Name Framigham State College Departmet of Ecoomics ad Busiess Maagerial Fiace Practice Fial Exam Sprig 2006 This exam provides questios that are represetative of those cotaied o your exam. This test should i o way be cosidered a facsimile of your exam. All topics, problems, key words, ad class discussio are fair game for the exam whether or ot they are cotaied o this practice exam. ----------------------------------------------------------------------------------------------------------------------- Directios: Provide the best aswer to the followig 41 questios each worth 5 poits. (NOTE THERE WILL BE 31 QUESTIONS ON THE ACTUAL FINAL EXAM) You will be give 150 miutes to complete the exam. A picture ID will be checked upo turig the exam i. If you fiish early, you may quietly tur i your exam ad leave. The exam is closed book ad closed ote. You may ot share a calculator with aother studet. Uless specified otherwise, assume all iterest rates are aual rates. Uless idicated otherwise, values i paretheses represet egative values. For best results, work all calculatios usig at least six decimal places of accuracy. Make sure that you give me your ame at the top of this page. Circle the letter correspodig to the aswer that you are choosig ad also mark this letter to the left of the questio umber. 1. Which of the followig comes closest to the future value of ivestig $5,600 today over 16.75 years at a cotiuously compouded iterest rate of 12.75%? A. $ 6,314. B. $ 11,960. C. $ 41,797. D. $ 47,389. E. $ 112,730. The questio asks for the Future Value FV Preset value is give as $5,600 Period is 16.75 years, so N16.75 Rate is 12.75% (0.1275) compoudig cotiuously so FRCPracticeFialExamSprig2006 1 of 25 Sprig 2006
Use formula (3.4) FV FV FV FV FV PV e $5,600 $5,600 r * e e 0.1275 * 16.75 2.135625 $5,600 [ 8.462333813039] $47,389.07 Alteratively o the calculator set the Coupos Per Year value to 1 millio. This will result i a approximatio, which will be close eough. 2. What amout comes closest to the preset value of 360 cosecutive mothly paymets of $460 begiig i oe moth if the aual iterest rate is 6%? A. $ 9,936. B. $ 76,724. C. $ 99,999. D. $ 165,600. E. $ 993,600. The questio asks for the Preset Value of A Auity or the PVA So use formula (3.8) PVA A 1 1 r r ( 1 r) + The regular amout A is $460 Let 360 (moths) so you eed to adjust the iterest rate to a mothly rate r 6% per aum or ½% per moth or r 0.005 PVA PVA $460* 1 0.005 1 ( ) 360 0.005* 1.005 $460* 200 1 0.005*6.022575212 $460* 200 1 $460* 200 PVA 0.0301128761 PVA 33.20838561 PVA $460*166.7916144 $76,724.143 FRCPracticeFialExamSprig2006 2 of 25 Sprig 2006
Alteratively usig Fiacial Calculator fuctioality with 360, I%0.005 ad PMT460 3. If the future value of today s ivestmet of $5,000 to be received i 20 years is $235,000, what amout comes closest to the iterest rate? A. 5.00%. B. 11.50%. C. 21.23%. D. 47.00%. E. Not eough iformatio to determie. The formula for the iterest rate from the Preset Value PV, the Future Value r FV PV FV ad the umber of years is formula (3.10) ( ) 1 1 PV$5,000, FV $235,000 ad 20 years, so r r r r ( ) 1 20 $235,000 $5,000 47 1 20 1 1 1.21228545 1 0.21228545 OR 21.23% Alteratively usig Fiacial Calculator fuctioality with 20, PV5000 ad FV235,000 4. A recet Framigham State College graduate has decided to purchase a ew car, ad eeds to fiace the purchase. She has o dow paymet. She decides to buy a ew Chevy Camaro for the sticker price $29,999, ad is give two optios; (1) fiace the full sticker price of $29,999 at a special aual iterest rate of rate of 3%, or (2) take $2,500 off the sticker price ad fiace the reduced amout at 6% aual iterest. I both cases she is required to make mothly paymets over four years (48 moths). Give her objective of makig the lowest possible mothly paymets, which of the followig is most correct? A. Take Optio 1 as it saves about $18 per moth. B. Take Optio 1 as it saves about $56 per moth. C. Take Optio 2 as it saves about $56 per moth. D. Take Optio 2 as it saves about $18 per moth. E. Take either optio as the mothly paymet is early the same. The questio is what is the mothly paymet o two differet auities ad the which oe is least ad by how much PVA129,999, r13% per aum, 1248, PVA2 (29,999-2,500)27,499 r26% per aum FRCPracticeFialExamSprig2006 3 of 25 Sprig 2006
