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FIN301Reserve - mi W‘s Him Q31:3 ifffltfi FIN301...

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Unformatted text preview: mi W‘s- Him Q31; :3 ifffltfi FIN301 MATERIALS topic of "capital hxdgetjng." Therefore, it Rakes sense to get used to ' seeing and dealing with them early on. Good luck ) End of Period cash Flows r Situation A situation 13 find 0“ Year I EEEEEEEEEEE—"§§§§§i£§ Withdrawals Eggggigg 0 $300 ' I " $40 1 R ,40 2 R V _ ' I 30 —n— 3 I R 40 4 “0— 40 a R 40 6 R 4c 7 1 7b :20 8 ' I 70 4o 9 30 4o 10 . 30 4o 11 30 ???? _ _ ._ ___._—___.__ {Qdestions appear ing on the following two gages refer to the table above.) NOTICE: This Manama: May 556 Pratede . By Copyright Law {We S?.-U.S.'.Codel - Nona-z: This Mafia? May 39 $th By Copyright Law {Title 1? US. Genie} 1. Situation A. Assmre'that you deposit $300 today in a savings account paying 6% compound annual interest. Given the pattern of cash withdrawals pictured in the table, what equal periodic withdrawal (R) can you make at the end of years 1, 2, 3, 5, and'6 such that your ending balance (after the last withdrawal in year 11) is zero? [Show your work in detailed step-by—step fashion and identify any interest factors used as to type, rate, and number of periods - e.g., (PVIF6%’10 yrI).] Answer: (lO'PtS-) Situation A: d 1 - 2 3 A 5 6 7 3 9 L9 11 -|.___.___I_.._..__ l____._1______l_______l_____ l___.__|v_____l-,_a‘_,___I-_____,_I_____l i l’ 3 l l I I I I \l f I ~3oo R R a o R R‘ 70 10 3o 30 3o : :_ : : : Y : : : (123.31) : E : Y* < ------------------------------ --: : J .: (90.46) : I i : x (80.19) - x# < ------------------------------------------- -—: (50.28) 1. Y. = (70)(PVIFA62,2) = (7o)(1.833) = 123.31 Y* (128.31)(PVIF 62,6) (128.31)(.705) = 90.46? 2; x_ a (30)(PVIFABZ;3) ' 2-féo)(2.673)»='80.19-' x* = (so.19)(pvxrsz'8) (80.19)(.627) = 50.23 it So 300 - 90.46 - 50.28 = 159.26 159.26 = R(PVIFAGZ$6) - R(PVIF62’4) 159.25 = a(4.917) - R(.292) = R(4.125) R = 159.26/4.125 = 38.61 e‘g" ( 6%,10 yr.)‘] ' Answer: (10 pts,) Situatiéfi‘h: ‘ a i 2 3 A 5 6 7 a 9 La 11 l_____‘___,__I_____l_____I_____I______l_______l______l_____I______l'_.____ Ir 5 I I 7: I I- n n l | l- I 40 #0 40 -3 40 40 A 20. 40 40 40 l—-—-- --—-- ----- ----- -~--— ----- ----- ----- -—-—- --> X minus ‘70 i : -------------------------------------------- u> Y 20 a I _ _ : ----------------- --> z .. I. X = (AO)(FVIFA62,11)(1.06)A ... annu1ty due = (40)(1A,972)(1.06) = 634.31 I g: ?'= (7o)(rv136z;8) = (io)t;.594)‘=-111.5s 3. z = (20)(FVIFGZ A) = (20)(1.262) = 25.24 X.-_Y - ZI= 634.81 - 111.58 - 25.24 = 497.99 “MU 531 “'"'"' HW’QLI ANNUITY PROBLEMS Dr. Wachowicz Finance 301 Frame A: Cash receipt at the END of year ... time f 0 l 2 3 4 _5 6 7 8 9 10 l I l I I l | l I l i ____1__l__l—_I____l-_—_l_—_.l—IiH____l___-l___-_l___| $ : A A R. R R. R. A A (a) (b) (c) (d) (e) , ' (f) Frame B Cash receipt at the END of year time E 0 l 2 3 4 S 6 7 8 9 10 I I I I I I i l I I l ._.__l_l____l____i___l___l____l____i_,___l___l___l.____l s i A A R R. R. R. A A (g) (h) (i) ' _ r ' (j) (k) (l) 1. Assume that the time lines in Frames A and B (above) depict annual cash flows of R dollars at the ends of the periods indicated. If the appropriate compound annual interest rate is 8 percent, what stream depicted in Frame A or Frame B equals $1,000 as of point (a)? point (b)? point (c)? point (g)? point (h)? point (i)? 