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**Unformatted text preview: **ﬁ- §OLUTIMI§ *- Midterm Exam
Cal Poly
Fundamentals of Finance
Finance — 342
Professor Larry Gorman
Fall 2006 Circle your answers. Put your name on the back of the last page. You have 1 hour and 50 minutes The exam is closed book and closed notes. Make sure you show ALL work, typically in the form of equations. Use a minimum of THREE signiﬁcant digits in all calculations. Partial credit for numerically correct answers not supported by an appropriate amount of work will not be given. Good luck. ‘4 52/
1 4 You are considering investing in Vanguard's S&P-500 Index mutual fund. You wish to determine the fair price for the S&P-500. The current actual price of the S&P500 is $1 144. You have decided to use a 2 stage dividend growth model. 0 The current market value of the S&P500 productive equity (=E0 (or =BV0) in the notation of the course) is $652/share. o In the ﬁrst stage of growth, which runs from today through the next 15 years, the ROE is expected to be 1 1.3% per year (nominal). During
this time the dividend payout ratio is expected to be 25%. o In the second stage of growth, which runs from the end of the 15‘h year to infinity, the ﬁrm ROE is expected to be 9.5% per year. During
this period, the dividend payout ratio is expected to be 38%. 0 The appropriate discount rate to use in valuing the stock is 10.3% (nominal) per year. 0 Inﬂation is expected to remain constant at a level of 2.1% per year. 0 Determine the fair value of the S&P-500, given your assumptions. Circle your answer. 3‘40 ‘5” é -0 ': (PMOJT: =(9?aj(.ii§\(.2s3 slam I
D. , (ﬁe-voyaou) > , 0-471 %’ :CROE)‘ i £79» —'~ (.112.>><.'7$B = paw—'75 Fade-“3 DUI/b gd ask—— N aunties-1“? 77> ,, I5 '9 é ‘ié.
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$ $77. 5;;
mega. $(ﬂog :é’oqa> (1’35) 9.55870 Maw ’0’ *‘7 °° 77% CF" D/AcizAM Lama; LIKE: (at, 2A. You have been given the price of US Treasury bonds below. Assume that these bonds pay annual (not semi-annual)
coupons. Construct the ‘term structure’ (i.e. the yield curve associated with zero coupon bonds) through t=4 years. Use the supplied Graph. Maturity Coupon Rate Actual Price
1 year 0% $941.34 $
2 year 0% $880.96 €399 3 year 0% $811.22
4 year 8.2% $1,042.44 ‘ CW7: . @V/Zéﬁmj 21%- Cam’s“? r—r'w‘v-Wmimmw zm—wvlq .43. ‘ ,L “7%? “f/ 51.0 (5: M axe: / W,sz Svadci‘w “55' ’\ f§~ Aéma w/ zww a.) 45“ WW. /i/ 2B. What is your best guess as to what a 2 year zero coupon bond will be selling for in 1 year? \ That is, What is the expected dollar price of a 2 year zero, one year from today? We” WANT“ K“ r t 3 ’
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(/‘07225535 {LO/pZEZj I+ 2C. Given the yield curve in question 2A, compute the price you would expect a 7%, 4 year Treasury bond to be selling for?
(assume it pays annual coupons). Circle your answer. 30‘70
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AZEWEAME W’ZTVNW‘. (0 Question #1 continued:
2D. Now assume that the 7%, 4 year coupon bond in question 2C is actually selling for $931.25 Is there an arbitrage opportunity here? (Answer YES or NO and circle your answer). If YES: How would you take advantage of any arbitrage opportunity. Be VERY speciﬁc. That is, using the
matrix provided below, tell me exactly what trades you would make (both buying and selling and the appropriate quantities) in order to make a sure (arbitrage) proﬁt. If NO: Show that an arbitrage does not exist. Use the matrix below to support your arguments. (i.e. show the
proﬁt from the possible arbitrage trade is zero). What is the arbitrage proﬁt you earned? NOTE: Assume that the only market that for zero coupon bonds is for zero’s with $1000 face values (i.e. you
cant sell a zero with, say, a $50, $70, or $100 face value). 7%.)?" ACW’Qw-I- PWﬁé «1’3" “ﬁber: £4.12»! (93/, 25*) Pacng
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7“ lag/.459 615/29: 7043. Ac'wﬁc— —- Name, = mp5 tram/47.
BuyorSell? Which bond What is the coupon What is it’s price? What quantity are Required Cash
maturig are you rate of the bond? you trading? Flow:
buyin; or sellin? l MW_WWW;IEZ
_ .- Continue work on next page if necessary... 3.
You have been offered the following investment: For the low, low price of $572 (paid now) you can obtain the right to a positive cash ﬂow stream of: 0 $120 paid to you 5 years from now, thereafter shrinking at an annual rate of 3%, for a total of 12 years. That is, you
receive cash in-flows at t=5, 6, , 16. (The nominal CF at t=5 is $120, the nominal CF at t=6 is 3% smaller etc...) o In addition, you will receive $70 (nominal) in twenty years, which will grow at a 5% nominal rate forever. (i.e. you get
$70 at t=20, $73.50 at t=21, etc. forever (i.e. a perpetuity, starting at t=20, with 5% nominal growth). - What is annualized effective (nominal) rate of return will you earn if you purchase this investment? Circle your answer. 7314? CF WMéL/A/éf 5: 509 A w 1 0 LWM4 ,
t 3 4' 5 {7 [b 20 2‘ ;& W W
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$170,, Mow; )[lom/ ’-’° 4610:05) ’-’° = 72;.27 60W 4. You just turned 24 years old and you are thinking about starting to save for retirement. You already have $2500 saved but
you know this is not enough. Unfortunately, you have a low paying job (because you didn’t learn ﬁnance Well) and so you are in
no position to begin making payments into a retirement account now. Instead you have decided to defer saving until your 35th
birthday (in II. years). At that time you will save 4% of your salary, and you will continue to save 4% of your salary each year
until you are 55 years old (i.e. you will make deposits on your 35’“, 36th, 54th and 55‘h birthdays). Your current salary is
$40,000/year, and this is expected to grow in £211 terms at 2.6% per year until you retire on your 65th birthday. All funds invested into the retirement account, including the existing $2500 balance, are expected to earn an inﬂation adjusted
(i.e. r_e_a_l) return of 6% per year forever. You plan to begin withdrawing funds from the retirement account on your 65th birthday. You will make a total of 20
withdraws (on birthdays 65, 66, 84). Each withdraw will be smaller than the previous withdraw by 1% in nominal terms.
The expected inﬂation rate is 3.6% per year. What is the nominal size of the withdraw you will make from the retirement account on your 76rd birthday? Circle your
answer. In Haw—AW 3 % .7 V f A , g. w... r... g F; A L L ptpos t g$ / LV
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f2;2( ,;2+,0§)Zf {73/ == $59? Z”?- N am L/NEWL szpa M72” 1' 35.0L> $7. 2. a L
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@4770: 3/5127 = .20/ X= ,/2 — ,20/{.oz> {#600 M w 1212:”.(002 1’ cf? I K v k x g! \uw“.
:- § Z $6253 ’ ' 40
ﬁi‘ejfﬂ’f + * *r 25:» a} 2f“ " a 5g“ E 'V " E / \E
ff 1“: g a. a“: rgv;> r 3 4’2]?! g.» A'ng ' _‘ ‘\ ff, g
= M/ 775 163’ ‘ W/mbﬁﬂg/ 731%: PM 0%: 7W5 “117%”ng M685?” £1§VAL> a» «f m A/om / “’“(ﬂ‘a/x
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