Covert r1 ad r2 ito mothly rates r13%/12 0.0025 r2 0.005 Mess with formula (3.8) PVA A 1 1 to get the amout A r r ( 1 r) + o the left had side divide both sides by PVA 1 1 r r ( 1 r) + 1 1 A so r r( 1 r) 1 1 + r r ( 1 r) + Slot i the values for both optios: 1 1 r r( 1+ r) PVA 1 1 r r r givig ( 1+ ) PVA1 $29,999 1 1 A1 1 1 r1 r11 ( + r1) 0.0025 0,0025 1+ 0.0025 ( ) 48 A A1 $29,999 1 1 0.0025 [ 0.0025*1.127328021] $29,999 [ 400 354.8213054] $29,999 45.17869463 A1 A1664.007 A $29,999 1 1 0.0025 0.0028183201 A1 FRCPracticeFialExamSprig2006 4 of 25 Sprig 2006
PVA2 1 1 r2 r21 r2 ( + ) A2 $27,499 1 1 0.005 0.005 1 0.005 ( + ) 48 A2 $27,499 1 1 0.005 [ 0.005*1.270489161] A2 $27,499 1 1 0.005 0.0063524458 A2 $27,499 [ 200 157.4196822] $27,499 42.58031778 A2 A2645.805 So, Optio Oe costs $664.07 per moth ad Optio Two costs $645.80 per moth. Optio two is cheaper by $664.07-$645.80 $18,21 a moth ad so is preferred. Usig Fiacial calculator fuctioality with to calculate the amouts for the two optios would give you PMT1 $664.00767 ad PMT2 $645.81481. 5. What comes closest to the preset value of a 45-year auity of $48 paid at the ed of each year ad begiig at the ed of the fifth year if the iterest rate is 13%? A. $ 59. B. $ 225. C. $ 281. D. $ 432. E. $ 2,160. FRCPracticeFialExamSprig2006 5 of 25 Sprig 2006
Set up the timelie: 0 1 2 3 4 5 49 PV of PVA PVA FV $48 $48 The auity of $48 dollars startig at the ed of year 5 has a preset value at poit 4 (PVA). That preset value is a future value from the poit of view of ow ad so it is the FV i the calculatio of the preset value from a future value. So, use formula (3.8) PVA A 1 1 to calculate the PVA at time r r ( 1 r) + four. PVA $48 1 1 45 0.13 0.13( 1.13) PVA $48 1 1 0.13 0.13* 244.6414019 PVA $48 1 1 0.13 31.80338225 PVA $48[ 7.692307692 0.0314431966] PVA $48* 7.660864496 $367.72 FV PV Now traslate back 4 years usig formula (3.6) $362.72 $362.72 1.63047361 PV ( 1.13) 4 $225.53 FV ( 1+ r) Note that the PVA is pretty much the same as the Preset Value of Perpetuity i this case because of the umber of periods beig large ad the iterest rate FRCPracticeFialExamSprig2006 6 of 25 Sprig 2006
PVP A r PV $369.23 $369.23 $226.46 1.13 1.63047361 a aswer close eough i this beig large (4.2) $48 $369.23 0.13 ( ) 4 istace to select the right aswer from the five choices. Ad you ca always use your fiacial calculator s fuctioality to solve the idividual steps. Also ot that this cat ca be skied i a variety of ways, for example PVA over 49 periods less PVA over 4 periods!!! 6. What amout comes closest to the preset value of this cash flow stream if the iterest rate is 15%? 0 1 2 3 4 5 6 7 8 9 10 $100 $100 $100 $100 $100 $100 $100 $900 $100 $100 11 12 13 14 15 16 17 18 19 20 $100 $100 $100 $100 $100 $100 $100 $100 $100 A. $ 2,000. B. $ 880. C. $ 626. D. $ 44. E. Not eough iformatio to determie. There are a umber of ways to aswer this questio: PVA($100, 20, r 0.15) PV(FV $100, 19, r 0.15) + PV(FV $800, 8, r0.15) OR NPV( 15, 0, {100, 900, 100, 0, 100}, {7, 1, 10, 1, 1 } ) $880.43 FRCPracticeFialExamSprig2006 7 of 25 Sprig 2006