2. Assume that the time lines in Frames A and B (above) depict_annual cash flows of R dollars at the ends of the periods indicated. If the appropriate compound annual interest rate is 8 percent, what dollar value does R take on if the future value of the cash flow stream depicted in Frame A or Frame B equals $1,000 as of point (d)? point (e)? point (f)? point (j)? point (k)? point (1)? Answers: Question 1 -- When the present value of the cash flow stream depicted in Frame A or Frame B equals $1,000 at point , R equals (a), $292.23; (b), $250.44; (c), $231.91; (g), $364.83; (h), $312.60; (i), $289.44 Question 2 -- When the future value of the cash flow stream depicted in Frame A or Frame B equals $lr000 at point , R equals (d), $170.44; (e), $157.83; (f), $135.28; (j), $212.72; (k), $197.01; (1), $168.83 .NOH ,OE: This Mamie-F ‘Ma' ‘ ' it _ , y Ba PM vs Shamang Lew mus I=7v££35mdixm annuity.def (revised) time § 0 1 2 3 4 5 6 7 3 9 10 _____I_ml_____1_____l_____I___h_1___,_I_____£,____1_____i_____I_____l $ I A R R R , R R R(PVIFA8% ’ 5)<_1__1—_1___I__1 (a) $1,000 <Hm——~—J , $1,000 -= R(PVIFA8%’5) x (PVIFBELZ) $1,000 - R(3.993) x (.857) — R(3.422) R - $1,000/3.422 = $292.23 when the present value of the cash flow stream equals $1,000 at point (a) time : 0 1 2 3 4 5 6 7 8 9 10 I I I l I I I I l I I l___l______l___l—__I______I_____l_—__l____l___l___l I $ 1 R R R R R $1,000<J__1—1*'I_*1 I (b) $1,000 s R(PVIFA8%'5) $1,000 :— R(3.993) R - $1,000/3.993 - $250.44 when the present value of the cash flow stream equals $1,000 at point (13) time , 0 1 2 3 4 5 6 7 8 9 10 I I l I I I I 1 l l I I I___l____1___l_,__l_____l___l___l__l______l___l____ $ 1 R R R R R $1,000<_I“1—I__I l (c) $1,000 = R + R(PVIFA8%’4) $1,000 = R + R(3.312) - R(4.312) R = $1,000/4.312 =- §231.91 when the present value of the cash flow stream equals $1,000 at point (C) IR + 23511? : 45,? u ‘ annuity. def (revised) time I 0 1 2 3 4 5 6 7 8 9 10 I I ' I I I I I I I I J 5 I __—__ Rf———1§——__1{hf—*hf__h—Rf——fih _——__ h———_ L_1_L_J_‘ > $1,000 ((0 $1,000 = R(FVIFA8% 5) - R(5.867) R - $1,000/5.867 - $170.44 when the future value of the cash flow stream equals $1,000 at point (d) time I 0 l 2 3 4 5 6 7 8 9 10 I I I I | I .I I I I I _.'__I___I_____l—_I___I___,_I___I____I___I_____l_—I,___I $ : R R R R {R wfilfoo 0?) $1,000 2 R(FVIFA8%’5) x (1.08) $1,000 - R(5.867) x (1.08) - R(6.336) R = $1,000/6.336 a $157.83 when the future value Of the cash flow stream equals $1,000 at point (e) - time I 0 l 2 3 4 5 6 7 8 9 10 l I l I I I l | I I | ] ____I_l.____l_____l_,_l____l______.l_____l___l__l_____l_____ $ : R R R R R I I l . >R(FVIFA8% , 5) Ifixlfioo l (f) $1,000 = R(FVIFA8%IS) x (FVIF8%'3) $1,000 - R(5.367) X (1.260) - R(7.392) R = $1,000/7.392 = $135.28 when the future value of the cash flow stream equals $1,000 at point (f) annuity.def (revised) —_..._._.._..—_—._——__._ ' R R R R R <.______h_J minus R $1,000 - {R(PVIFA8%;5Q x (PVIF8%’2)} - R(PVIF8%’5) $1,000 - [R(3.993) x (.857)] - R(.601} S $1,000 a R(3.422) — R(.681) - RC2.741) R - $1,000/2.741 - $364.83 when the present value of the cash flow stream equals $1,000 at point (g) annuity.def (revised) time —......