IND E 20 Fnal Exam Solutons June 8, 2006 Secton A. Multple choce and smple computaton. [ ponts each] (Verson A) (-) Four ndependent projects, each wth rsk free cash flows, have the followng B/C ratos: Project A B C D B/C 0. 3. Crcle all of the projects that have NPV > 0? a) A b) B c) C d) D e) can t tell 2. Crcle all of the projects that have NPV < 0? a) A b) B c) C d) D e) can t tell 3. Wth an unlmted budget, n whch project(s) would you nvest? a) A b) B c) C d) D e) can t tell. Suppose each project s mutually exclusve and has the same PV of costs. Wth an unlmted budget, n whch project(s) would you nvest? a) A b) B c) C d) D e) can t tell (-7) You ve developed a new medcal devce that recently receved FDA approval. You would lke nvest n formng a manufacturng company to produce and sell the devce. Based on a hurdle rate of % and the large estmated profts you wll earn nto the foreseeable future, you calculate a postve NPV.. Whch of the followng must be true? a) Investng now s optmal snce the estmated Net Present Value s postve. b) Before nvestng you should nvest n market research snce there s a postve real opton value. c) There s an IRR of at least % on the estmated cash flows. d) The estmated payback perod s negatve. 6. If the hurdle rate precsely captures all opportunty costs, whch of the followng must be true? a) Investng now s optmal snce the estmated Net Present Value s postve. b) Before nvestng you should nvest n market research snce there s a postve real opton value. c) There s an IRR of at least % on the estmated cash flows. d) The estmated payback perod s negatve. 7. If the hurdle rate doesn t capture the opportunty cost of delay, whch of the followng must be true? a) Investng now s optmal snce the estmated Net Present Value s postve. b) Before nvestng you should nvest n market research snce there s a postve real opton value. c) There s an IRR of at least % on the estmated cash flows. d) The estmated payback perod s negatve. Page of 8
B IND E 20 Fnal Exam Solutons June 8, 2006 8. You purchased an at the money Call opton on IBM three months ago that matures today. If the return on IBM stock was -0% over ths perod, what s the value of the opton to you today? a) (-.)K b) 0 c) K d) (.)K e) can t tell 9. You wrote an at the money Call opton on IBM three months ago that matures today. If the return on IBM stock was 230% over ths perod, what s the value of the opton to you today? a) (-2.3)K b) 0 c) -K d) (2.3)K e) can t tell 0. You purchased an n the money Call opton on IBM three months ago that matures today. If the return on IBM stock was -0% over ths perod, what s the value of the opton to you today? a) (-0.)K b) 0 c) (0.)K d) (0.9)K e) can t tell (-2) Starbucks recently ssued the followng, Grade A, corporate bonds: A: 3 year, $,000 face value, 0% coupon, P A = $,000 B: 3 year, $00 face value, 8% coupon, P B = $96 C: year, $,000 face value, 0% coupon, PC = $80 D: 3 year, $00 face value, 0% coupon, P D = $86. E: 3 year, $00 face value, % coupon, P E =?. What s the prce, P E, of E? a) $90 b) $9 c) $96 d) $00 e) none of the above 2. What s the 3 year spot rate on Grade A corporate bonds? a).% b) 3.6% c).% d).% e) none of the above (3-) Assume Revenue s lnear n q, Cost s convex n q, and q s non-negatve. 3. If MR(q) > MC(q) then whch of the followng s true? a) q < q b) q = q c) q > q d) F > 0 e) Proft s lnear n q. You re consderng two producton technologes, () and (2), nether of whch affect revenue. If you prefer () to (2) when each s at ts optmal producton level, q, whch of the followng must be true? a) MC ( q ) < MC( ) b) MC ( q ) = MC( ) c) MC ( q ) > MC( ) d) none of the above q2 q2 q2. If TC (q) = 7 + 2q 2 and TC 2 (q) = 6 + q 2 then the break-even volume a.) q b < 3 b) q b = 3 c) q b > 3 d) does not exst Page 2 of 8