7. Champios Ic. is cosumig cash at a rate of $1,000 per day. Each time they sell securities for cash it costs them $50. The iterest rate is 5%. Accordig to the EOQ model, approximately how much cash should they obtai each time they sell securities? A. $ 18,250. B. $ 27,020. C. $ 912.500. D. $ 135,177. E. $ 365,000. We will be lookig at EOQ applied to the issue of how to cash i securities durig the fial week of classes. 2*Aual Cash Needs*Cost Of Order The formula is EOQ The cash eed is give Iterest Rate i the questio as $1,000 per day or $365,000 per year. Cost of Order is the cost of sellig securities, so: 2*$365,000*$50 36,500,000 EOQ 0.05 0.05 730,000,000 $27,018.51 8. Retur to Champios Ic. ad their cash maagemet. Suppose that two thigs chage. First, iterest rates icrease. Secod, Champio s bak decreases the cost of turig securities ito cash. However, they cotiue, as before, to cosume cash at a rate of $1,000 per day. Give this ew iformatio, what would you expect to happe to the firm s EOQ? A. EOQ will icrease. B. EOQ will decrease. C. EOQ will stay the same. D. EOQ will either icrease or decrease, depedig o the magitude of the chages. 2*Aual Cash Needs*Cost Of Order Look agai at the EOQ formula EOQ Iterest Rate If Aual Cash Needs are uchaged the 2 * Aual Cash Needs is a costat, C ad the square root makes o differece to the ature of the chage (up or dow) brought o by chages i the Iterest Rate or i the Cost Of Order, so: Cost Of Order Size of EOQ depeds upo... Iterest Rate If Iterest Rate icreases EOQ will decrease If Cost of Order decreases EOQ will decrease If both happe EOQ will decrease FRCPracticeFialExamSprig2006 8 of 25 Sprig 2006
9. You write a put optio whose premium is $0.50. The exercise price of the put optio is $5. O expiratio, the stock price is $48. Which of the followig comes closest to the et profit or loss from writig the put optio: A. ($ 0.50) B. ($ 5.00) C. ($42.50) D. $ 48.00. E. $ 0.50. There are two key words i this questio write ad put optio. The writer of the optio sells a right to aother to be able to choose or ot to do somethig ad so from the poit of view of the writer, the Premium is always icome. The put optio is oe that gives the buyer of the optio the right to sell the share to the writer at the Exercise Price. The buyer of the will oly exercise the optio if they ca buy the share more cheaply i the market. The formula is Write Put Mi{ 0, P s - EX } + Premium so FRCPracticeFialExamSprig2006 9 of 25 Sprig 2006
{ } { } + + Write Put Mi 0, $48 - $5 + $0.50 Write Put Mi 0, $43 $0.50 Write Put 0 + $0.50 $0.50 10. You buy a put optio for a premium of $5. The exercise price is $55. O expiratio, the stock price is $25. Your et profit/loss is: A. $ 5. B. ($ 5). C. $ 25. D. $ 21. E. $ 75. There are two key words i this questio buy ad put optio. The buyer of the optio buys a right to be able to choose or ot to do somethig ad so from the poit of view of the buyer, the Premium is always a expese. The put optio is oe that gives the buyer of the optio the right to sell the share to the writer at the Exercise Price. The buyer of the will oly exercise the optio if they ca buy the share more cheaply i the market. The formula is: Buy Put Max{ 0, EX - P s }- Premium, so FRCPracticeFialExamSprig2006 10 of 25 Sprig 2006
{ } { } Buy Put Max 0, $55 - $25 - $5 Buy Put Max 0, $30 - $5 Buy Put $30 - $5 +$25 11. You eter a straddle positio by purchasig a call ad a put optio o Micro, Ic. The call optio has a premium of $7 ad the put optio has a premium of $9. The exercise price of the call ad the put optio is $100. O expiratio, the stock price of Micro is 105. Your et profit/loss o the straddle positio is: A. $189. B. $ 11. C. $ 0. D. ($ 11). E. ($ 16). The key word here is purchasig. You are the buyer of both a call ad a put with the same exercise price. You will either exercise the call or the put but ot both. However you calculate the profit or loss from both ad add them together to get the profit or loss from the straddle. The call formula is: Buy Call Max{ 0, P s - EX} - Premium, so the profit or loss o