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MA373 S10 Test 3 Solutions

# MA373 S10 Test 3 Solutions - Spam 920/0 7;7’5 1 Tian...

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Unformatted text preview: Spam, 920/0 7?;7’5 1. Tian purchased a 10 year callable bond with a par value of 10,000. The bond matures for par and pays semi~annual coupons at a rate of 8% per year. The bond is also callable at the end ofyears 6 through 9. The bond is callable at the following values based on the year of call: End of Year Tian buys the bond to yield 6% convertible semi-annually. Calculate the price that Tian paid for the bond. M5 a with nﬂmﬂaée 1:me Lice? fr/v ‘ N LL M T: knew ll, ‘4'“?! 3‘5 H ”530 )iil-lIQOJ'7 H0 10 9’00 / ‘2; [g 10,100 ”I, 49;:‘85 \$29 [@0670 My L187 76¢ 2. A one year bond matures for 1000 and has annual coupons of 50. The price of this bond is 1000. A two year bond matures for 1000 and has annual coupons of 50. The price ofthe bond is 975. A three year bond matures for 1000 and has annual coupons of 50. The price of the bond is 950. Giving all answers as percents to 4 decimal places (e.g. 1.2345%), complete the following table: “Ti/QC \iéﬁfﬁm Bop]: ”71mg, yam“ EMA l 57? ﬁWW if r; = [0.4059 ,. o l 3“ ‘3 950 05b (9 50 +- LI—a—m 3. Ben owns a two year bond with annual coupons of 50 and a maturity value of 1000. Calculate the Modiﬁed Convexity of Ben’s bond at 20% interest. /OOO .. 5 0 5’0 Scott Corporation sells a preferred stock that pays a quarterly dividend. The first dividend, payable in 3 months, is D. Each subsequent dividend is 0.50 greater than the previous dividend. in other words, the first dividend is D, the second dividend is D + 0.50, the third dividend is D + 1.00, etc. If the preferred stock is sold to provide an annual effective yield of 15%, the price of the preferred stock is 500.07. Calculate D. 5 . iv a _ D + _« f 7 >1 . v ~_'___,__. "‘7‘“ "‘ , ’ (7 5730107” L if .035558076 W \$500.07.. klmasssewé 3 3.72., 55599. so“; 919 H—r, C? 33318402.; a; r. : 5,2355% 5. Wang Life Insurance Company issues a three year annuity that pays 40,000 at the end of each year. Wang uses the following three bonds to absolutely match the cash flows under this annuity: a. A zero coupon bond which matures in one year for 1000. b. A two year bond which matures for 1200 and pays an annual coupon of 100. This bond is priced using an annual yield of 7%. ' c. A three year bond which matures for 2000 and pays annual coupons of 75. This bond ‘ has a price of 1,750. It cost Wang 104,000 to purchase all three bonds to absolutely match this annuity. Calculate the one year spot interest rate. 774 'anwaJﬁ) Wad 21.9 4m; W Price ”64226 OYVQ W 2Q“? (EMA CL} Lb waging baa/i élﬁo‘d (”6% I M 3cm} Q “h; Pmrgwo vFVeizoo ZEN-=7 ' arr PV=l228ﬂZ\$3 Earth ‘9 ECLEF ? I750 BDYQ CL 75 ' W7 Z 3 iii? btiaoo)t09.277l03q:>f 33;" C. ~73“ J QCBOCDO quoO‘bﬁ'j’j-"D 3 ‘1 09 + Q L755 *3 ”0/ 000 _ (“(090869 \9\ Cl (C?) + b ( l—SOO) b/flqdp's’nﬁﬁ'na‘r‘zwe ,. tempos) f “ (000)+.(1%.059089®(1<>D>+l?.277l0843l7=)=‘l:3/°" Q I 9.557%?93000)—l9~”wmsw 0893 W a = [(2:29 0 e 5534388507 as i "Pane" Qr: a: 3B) 7‘39‘9'9 Zhang LTD does not currently pay a dividend. However, it is expected that Zhang will pay a dividend beginning at the end of the fifth year from the current date. The dividend at that time is expected to be 20.00. The dividend will be payable annually and is expected to increase by 8% per year. Calculate the price of the common stock of Zhang LTD in order to yield 20%. RP 2906??) 9.00”be w» 5 (a *7 0 ’ W ct.» I? z 7 x H W = ROW—r AOU‘DfQVto-iv A0 (1.06) \I «r , ‘5 O > 5“ 9\O\l , 7. A four year annuity due has annual payments of 1000. You are given the following yield curve: Calculate the accumulated value of this annuity at the end of four years. "““ l 000 -l- 1000 IUD”: +LQE£ H. 8 ﬁt 72;: (11%qu Ll IDOL?” 3000 125.12.. . (35> “ﬁllies”: + Q‘OBS)"+ (3.0%,33 [I \ 3 <3 G .43— 8. A five year bond matures for 20,000. The bond pays coupons of: i. 3000 at the end of the first year, ii. 1500 at the end of the second year, iii. 1000 at the end of the third year, 0 IV. 750 at the end of the fourth year, and II? o g) {90 O \b \ “i v. 600 at the end of the fifth year. Z A ‘ immywimwiwmtwmd Calculate the Macaulay Duration of this bond at 5%. O i ”3' 3 Le 33 v3+ "750 WW: ‘8" ' " V L! +. 410 hoax/5’ . v, taco 1 W ; migl‘it} m )1 @59J905’b 9. You are given the following spot yield curve: Using the spot yield curve, calculate the price of a two year bond which matures for 5000 and pays semi-annual dividends of 160. ) [[90 mo /90 / 0 VV ) 3/2/ 7/ l E g l 4\ 5106:: loo +/ ”F A” «r V, w 0MB NOD L” ”A ’ o 900 __, w + “‘0 + b u ‘" [TS-223' 10. Jacque owns the following portfolio. Macaulay Macaulay --“ 30,000 20,000 “— The price, Macaulay Duration, and Macaulay Convexity were calculated at an annual effective rate of 5%. Calculate the Modified Convexity of this portfolio. ml-lc CONU 1- WW" ME’ Mot/D Cam? 'I’ M m M 60ml F’m’é magenta \l WM" 11. Calculate the modified duration at 7% interest for a 30 year annuity due with level annual payments of 1000. 000 000 lot)" '°°D l l mob buezv (We W15 "2:. at; w “W Eiggjvﬁ er‘le Ma» r: [000020 + I000 M 1000 23:5] ,ooaﬁm 303727 “C: — 2%le , .4EEﬂpw—ﬁ“ 319.43435b : ‘ ”wﬂ,wwrﬁ”“ \$3 \3 1’77b7k" “an a q ne‘ﬁﬁwz’ 12. A twenty year bond is callable at the end of ten years or at the end of fifteen years. The bond pays annual dividends of 100 and matures for 1000. There is no call premium. The cost of the bond is 800. Calculate the minimum yield on this bond. ?/}’)T: /00 pv : /000 P\/ 3’80'0 N . M “‘3’ 13. \$057“ 20 [2.9l3Q WPﬂZ'Q/k: uouﬁééf “TS? g \Sia 0/0 ...
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MA373 S10 Test 3 Solutions - Spam 920/0 7;7’5 1 Tian...

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