IND E 20 Fnal Exam Solutons June 8, 2006 Smple computatons 6. If you make payments of $0 per month on a loan wth 6% nomnal nterest, compounded b-annually, and no fees, what s the effectve monthly nterest rate? r = ( + 0.06 / 2) / 6 = 0.9% 7. Suppose you make the payments n (6) for a total of 0 years. How much dd you borrow? P= 20( P\ A,0.08,) + 30( P\ G,0.08,) + + P = 20 + 30 ( 0.08) ( 0.08) 0.08 2 0.08( + 0.08) 0.08 ( + 0.08) P = 79.2 + 22.7 P = $700.29 8. On a certan pece of machnery, t s estmated that the mantenance wll be $00 at end of year 2 and ncrease by $00 per year through the end of year. What s the Equvalent (unform) Annual mantenance cost f the nterest rate s 6% compounded annually? 0 P = 0( P \ A,0.009,20) = = $,8.7 20 0.009 ( + 0.009) 9. You have purchased a new car and want to depost enough money n the bank to pay for mantenance on the car for the frst years. Mantenance wll cost $20 for the frst year and ncrease by $30 per year. Assume the mantenance costs occur at the end of each year and the bank pays 8% nterest. How much should you depost n the bank? A= 00( A\ G,0.06,) n A = 00 = 00 = $88.36 n ( ) 0.06 + ( + 0.06) 20. You want to be a mllonare by the tme you turn 60 and beleve that you can obtan a % rate of return on your nvestments. You decde to contrbute annually to a mutual fund begnnng on your 30th brthday and endng on your 9th brthday. How much money should you nvest each year to reach your goal? A=,000,000( A\ P,0.,30) 0.( + 0.) A =,000,000 ( 0.) + A = $7,07.0 Page 3 of 8
IND E 20 Fnal Exam Solutons June 8, 2006 Secton B. Short Answer [00 ponts total]. [0] You are evaluatng a cash flow for a large, prvately owned, engneerng frm wth a B grade credt ratng. a) Gven the set of nvestment opportuntes avalable to you, as descrbed below, what s the most you would be wllng to pay today for the cash flow? (amounts gven n thousands of dollars) b) How much are you payng (earnng) n rsk premums? 00 00 0 2 3-0 -00 t (yrs) You wll have to rase captal to cover the negatve cash flows. The postve cash flow n year 2 s from a US government contract; whereas, the cash flow n year 3 s from a contract a wth new start-up company. You re worred that ths company wll not follow through on ther contractual oblgatons (.e., you do not consder them to be as relable as your own company). There are no floatng costs for ssung a bond. Opportuntes Term Bonds/Grade yr 2 yrs 3 yrs yrs yrs Spot US Gvt..% 6.% 6.% 6.8% 7.0% Rates Corporate/A 6.0% 7.0% 7.% 8.0% 8.% Corporate/B 6. 8.0% 8.% 9.0% 9.% Corporate/C 8.0% 0.0%.% 3.0%.% Yelds US Gvt. 3.% 3.% 3.9% 3.9%.% Term Bank 6.% 8.% 8.0% 9.% 9.7% Loans Bank 2 6.% 8.% 8.3% 9.% 9.7% (APR) Bank 3 6.3% 7.7% 8.2% 9.2% 9.3% Soluton: a) [30] For each separate cash flow you have to determne whch opportuntes are comparable (n terms of rskness) and among the comparable alternatves, whch one consttutes the best alternatve opportunty. Year : Comparable Opportuntes ssue a B rated corporate bond at 6.% nterest, or take out a year term loan at 6.%, 6.%, or 6.3% nterest. The best avalable opportunty s borrowng $00,000 from Bank 3 at 6.3% nterest. Year 2: Comparable Opportuntes Purchase a 2 year US zero-coupon bond that pays 6.