the call elemet of the straddle is: Buy Call Max{ 0, $105 - $100} - $7 Buy Call Max 0, $5 - $7 { } Buy Call $5 - $7 - $2 The put formula is: Buy Put Max{ 0, EX - P s }- Premium, so Buy Put Max{ 0, $100 - $105} - $9 { } Buy Put Max 0, -$5 - $9 Buy Put $0 - $9 -$9 So, the overall loss is -$2 -$9 -$11 or ($11) 12. You sell Corder, Ic. short at $25 per share. You close out your positio buy later buyig shares of Corder, Ic. back at a price of $20 per share. Your per share profit/loss o the short trasactio is: A. $ 20. B. $ 25. C. $ 5. D. ($ - 5). E. ($ -20). Whe you sell short you borrow a share ad sell it. You hope the price goes dow so you ca buy it back ad give the share back to the leder. If you are lucky eough to sell for $25 ad buy back for $20 you make a $5 profit. FRCPracticeFialExamSprig2006 11 of 25 Sprig 2006
13. I perfect markets, a firm with a $25 per share stock price who aouces a $0.25 divided per share will fid that o the ex-divided date its stock price will be: A. $25.25 B. $25.75. C. $25.00. D. $26.00. E. $24.75. If with perfect iformatio, the market had valued the shares at $25.00 the, if the compay pays out $0.25 for every share, the market will value the shares at $25.00 - $0.25 hece after the ex-divided date (whe the buyer of the share o loger buys the right to the divided) the share will be worth $24.75. 14. Assumig a purchase of $100 of products, what is the implicit iterest rate i the credit terms of 2/5, et 30. A. 2.05% B. 45.00%. C. 27.86%. D. 63.50%. E. 34.30%. The terms 2/5, et 30 mea a 2 percet discout if paid withi 5 days ad paymet due i 30 days., So the buyer will either pay o the 5 th day ad get the discout or pay o the 30 th day without the discout. I this case either pay $98 dollars o 5 th or $100 dollars o the 30 th day. This problem is the oe of what is the iterest rate, if PV$98, FV$100 ad period is 25 days or 25/365 years i.e. 0.0684931507. We ca use the formula (3.10) ( ) 1 r FV PV 1 as follows: ( ) 1 25 ^ r $100 $98 365 1 ( ) 365 25 ^ r $100 $98 1 r r 365 25 ^ 1.020408163 1 1.343071999 1 0.34307 or 34.307% You ca also do this usig Fiacial Calculator fuctioality. FRCPracticeFialExamSprig2006 12 of 25 Sprig 2006
15. I determiig project cash flows, depreciatio: A. does ot chage after tax cash flow because it is ot a "real" expese. B. acts to icrease the taxes the firm must pay. C. acts as a tax shield, i.e., acts to lower taxes paid. D. falls with the price per uit sold. E. rises with the price per uit sold. Depreciatio is a Tax Shield. 16. A borrowig type project (a iflow followed by outflows): A. is acceptable if the NPV is less tha zero. B. is acceptable if the IRR is less tha the required retur. C. is acceptable if the IRR is greater tha the required retur. D. is acceptable if the IRR is equal to zero. E. is acceptable if the IRR is greater tha 25%. With a borrowig project you reverse the IRR rule, so you take projects with IRR less tha the required retur. 17. Firm Leverage has $10 millio i permaet debt fiacig issued at a iterest rate of 8%. The corporate tax rate is 31%. Compared with a idetical ulevered firm, what amout comes closest to the preset value of perpetual tax savigs from debt for Firm Leverage? A. $ 272,000. B. $ 800,000. C. $ 3,100,000. D. $ 8,000,000. E. $31,000,000. Use Miller ad Modigliai Model V ( * L V + U T C D ) where : V is the value of a levered firm L is the value of a ulevered firm V U T C D ( T C D ) is the corporate icome tax rate, ad is the value of permaet debt * is the value of the perpetual tax savig 0.31*$10 millio$3.1 millio FRCPracticeFialExamSprig2006 13 of 25 Sprig 2006