_——.—.—._..—_'_—._._.——___...__ The above pattern is equivalent to R R R R R <p_e_eJ_____J_____J_____J_____J minus <%__—__l $1,000 a R(PVIFA8%,5) - $1,000 = R(3.993) - R(.794) c R(3.l99) R - $1,000/3.199 a $312.60 when the present value of the cash flow stream equals $1,000 at point (h) -—..._ R. R R R R i_Ll__l__l minus R <_____~___e_J $1,000 = R + R(PVIFA8%’4) - R(PVIF8%’2) $1,000 - R + R(3.312) - R(.857) = R(3.455) R - $1,000/3.455 - $289.44 when the present value of the cash flow stream equals $1,000 at point (i) annuity.def (revised) time : 0 1 2 3 4 5 5 7 8 9 10 I I I I I I I I I l I ______I‘_I_____I—__ ____l____f___,__l____l_____l______1_'___l_,__l $ : R R R R LJ‘_L’ > $1,000 (5) mi nus R g) $1,000 - R(FEIFA8%’5) - RCFVIF8%’2) _$1,000 = R(5.8§7) ~ R(l.166) a R(4.701) R = $1,000/4.701 = $212.72 when the future value of the cash flow stream equals $1,000 at point (j) annuity.def (revised) time } 0 l 2 3 4 5 6 7 8 9 10 I_! i E E 1 E F i i I I 3 t R R R R w>$l , 000 l (k) , The above pattern is equivalent to R R R R R l‘l——'_L_[‘> minus R $1,000 = [R(FVIFA8%'5) x (1.08)] — R(FVIF8%,3) $1,000 = [R(5.867) x (1.08)] - R(l.260) $1,000 a RC6.336) - R(1.260) 4: R(5.076) R - $1,000/5.076 - $197.01 when the future value of the cash flow stream equals $1,000 at point (k) annuity.def (revised) -___————_-—_._ minus $1,000 - [R(FVIFA8%,5) x (FVIF8%,3)] - R(FVIFv8%,5) $1,000 = [R(S.367) x (1.260)] - R(1.469) $1,000 - R(7.392) -_R(1.469) - R(5.923) R - $1,000/5.923 a $168.83 when the future value of the cash flow stream equals $1,000 at point (1) annuity.def (revised) V'V‘Gu div-Vii UH run-vy- i s i . RESERVE " Exam, 7x 1 no Not REMOVE STAPLES NOTICE: This Material Hay Boflrotect‘ed By .Copyright LawlTxtle IT U.S. Code} ‘ FINANCE 301 I PINK exam Dr. Wachowxcz Second Exam Fall 1990 PRINT your name here: SIGN your name here: ___._________________“________. Max. Estimated Time in Minutes Qfl Max. Pts. ‘1 M 3 1 6 lees-easescooe ' f 3 2 6 III-cocooeo-uo 99‘0 “o I . 3 3 6 IOOCOOCICICIOO ‘3' o M ‘0‘ 99' v3 ' bl: v0 3 A 4 III-IOOI'OIIIO- . 0 ’ (M 0 “9 IQ 9 5 CIOUIIIOIIICII / Irv/9M (ED 7 6 13 {3 1o 7 15 19 8 .11 _.__.._.__..__. 48 I? RESER¥E_ROOM flew a) To get any credit, you must show your work on problems. Calculations must be expressed in a manner which clearly indicates the nature of the formulas and/or logic used. b) It's quality of work, not quantity, that counts. c) no NOT mm THIS 300nm APART. - d) Make sure that you have all six (6) pages of questions plus fun: (4) pages of Present and Future Value tables before you beg:n!!1!! 9) PRINT your name on the very back of this booklet. f) Budget your time -- see estimated time in minutes for each question. ‘ 8) RECEIVING OR GIVING AID IN AN EXAMINATION 15 A CAUSE FOR DISHISEQL FROM THE UNIVERSITY. FOR USE IN NOTICE: This Maternal May Be Protectda IBy Copyfight.LsnvilhflatIZFUJEZGBdel “,4: yM/IQ“~ 74.314! - 0. fl Q A. I - V I “it. 1. Which amount is worth more at an 8 . $2,000 today or $3, work.) (6 pus.) [ J $2,000 today is worth more at 8!. $3,000 received after 6 years is worth mere at 82. at 82, both are worth the same. will increase his weight at 3 Currently. he weighs 150 pound percent a year. birthday? . What will he weigh on his 