual iterest rate makig paymets oce each year. O September, 203, Al receives his first coupo paymet of $750. At that time, the market iterest rate o bods like Al's has rise to 6 percet. Al sells his bod to Biff at that time, for a price equal to the preset value of the bod's paymets. A. How much does Biff pay Al for the bod? B. Calculate Al's curret yield, capital-gais yield, ad total retur for the year. O September, 204, Biff receives a coupo paymet of $750. The market iterest rate o bods like his remais 6 percet. Biff sells his bod to Cass at that time, for a price equal to the preset value of the bod's paymets. C. How much does Cass pay Biff for the bod? D. Calculate Biff's curret yield, capital-gais yield, ad total retur for the year. Page 4 / 7

5 O September, 205, Cass receives a coupo paymet of $750 ad the pricipal of $5,000. Over the course of the year (betwee September, 204, ad September, 205), the market iterest rate o bods like his rose to 7 percet. But Cass decided to keep the bod. E. What is Cass's total retur for the year? Explai ad show all your work for each part. 9. Aswer: 750 5,750 A. P 2 $4, B. Curret yield= % ad Capital-gais yield = 5,000 4, , % 5,000 Therefore, Total retur = curret yield + capital gais yield =5% -.83% =3.7% C. P 5, $4, D. Curret yield= 4, , % 4, % ad Capital-gais yield = 4, Total retur = curret yield + capital-gais yield = 5.09% + 0.9% = 6%. You should expect this because Biff bought the bod at a yield to maturity of 6 percet ad held it for a year, ad the market iterest rate did ot chage. E. Six percet, sice Cass bought it whe the yield to maturity was 6 percet ad held it util it matured. You could also do this oe the hard way: Curret yield= 5, 000 4, % 4, % ad Capital-gais yield = 4, Total retur = curret yield + capital-gais yield = 5.05% % = 6% Page 5 / 7

6 0. O February, 203, Jaet buys a bod for $0,000 that makes coupo paymets of $600 after each of the followig two years ad returs its pricipal of $0,000 at the ed of the secod year. I other words, it is a stadard coupo bod with a 6 percet aual iterest rate makig paymets oce each year O February, 204, Jaet receives her first coupo paymet of $600. At that time, the market iterest rate o bods like hers has falle to 4 percet. She sells her bod to Justi at that time, for a price equal to the preset value of the bod's paymets. A. How much does Justi pay Jaet for the bod? Both Jaet ad Justi have tax rates of 30 percet o iterest icome ad 20 percet o capital gais. (Note that if someoe has a capital loss, you may assume that he or she ca reduce taxes by the amout of the capital loss times the tax rate of 20 percet.) B. Calculate Jaet's after-tax rate of retur for the past year (from Feb., 203, to Feb., 204). Justi holds oto the bod from February, 204, to February, 205, so it matures ad he receives the secod coupo paymet ad the pricipal. C. What is Justi's after-tax rate of retur for the year from Feb., 204, to Feb., 205? Explai ad show all your work for each part. You may assume, of course, that the market works ad does ot malfuctio. 0. Aswer: A. The bod has oe year left to maturity, which pays iterest of $600 ad repays pricipal of $0,000, so the price of the bod is P=0,600/0.4=0,92.3 B. Her total retur cosists of curret yield plus capital-gai yield. Doig these i after-tax terms meas subtractig off the taxes for each. * Iterest paymet = $600 * Tax o iterest paymet = $ = $80 * Iterest after taxes = $600 $80 = $420 * After-tax curret yield =$420/$0,000=0.042=4.2% * Capital gais = $0,92.3 $0,000 = $92.3 * Tax o capital gais = $ = $38.46 * Capital gais after taxes = $92.3 $38.46 = $53.85 * After-tax capital-gais yield =$53.85/$0,000= 0.05 =.5% * Total after-tax retur= after-tax curret yield + after-tax capital-gais yield = 4.2% +.5%= 5.7% Page 6 / 7

7 C. Justi gets $600 i iterest, so his iterest after taxes is the same as Jaet's was, which is $420. But he paid more, so his curret yield will be lower: * After-tax curret yield =$420/0,92.3 = 0.04 = 4.% Justi gets a capital loss because he bought the bod for $0,92.3 ad it pays oly $0,000 whe it matures. * Capital gais = $0,000 $0,92.3 = $92.3 * Tax o capital gais = $ = $38.46 * Capital gais after taxes = $92.3 ( $38.46) = $53.85 * After-tax capital-gais yield =-$53.85/0,92.3= 0.05 =.5% * Total after-tax retur = after-tax curret yield + after-tax capital-gais yield = 4.2% + (.5%)= 2.6% Page 7 / 7