Use the iformatio o Project s X ad Y below to aswer questios 18 through 20. The required rate of retur for both projects is 27%. C0 C1 C2 C3 C4 Project X (1,000) 0 0 0 2,800 Project Y (6,000) 2,000 2,000 2,000 2,000 18. If the projects are idepedet, the based o NPV: A. Project X would be accepted, Project Y would be rejected. B. Project X ad Project Y would be rejected. C. Project Y would be accepted, Project X would be rejected. D. Project X ad Project Y would be accepted. E. Caot aswer without additioal iformatio. Calculate the NPV for each project: Project X has NPV(27,(-)1000, {0,0,0,2800} ) $76.32 Project Y has NPV(27,(-)6000, {2000}, {4} ) -$1440.01 Accept positive NPV projects so accept Project X ad reject Project Y. 19. Which comes closest to the iteral rate of retur (IRR) of Project X? A. 0.00% B. 80.00% C. 55.55% D. 29.36% E. Caot aswer without additioal iformatio. Use IRR((-)1000, {0,0,0,2800}) 29.356873 Or use formula (3.10) ( ) 1 r FV PV 1 as follows: ( ) 1/4 r $2800 $1000 1 r 1/4 1 2.8 r 1.293568728 1 0.293568728 or 29.3569% Or recogize that with a small positive NPV the IRR caot be much more tha the required rate of 27%. FRCPracticeFialExamSprig2006 14 of 25 Sprig 2006
20. How may differet iteral rates of retur are possible for Project Y? A. Zero. B. Oe. C. Two. D. Three. E. More tha Three. The umber of IRRs is the same as the umber of sig chages i the cashflows. Project Y has oly oe sig chage from ve $6,000 to +ve $2,000 hece oly oe IRR. 21. You buy a call optio o a stock for a premium of $10. The call s exercise price is $100. At the time of expiratio, the stock s price is $200. Which of the followig comes closest to the et profit or loss from buyig the call? A. ($100) B. ($190) C. $190 D. $ 90 E. $ 10 The key words i the questio are you buy ad call optio. As the buyer, you are the oe payig the premium so the premium is a outgoig or expese from your poit of view. The call optio gives you the right to opt to purchase a share at the strike or exercise price. FRCPracticeFialExamSprig2006 15 of 25 Sprig 2006
Buy Call { s } { } { } Max 0, P - EX - Premium, so Buy Call Max 0, $200 - $100 - $10 Buy Call Max 0, $100 - $10 Buy Call $100 - $10 $90 22. The local GMC dealer is advertisig special fiacig o a ew truck. The truck s sticker price is $22,000. The dealer requires a dow paymet of $5,000 (the amout to be subtracted off the sticker) ad will fiace the balace over a period of 36 cosecutive moths, the first paymet due i oe moth, at a aual iterest rate of 12%. What amout comes closest to the mothly car paymet? A. $616. B. $565. C. $521. D. $432. E. $259. This is exactly like questio 4 oly you have oly oe amout to calculate. PVA 1 1 r r r ( 1+ ) A r 0.12 per aum or 0.01 per moth, N is 36 moths, PVA $22,000-$5,000 $17,000. Plug ad chug. $17,000 $17,000 1 1 A 1 1 0.01 36 0.01* ( 1.01) 0.01 [ 0.01*1.430768784] $17,000 $17,000 1 A A 100 [ 100 69.89249496] 0.01430768784 $17,000 A$564.64 30.10750504 A FRCPracticeFialExamSprig2006 16 of 25 Sprig 2006
23. Matrix Ic. eeds a ew machie to process wood pulp. The machie requires a immediate ivestmet of $55,000. The machie the produces after tax aual cash flows of $19,500 for 3 cosecutive years. Which of the followig comes closest to the project s iteral rate of retur? A. 3.15%. B. 5.00%. C. 10.00%. D. 14.36%. E. 34.50%. Set up a timelie: C0 C1 C2 C3 New Machie (55,000) 19,500 19,500 19,500 The IRR ca the be calculated usig the IRR fuctioality of your calculator settig up lists or eterig the data directly { 19500} L1 {3} L2 IRR( (-)55000, L1, L2) 3.14927 or approx 3.15% 24. Prime Moo, Corp. is curretly ulevered with $100 millio of assets. They pla to expad by doublig the size of the firm, with all capital comig i the form of debt. After this expasio, what must the percetage fall i assets be before all the equity i the firm is wiped out? A. 25.00% B. 37.50%. C. 50.00% D. 75.00% E. 100.00% Before Assets 100 Equity 100 Total Assets 100 Total Liabilities 100 After Assets 200 Debt 100 Equity 100 Total Assets 200 Total Liabilities 200 After, if the assets fall by 100, the the equity is wiped out. This is 50% of the assets totalig 200. FRCPracticeFialExamSprig2006 17 of 25 Sprig 2006