60th Answer: (6 pts.) “ ~05fl1 can 4W.m 1 3. Roy's Orbs & Sons, Inc. stock isaue outstanding. On January 1 the market price per share is $70. Dividends are pa' id annually on December 31. If you require a 14 percent annual return on this investment. what is its value to you (on a per share basis) on January 17 4. In connection with the U.S. Bicentennial, the U.S. Treasury once contemplated offering a savings bond for $1,000 which would be worth $1 million in 100 years. What compound annual interest rate is implied by these terms? (HINT: make use of the formula at the top of one of the Tables.) Answer: ________ (4pm.) A. C. -I.a (u. The future value of this annuity is calculated as of one period after the last cash flow. (3 pta.) a. _ ordinary annuity b. annuity due c. simple annuity The market value of a firm is the higher of its or its ... (3 pts.) going-concernhvalue a. book value. ' b. intrinsic value. c. liquidation value. A zero-coupon bond would most likely be originally sold at (a) (3pts.) a. discount. b. c. premium.‘ par. If a bond sells at a discount. then its yield-to-maturity (YTM) is _______________ its coupon rate. (3 pts.) a. less than L?' b. greater than c. equal to ' If the constant dividend growth model was appropriate to apply to a particular share of common stock, the market-dc ermined ield on the common stock would be equal to ... (3 pts.) a. 01/(ké-'s)' . . .b.- (DI/Po)+-s c. (Di/P0) . The approximate zield-to-matugitx on a bond can be thought of as ... (3 pta.) a. (average annual income)/(average price). b. (annual interest payment)/(average price). c. (P1 - Po)/PO. M— 6. You have a choice of purchasing a one (CD) from 2 different banks. Bank A of 12.352, compounded yearly. Bank B of 122. compounded quarterly. ~year certificate of deposii quotes a nominal annual rat: offers a nominal annual _rate A. What is the effective a nnual interest rate (or APR) on the CI from Bank A? . Answer: ' (5 pts.) B. What is-the effective annual interest rate (or APR) on the CD from Bank B? Answer: _ (5 pts-) C. (Briefly) Which CD should you buy and why? [ ] Buy the CD from Bank A. Buy the CD from Bank B. Because ... (3 pts.) ‘,- ,“I '1" .‘Ae— 7. The 10 percent coupon rate bonds of U.S. Blivet Corporation have 12 years remaining to maturity. The current market value of one of these $1,000 par value bonds is $800. Interest is paid semiannually, Tammy Whynot places a nominal annual required rate of return of 14% on these bonds. A. What dollar value would Tammy place on one of these bonds (assuming semiannual discounting)? Answer: (10 pts.) B. What is the current yield on one of these bonds? Answer: (5 pts.) t2301.f90 8. Assume that you will be open a savings account today by depositing $100,000. The savings account pays 6% compound annual interest. One year from today you will start making withdrawals to achieve the following pattern of cash flows over time. (NOTE: Today is time period zero; one year from today is the end of time period 1; etc.) Cash deposits at the END of year ... time} 0 l 2 3 4 5 6 7 8 9 I I I I I I I I I I I I I I I l I I I I I I ____l_l______I______I______I______l_"_m“mlhh____l______l______l______l I I I I I I I I I , I I $ l R R R 9,000 9,000 9,000 9,000 9,000 9,000 How large must each identical R Withdrawal be to leave you with exactly a zero balance after your final $9,000 dollar withdrawal is made in year 9? Answer: (12 pts.) t230l.f90 TIN" ,81.1t11r0..701110111t01'001 70-0002 _ r - .