% nterest. Year 3: Comparable Opportuntes Purchase a 3 year C-grade zero-coupon corporate bond that pays.% nterest. Year : Comparable Opportuntes ssue a B rated corporate bond at 9.0% nterest or take out a year term loan at 9.%, 9.%, or 9.2% nterest. The best avalable opportunty s ssung a Grade B corporate bond payng 9.0% nterest. PV = 00.063 + 00 (.06) 00 + (.) 0 (.09) = 2 3 $3,77 b) [0] The rsk premums are the nterest rates used above subtract the US bond rate for the same term. They are 0.8%, 0%, %, and 2.2%, for years, 2, 3, and, respectvely. The boldface premums are those that you pay as a class B frm. In year 2 you do not earn a rsk premum snce the cash flow s wthout rsk; whereas, n year 3 you earn a hefty % premum snce you re dealng wth a clent that s lkely to default. Page of 8
IND E 20 Fnal Exam Solutons June 8, 2006 2. [30] You are lookng for debt only fnancng of a potentally lucratve R&D project wthn your company. Your company prefers a debt mxture of approxmately 80% term debt and 20% bond ssues (Grade A wth annual coupon). For ths project the bond maturtes and loan term wll each be years. For year term loans your commercal bank charges 8% nomnal nterest, compounded quarterly, plus a 3% handlng fee deducted drectly from the ntal loan amount. The loan wll requre annual payments begnnng year from today. To ssue a Bond you wll pay the nvestment bank a 7% floatng charge. Suppose you ssue 22 par bonds, each wth a face value of $,000 and the spot rates and your rsk premums gven at the rght: a) How much wll you rase from the bond ssue? b) What coupon rate must you pay on the bond? US Bond Spot Rates A Grade Rsk Premum yr 2 yrs 3 yrs yrs yrs.3%.9% 6.3% 6.8% 7.0% 0.7%.%.2%.2%.% c) If you need $00,000 to fnance the project, how much wll you need to borrow wth a term loan? d) What s your APR on the term loan? e) Calculate your annual payment on the term loan. f) Draw a table and/or cash flow dagram descrbng your overall fnancng. What s the present value of ths cash flow and descrbe, n words, what t tells you? Soluton: a) [] Par bonds mples you sell them each for the face value of $,000. Takng out the floataton charge you are left wth $22,000(-0.07) = $20,60. b) [] To make t a par bond, C must satsfy:,000 =,000C + + + 2 3.06.07.07 C = /.02 = 8.33%.08.08 +.08,000 +.08 c) [] After fees have been deducted you wll need $00,000 - $20,60 = $79,0. So you wll need to fnd X satsfyng X( 0.03) = $79,0, mplyng that X = $82,000. d) [] Ignorng the loan fees, the effectve annual rate of nterest s ( + 0.08 / ) = 8.2%, but we have to account for the 3% fee n the APR. Instead of $ n debt today growng to $.082 n a year, we have $0.97 growng to $.082, so the rate of growth n our debt s actually r =.082/ 0.97 = 8.% e) [] A = rp /[ ( + r) ] = (0.08)(82,000) /[ (.08) ] = $20,807. 80 f) [] In $,000: 00 0 2 3-22.6 t -.6 Page of 8
IND E 20 Fnal Exam Solutons June 8, 2006 Year Bond Loan Net 0 20,60 79,0 $00,000-22,000(0.0833) -20,808 -$22,60 2-22,000(0.0833) -20,808 -$22,60 3-22,000(0.0833) -20,808 -$22,60-22,000(0.0833) -20,808 -$22,60-22,000(+0.0833) -20,808 -$,60 Snce the cash flows are rsk free, to fnd the NPV we dscount usng the spot rates: NPV 22 22,000 =,60 + + + + + 00,000 = $9,766 2 3.03.09.063.068.07.07 Ths s the equvalent prce you would have to pay today to fnance your project (n addton to the $00,000). Page 6 of 8