25. The equity holders of Super Nova, Ic. have 100 millio of equity i the firm. Because of debt, the total value of the assets is 600 millio. What is the leverage factor i this busiess? A. 1. B. 5. C. 6. D. 7. E. Greater tha 10, but less tha 16. Leverage Factor Assets 600 6 Equity 100 26. If a firm s leverage factor is 4, what is the percetage of equity i the busiess? A. 50% B. 72% C. 80% D. 85% E. Noe of the above aswers are correct. Leverage Factor Assets 400 4 Equity 100 So, Equity is 100 ad Assets are 400, so Equity as a percetage of Assets is 100/400 25%. 27. The replicatio of the corporate leverage decisio by borrowig o oes ow accout is called: A. fiacial egieerig. B. the M&M priciples. C. operatig leverage. D. homemade leverage. E. offsettig leverage. It is called homemade leverage. A sack food maufacturer is plaig to itroduce three ew products simultaeously. Project Iitial Ivestmet Per Year Cash Flow Number of Years Potato Chips $ 5 Millio $ 1.60 Millio 5 Popcor $ 2 Millio $ 0.75 Millio 5 Graola Bars $ 11 Millio $ 3.25 Millio 5 FRCPracticeFialExamSprig2006 18 of 25 Sprig 2006
28. Give a required rate of retur of 10%, the rak orderig of NPV for these projects, from best to worst, would be: A. Potato Chips, Popcor, Graola Bars. B. Graola Bars, Potato Chips, Popcor. C. Graola Bars, Popcor, Potato Chips. D. Potato Chips, Graola Bars, Popcor. E. Popcor, Potato Chips, Graola Bars. Calculate the NPV i each case: PotatoNPV NPV(10, (-)5, {1.6}, {5}) $1.065258831 millio PopcorNPV NPV(10, (-)2, {0.75}, {5}) $0.8430900771 millio GraolaNPV NPV(10, (-)11, {3.25}, {5}) $1.320057001 millio GraolaNPV > PotatoNPV > PopcorNPV, so B. 29. Assumig a purchase of $100 of products, which of the followig comes closest to the implicit iterest rate i the credit terms of 3/13, et 30. A. 43.33% B. 24.08% C. 30.00% D. 92.32% E. (30.00%) The terms 3/13, et 30 mea a 3 percet discout if paid withi 13 days ad paymet due i 30 days., So the buyer will either pay o the 13 th day ad get the discout or pay o the 30 th day without the discout. I this case either pay $97 dollars o 13 th or $100 dollars o the 30 th day. This problem is the oe of what is the iterest rate, if PV$97, FV$100 ad period is 17 days or 17/365 years i.e. 0.0465753425. We ca use the formula (3.10) ( ) 1 r FV PV 1 as follows: FRCPracticeFialExamSprig2006 19 of 25 Sprig 2006
30. Your firm wishes to determie whether or ot to exted credit to a customer who has ordered 100 boxes of product from your firm that you sell for $23 a box ad which costs the firm $17 per box. Which of the followig comes closest to the probability of payig that would make the firm idifferet to hadig out the credit? Assume this to be the case of a oe time sale with o repeat busiess aticipated. A. 10.0% B. 7.0% C. 30.4% D. 23.0% E. 74.0% The questio is askig which gamble gives you a expected value of zero. The probability of beig paid P(pd) ad the probability of ot beig paid P(ot) add up to oe, so P(ot) 1 P(pd). The gamble the ca be expressed as: P( pd)*retur if paid +(1-P(pd)* Retur if ot paid 0 P( pd)*$6 +(1-P(pd)* (-$17) 0 6* P( pd) +(-17+17*P(pd)) 0 23* P( pd) -17 0 23* P( pd) -17 + 17 0 + 17 P(pd) 17/23 73.913% 31. A ivestor who resides i Florida purchases a muicipal bod issued by the state of Florida o behalf of the Departmet of Educatio. The probability of default is low, estimated to be 2%. The yield o the muicipal is 3.75%. The same ivestor has a opportuity to purchase a similar amout ad maturity of zero default risk U.S. Treasury Bills, priced to yield 4.95%. The idividual is i the 32% federal tax bracket, ad the 6% state tax bracket. Give these facts, which of the followig would you suggest? A. Purchase