# Framingham State College Department of Economics and Business Managerial Finance Practice Final Exam Spring 2006

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2 Use formula (3.4) FV FV FV FV FV PV e \$5,600 \$5,600 r * e e * \$5,600 [ ] \$47, 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 PVA PVA \$460* ( ) * \$460* * \$460* \$460* 200 PVA PVA PVA \$460* \$76, FRCPracticeFialExamSprig of 25 Sprig 2006

4 Covert r1 ad r2 ito mothly rates r13%/ r 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) A so r r( 1 r) 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, A1 1 1 r1 r11 ( + r1) , ( ) 48 A A1 \$29, [ * ] \$29,999 [ ] \$29, A1 A A \$29, A1 FRCPracticeFialExamSprig of 25 Sprig 2006

5 PVA2 1 1 r2 r21 r2 ( + ) A2 \$27, ( + ) 48 A2 \$27, [ 0.005* ] A2 \$27, A2 \$27,499 [ ] \$27, A2 A So, Optio Oe costs \$ per moth ad Optio Two costs \$ per moth. Optio two is cheaper by \$ \$ \$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 \$ ad PMT2 \$ 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. FRCPracticeFialExamSprig of 25 Sprig 2006

6 Set up the timelie: 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 \$ ( 1.13) PVA \$ * PVA \$ PVA \$48[ ] PVA \$48* \$ FV PV Now traslate back 4 years usig formula (3.6) \$ \$ PV ( 1.13) 4 \$ 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 FRCPracticeFialExamSprig of 25 Sprig 2006

7 PVP A r PV \$ \$ \$ a aswer close eough i this beig large (4.2) \$48 \$ ( ) 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%? \$100 \$100 \$100 \$100 \$100 \$100 \$100 \$900 \$100 \$ \$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 } ) \$ FRCPracticeFialExamSprig of 25 Sprig 2006

8 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. \$ 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 ,000,000 \$27, 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 FRCPracticeFialExamSprig of 25 Sprig 2006

9 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. \$ E. \$ 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 FRCPracticeFialExamSprig of 25 Sprig 2006

12 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. \$ C. \$ D. \$ E. \$ 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 \$ \$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 \$ 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 %. C %. D %. E %. 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 We ca use the formula (3.10) ( ) 1 r FV PV 1 as follows: ( ) 1 25 ^ r \$100 \$ ( ) ^ r \$100 \$98 1 r r ^ or % You ca also do this usig Fiacial Calculator fuctioality. FRCPracticeFialExamSprig of 25 Sprig 2006

13 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 FRCPracticeFialExamSprig of 25 Sprig 2006

14 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) ,800 Project Y (6,000) 2,000 2,000 2,000 2, 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} ) -\$ 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 % C % D % E. Caot aswer without additioal iformatio. Use IRR((-)1000, {0,0,0,2800}) Or use formula (3.10) ( ) 1 r FV PV 1 as follows: ( ) 1/4 r \$2800 \$ r 1/ r or % Or recogize that with a small positive NPV the IRR caot be much more tha the required rate of 27%. FRCPracticeFialExamSprig of 25 Sprig 2006

15 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. FRCPracticeFialExamSprig of 25 Sprig 2006

16 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 \$ 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, A * ( 1.01) 0.01 [ 0.01* ] \$17,000 \$17,000 1 A A 100 [ ] \$17,000 A\$ A FRCPracticeFialExamSprig of 25 Sprig 2006

17 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 %. D %. E %. 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) 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 % B %. C % D % E % 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. FRCPracticeFialExamSprig of 25 Sprig 2006

18 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 Equity 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 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 FRCPracticeFialExamSprig of 25 Sprig 2006

19 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}) \$ millio PopcorNPV NPV(10, (-)2, {0.75}, {5}) \$ millio GraolaNPV NPV(10, (-)11, {3.25}, {5}) \$ 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 % B % C % D % 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 We ca use the formula (3.10) ( ) 1 r FV PV 1 as follows: FRCPracticeFialExamSprig of 25 Sprig 2006

20 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) * P( pd) P(pd) 17/ % 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 FRCPracticeFialExamSprig of 25 Sprig 2006

21 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 FRCPracticeFialExamSprig of 25 Sprig 2006

22 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, \$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 FRCPracticeFialExamSprig of 25 Sprig 2006

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