IND E 20 Fnal Exam Solutons June 8, 2006 3. [30] Consder a modfcaton of the pzza delvery captal budgetng problem. You wll run the busness out of the UW resdence halls for the next four years, use a 0% MARR, and pay a tax rate of 30%. You are consderng the purchase of at most one of the followng four alternatves. As long as t has value, you wll salvage any vehcle after year. The Moped and Vespa each lose $200/yr n resale value. ) A new 0cc Moped has a cost bass of $,000 and a year useful lfe. 2) A used 0cc Vespa has a cost bass of just $600, but only a 3 year useful lfe. If you purchase a Vespa, after 3 years you wll replace t wth another Vespa at the same prce. 3) A 0cc Wldfre has a cost bass of $,00 and a useful lfe of years, but provdes $200/yr more n after tax profts than a Moped ) A used 800cc Harley Davdson has a cost bass of $7,000 and a useful lfe of years, but provdes $,000/yr n after tax profts You are also consderng an expanson of your busness by purchasng a new mega-toaster oven for your dorm room. If you expand, you wll be forced to purchase ether the Wldfre or the Harley to be able to delver the extra pzzas on tme. You have estmated the pre-tax cash flow of the oven n the table below (data s n $00 and assumes you re able to delver all of the pzzas). The oven s n the 3 year property class and has the followng MACRS schedule, whch swtches from.db to SL deprecaton n year 3. Tme Pre-tax cash flow 3 year MACRS Deprecaton Book Value Taxable Income Tax After tax cash flow 0-2 0 0 2 0 0-2 7 33.33% 2 3..% 9.3 3 3 % 9.3 % a) Usng the assumptons of MACRS, fll n the detals of the above table and determne the NPV of busness expanson. (Round the deprecaton values up to two decmal places, as n yr 2 above.) b) The Moped and Vespa alternatves wll brng n $3,300 per year n after tax profts and you have a $9,000 budget. Gvng specfc values for each parameter, formulate an optmzaton problem to fnd the best mx of alternatves. (Hnt: consder how salvage values wll affect your budget.) c) By nspecton of (b), what choces do you thnk are optmal? Assume the oven has no salvage value. Soluton: a) [0] Tme Pre-tax cash flow 3 year MACRS Deprecaton Book Value Taxable Income Tax After tax cash flow 0-2 0 0 2 0 0-2 7 33.33% 7.00 0 3 2 3..% 9.3.66 3.8. 2 3 3.8% 3.2. 0 0 3 9.3 7.%. 0 7.8 2.3 7 Usng the usual formula we fnd a NPV after taxes of $8,680. b) [] Let x = f we nvest n transportaton alternatve, and x = 0 f we do not nvest n ths alternatve. Let x denote the bnary decson of whether or not to nvest n the busness expanson. We formulate the optmzaton problem as follows: Page 7 of 8
IND E 20 Fnal Exam Solutons June 8, 2006 max s. t. = = c x = $9,000 x p x Max NPV Budget Mutual Excluson x x3 + x Expand only f buy Harley or Wldfre x = 0 or for = to Yes/No Decsons x There are two challengng parts of ths problem. One s defnng the expand only f constrant and the other s that salvage costs reduce your costs and may make otherwse nfeasble alternatves feasble. Note we could have wrtten the constrant as: x3 + x x 0. The parameter values are as follows: p = PV(benefts) + PV(salvage - costs) = PV(benefts) + c for opton (n $,000) p = (3.3/0.)[ - (.) - ] + [0.2(.) - ] = $9,280 p 2 = (3.3/0.)[ - (.) - ] + [0.(.) - (0.6 + 0.6(.) -3 )] = $9,366 p 3 = (3./0.)[ - (.) - ] + [0.] = $9,278 p = (/0.)[ - (.) - ] + [0 7] = $8,89 so the parameter values are: c p $863 $9,280 2 $778 $9,366 3 $,00 $9,278 $6,37 $9,32 $2,00 $8,680 c) [] Buyng a Harley and expandng wll gve you the maxmum NPV = $8,22. Lookng strctly at ntal costs, ths alternatve appears nfeasble ($7,000 + $2,00 > $9,000), but recoverng the salvage value reduces the effectve cost of the Harley enough to make ths opton feasble. Page 8 of 8