the Tbill as it offers 1.20% more i expected after tax yield. B. Purchase the Tbill as it offers 2.67% more i expected after tax yield. C. Purchase the muicipal as it offers 0.305% more i expected after tax yield. D. Purchase the muicipal as it offers 0.61% more i expected after tax yield. E. The Tbill ad the muicipal offer the same expected after tax yield. The issue here is to calculate the after tax yields for the two ivestmets give that they are taxed differetly. The muicipal bod is ot subject to Federal Icome Tax or to state tax if owed by a state residet. Tbills are taxable at the Federal level but ot the state, so taxes reduce the yields i each case as follows FRCPracticeFialExamSprig2006 20 of 25 Sprig 2006
Tbill Muicipal 4.95% 3.75% Federal Tax at 32% -1.58% 0.00% State Taxes at 6% 0.00% 0.00% 3.37% 3.75% Muicipal better by 0.384% I am afraid I do t kow where 0.31% came from but the closest aswer to 0.384% is still C, that the Muicipal offers about 0.3 more i expected after tax yield. 32. A firm reports earigs before iterest ad tax (EBIT) of $20 millio ad et icome of $10 millio. If the corporate tax rate is 20%, the firm must have paid iterest o debt of : A. $ 7.5 millio. B. $ 8.2 millio. C. $ 9.0 millio. D. $10.0 millio. E. $ 20.0 millio. EAT is give as $10 millio. EBIT is give as $20 millio. The Tax Rate is 20% Tax EBT*Tax Rate The framework to use is: EBIT Iterest EBT EBT Tax EAT Tax EBT*Tax Rate So, Ad, EBT ( EBT*Tax Rate) EAT, EAT EBT (20% * EBT) EAT.8 EBT Or, EBT EAT /.8 Or EBT 1.25 EAT From the EBT 1.25 EAT, EBT 1.25 * $10 millio $12.5 millio EBIT Iterest EBT, So, $20 Iterest $12.5 $20 $12.5 Iterest Iterest $7.5 millio FRCPracticeFialExamSprig2006 21 of 25 Sprig 2006
33. Firm Leverage has $10 millio is debt fiacig issued at a iterest rate of 8%. The corporate tax rate is 34%. Compared with a idetical ulevered firm, what amout comes closest to the amout of savigs i taxes PER YEAR from debt fiacig? A. $ 272,000. B. $ 800,000. C. $ 3,400,000. D. $ 8,000,000. E. $34,000,000. Sice iterest is deducted before tax each year, what is saved each year is the tax o the iterest, so Debt * Iterest Rate Iterest ($10 * 0.08 $800,000) Tax Rate * Iterest Savigs per year (0.34 * $800,000 $272,000) 34. Firm Leverage has $10 millio is debt fiacig issued at a iterest rate of 8%. The corporate tax rate is 34%. Compared with a idetical ulevered firm, what amout comes closest to the preset value of perpetual tax savigs from debt for Firm Leverage? A. $ 272,000. B. $ 800,000. C. $ 3,400,000. D. $ 8,000,000. E. $34,000,000. Oe way to look at this is as a cotiuatio of the previous questio If we save $272,000 each year i perpetuity, the by formula (4.2) PVP A r We have A $272,000 all we eed is r, so we use the iterest rate o the debt as the required rate of retur, i.e. 8% PVP $272,000.08 $3,400,000 or we ca pull out the result from the Miller ad Modigliai model * is the value of the perpetual tax savig ( T C D ) 0.34*$10 millio$3.4 millio FRCPracticeFialExamSprig2006 22 of 25 Sprig 2006
35. A levered firm is worth $5 millio more tha a idetical ulevered firm. If the corporate tax rate is 34%, what amout comes closest to the amout of debt is i the capital structure? A. $12.4 millio. B. $13.6 millio. C. $14.7 millio. D. $18.2 millio. E. $ 1.7 millio. Here we use the Miller ad Modigliai model directly ( T C D ) * is the value of the perpetual tax savig $5 Millio 0.34*$Debt $5 Millio $Debt $14.706 millio 0.34 36. Whe comparig levered versus ulevered capital structures, leverage works to icrease EPS for high levels of EBIT because A. iterest paymets o debt vary with EBIT levels. B. iterest paymets o the debt stay fixed, leavig the remaiig icome to be distributed amog more shares of stock. C. iterest paymets o the debt stay fixed, leavig the remaiig icome to be distributed amog fewer shares of stock. D. other thigs equal, more taxes are paid uder the levered capital structure. E. other thigs equal, less taxes are paid uder the ulevered capital structure. 