‘ '-, 'l of $1 01: 12 at the 81111 of .n_P01.-10d0 (Purim) ' n . '.' - (“H.011 533‘}. 96:..‘1; . . . z" a. _ ‘ .l, f 1701' I 0" 1.000 1.000 1.000,. L _ _--- . j 1 1.010 1.020 1.000‘ 1.040 . ._ . ' 1.000 .i_ 2' 1.020 _1.040 1.001 1.002 [1.102)- 1.124 __ 1.140 1 1.100. 0 1.000 1.001 1.000 1.120 “4.100 1.101 1.220 ' 1.200, '4 1.041 1.002 -1.120 1.170 1.210 1.202 1.011 1.0017 0 1.001 1.104 1.100 1.217! '1.270 1.000, 1.400_ .1._400I'_ 0 1.002 1.120 1.104 1.200. 1.040 1.410' 1.001 1.007 f ‘ 7. 1.072 1.140 1.200 1.010 1.407 1.004 1.000 1.714" .0 1.000 1.172 1.207 1.000 1.477 1.004 1.710 , 1.001 .0 1.004_ 1.100 - 1.000 1.420 . 1.001 1.000 1.000 1.000 10 1.100 1.210 1.044 1.400 1.020 1.701 1.007 2.100 11 1.110 1.240 1.004 1.000 1.710 1.000 2.100 2.002 12 1.127 1.200 1.420 1.001 1.700 2.012 2.202 2.010 10 1.1001 1.204 1.400 1.000_ 1.000 2.100 2.410 2.720 . .. ' . ., 14 1.140 1.010 1.010 1.702 1.000 2.201 2.070 2.007 . . - . 4.007.:-' 0.001; 10 1.101 1.040 1.000 1.001 2.070 2.007 2.700“ 0.172 0.042 4.177 4.700 0.474 ‘ 0.20.1; 10 1.170 1.070 1.000 1.070 2.100 2.040 2.002. 0.420 0.070 '4.000. 0.011 0.100 " 7.0013 17 1.104 1.400 1.000 1.040 2.202 2.000 0.100 r 0.700 4.020 0.004 0.000 0.000 7.0013 10 1.100 1.420 1.702 2.020 2.407 2.004 0000 0.000 4.717 0.000 0.044 7.000. 002-, 10 1.200 1.407 1.704 2.107 2.027 0.020 0.017 4.010 0.142 _0.110 7.200 0.010______ 19.103; 20 1.220 1.400 1.000 2.101 2.000 0.207 0.070 4.001 0.004 0.720 0.002 0.040 11.02:; 24 1.270 1.000 2.000 2.000 0.220 4.040 0.072 0.041 7.011 0.000 I 12200 10.170 10.701}- 20 1.202 1.041 2.004 2.000 0.000 4.202 0.427 0.040 0.020, 10.000 10000 17.000 21.20;. 00 1.040 1.011 2.427 0.240 4.022 0.740 7.012. 10.000 10200 17.440 22.002 20.000 00.1111 40 1.400- 2.200 0.202 4.001 7.040 10.200 14.074 21.720 01.400 40.200 00.001 00.001 102.701?E 00 1.040 2.002 4.004 7.107 11.407 10.420 20.407 40.002 74.000 117.001 104.000 200002 400.701.- 00 1.817 8.281 6.882 10.620 18.878 82.988 67.948 101.267 178.081 804.482 624.067 887.697 - . . ...- - —-.-........ .. ......._.—...—‘.-Q; ,._.. . . I I i 1: 115111017. . ‘.- I 77 14"» 15".. 16% 17% 18'1- 199. 10'}. 14'.- 1890 3196 _..._.. .. ————-—-——..__.—.__________ ' 0 1.090 1.000 1.000 1.000 LM 1.1181 1.1817 1.1!!) 1.000 1.000 I 1.148 1.150 1.160 1.170 1.180 1.190 1.100 1.140 1.180 ‘ 1.810 1 1.100 1.311 1.346 1.369 1.391 1.416 1.440 1.538 1.688 1.741 3 1.481 1.511 1.561 1.601 1.648 1.685 1.718 1.907 1.067 2.000 4 1.689 - 1.749 1.81 1 1.874 1.939 1.1785 1.874 1.364 1.684 8.1136 5 1.915 1.01 I 1.100 1.191 1.188 1.886 1.488 1.931 8.486 4M? 5 1.195 1.318 1.486 1.565 0.700 1.8411 1.986 8.685 4.898 5190 " 2.501 1.660 1.816 8.1811 8.185 8879 8.583 4.5“ ' 5.619 6.988 I ‘ I 1.858 3.059 8.178 8.511 8.759 4.811 4000 5.590 7.186 9.117 8 8.151 8.518 8.808 4.108 4.485 4.785 5.160 6.931 , 9.118 11.166 .18 8.707 4.1146 4.411 4.807 5.184 5.695 6.191 8.594 11.806 . 16.060 I 88 4.116 4.651 5.1 17 5.614 6.176 6.777 7.4811 10.657 15.111 ' 11.199 81 4.818 5.850 5.916 6.580 7.188 8.064 8.916 18.115 19.848 17.988 . 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