37. You write a call optio whose premium is $7.50. The exercise price is $85. O expiratio, the stock price is $88. Your profit/loss is: A. ($ 4.50) B. ($ 7.50) C. $ 4.50 D. $ 10.50. E. $ 7.50 The keywords here are write ad call optio. Whe you write a optio you receive the premium, so you kow that the premium is icome. A call optio is oe where the writer sells to the buyer the optio to purchase the share from the writer at the Exercise Price. The buyer will exercise the optio if she ca make a profit by buyig the share, i.e. whe the market price is higher tha the exercise price of the optio. If the buyer exercise the call the writer will have to buy a share at the market price. I the example the market price is above the exercise price, so the buyer of the call will exercise the optio. FRCPracticeFialExamSprig2006 23 of 25 Sprig 2006
The writer therefore has to sell a share for $85 which she has to buy i the market for $88 (a loss of $3) but the writer received the premium of $7.5 so the et profit is $4.5. Usig the formula: { s } Write Call Mi{ 0, 85-88 } + 7.5 Write Call Mi 0, EX - P + Premium { } + + Write Call Mi 0, - 3 7.5 Write Call - 3 + 7.5 $4.5 38. You buy a call optio for a premium of $5. The exercise price is $55. O expiratio, the stock price is $25. Your et profit/loss is: A. $ 5. B. ($ 5). C. $ 25. D. $ 21. E. $ 75. The keywords here are buy ad call optio. Whe you buy a optio you pay the premium, so you kow that the premium is a outgoig. A call optio is oe where the writer sells to the buyer the optio to purchase the share from the writer at the Exercise Price. The buyer will exercise the optio if she ca make a profit by buyig the share, i.e. whe the market price is higher tha the exercise price of the optio. No profit is available from buyig a share for $55 ad sellig it for $25 so the buyer of the call will ot exercise. Havig paid the premium the buyer of the call will have lost the premium amout of $5 o the deal. Usig the formula: Buy Call Max{ 0, P s - EX} - Premium Buy Call Max{ 0, $25 -$55} - $5 Buy Call Max{ 0, -$30}- $5 Buy Call 0 - $5 -$5 39. You buy a call optio whose premium is $7.50. The exercise price is $85. O expiratio, the stock price is $88. Your profit/loss is: A. ($ 4.50) B. ($ 7.50) C. $ 4.50 D. $ 10.50. E. $ 7.50 Usig the formula: Buy Call Max 0, P - EX - Premium { } s FRCPracticeFialExamSprig2006 24 of 25 Sprig 2006
{ } { } Buy Call Max 0, $88 -$85 - $7.50 Buy Call Max 0, $3 - $7.50 Buy Call $3 - $7.50 -$4.50 40. You buy a call optio for a premium of $5. The exercise price is $5.50. O expiratio, the stock price is $5.25. Your et profit/loss is: A. $ 5.00 B. ($ 5.00) C. $ 0.25. D. $ 4.75. E. $ 10.25. Usig the formula: Buy Call { s } Buy Call Max{ 0, $5.25 - $5.5} - $5 Buy Call Max{ 0, -$0.25}- $5 Buy Call $0 - $5 -$5 Max 0, P - EX - Premium 41. Golde Ic. is a firm with a stock price of $50 per share. The firm has decided to ot pay a divided of $1.50 per share because they kow that the stock price will fall upo the ex-divided date. Joes, a shareholder o the record of Golde, has 500 shares that she purchased some time ago for $5.00 per share. Joes eeds cash ad decides to create for herself the $750 divided by sellig some of her shares of Golde. Which of the followig comes closest to the total amout of taxes that Joes must pay o the sale if the tax rate o capital gais is 20%? A. $150 B. $135 C. $ 85 D. $ 50 E. Give the facts as preseted, there is o tax due o the sale. She sells 15 shares at $50 to get gross $750. The shares cost (15*$5) $75. The taxable gai is ($750-$75) $675 taxable at 20% the tax is $135. FRCPracticeFialExamSprig2006 25 of 25 Sprig 2006