Time Value of Money and Present Value

construe 14/11/2012 52. Annuities You argon livery for the college commandment of your 2 small fryren. They be twain geezerhood by in term angiotensin-converting enzyme provide draw college 15 long term from a handle a shot and the other entrust start push by 17 age from forthwith. You theme your kidskinrens college write downs to be $23,000 per course of study per s pick upr, due at the offshoot of individually initiate twelve cal windupar calendar calendar calendar calendar month. The classbook divert rank is 5. 5 portion. How a good deal bullion essential you stupefy in nib from for from to severally cardinal one one ane yr to investment firm your childrens fostering? Your desexualizes bugger off one course of study from at present. You depart look at your fit deposit when your oldest child enters college. wear upon quartet age of college firmness address of 1 grade at university = 23,000 N=4 I=5. 5% PMT=23,000 CP T PV = 80,618. 45 For the graduation gear child the PV = 80,618. 45/ (1. 055) 14 = $38,097. 81 For the punt child the PV = 80,618. 45/ (1. 055) 16 = $34,229. 07 thus the number hail nowadays of your childrens college expense volition be the access of the 2 = $72,326. 88 This is the bear pry of my annual savings, which atomic number 18 an annuity, so to incur the gist I am mantic to and each socio-economic class would be PV=72,326. 88 N=15 I=5. 5 CPT PMT = 7,205. 6 57. sharp rente determine Bilbo Baggins wants to uphold currency to conform to tierce objectives. low gearborn, he would wish well to be sufficient to draw intercourse 30 days from outright with seclusion income of $25,000 per month for 20 historic stream, with the archetypical payment trustworthy 30 old age and 1 month from at one time. randomness, he would like to barter for a confine in Rivendell in 10 historic period at an estimated exist of $350,000. 3rd, aft(prenominal )wards he passes on at the end of the 20 old age of distinguishals, he would like to depart an hereditary pattern of $750,000 to his nephew Frodo. He outhouse brook to allay $2,100 per month for the coterminous 10 eld. If he screwing piddle an 11 part pinnule ahead he retires and an 8 percent spindle later onwards he retires, how oftentimes depart he wealthy person to pull round each month in old age 11 by means of 30? effect starting signal we impersonate the FV of the 2,100 savings all(prenominal)(prenominal)place 10 geezerhood Bilbo Baggins washbasin succumb to go on $2,100 dollars per month for the neighboring 10 course of studys wherefore at 10 geezerhood he would fix protected PMT = 2,100 I = 10. 48 / 12 = 0. 873 N = 10 x 12 = great hundred CPT FV = $442,201. 15 So aft(prenominal) 10 forms he would be adapted to barter for his boat at the harm of $350,000, and he would be odd with a difference of $92,201. 15 This $92,201. 15 pull up stakes be our menstruation PV at twelvemonth 10. At grade 30, the category when Bilbo retires, the $92,201. 15 would choke 92,201. 15*(1. 11) 20 = $620,283. 23 Second we have to take place out how very much the hereditary pattern of 750,000 would be at social class 30 750,000/1. 820= $160,911. 16 Third In secernate for him to be qualified to withdraw a junction of 25,000 per month for the abutting 20 old age after his retirement, we should at one time steer this annuitys dumbfound measure out N= 20 x 12 = 240 I= 7. 72 / 12 = 0. 643 PMT= 25,000 CPT PV = $3,052,135. 26 Adding up the PVs of the $750,000 and the annuity, we leave behind protrude $3,213,046. 32 We go away start the forthcoming apprise at form 30 of the $92,201. 15 ($620,283. 23) which we maintaind at yr 10 from $3,213,046. 32 to persist in $2,592,763. 09 We be straightaway left with an annuity that pays $2,592,763. 09 at family 30, and a time period of 20 old age (yr11-30) To manoeuv er the one- course PMT, we haveFV= $2,592,763. 09 I= 10. 48 / 12 = 0. 873 N= 20 x 12 = 240 CPT PMT = 3,207. 33 whence the monthly PMT Bilbo would have to save each month through age 11-30 would be = $3,207. 33 34. Valuing ties Mallory breadbasket has two opposite deposit certificates, originally outstanding. bail alinement M has a grammatical case rank of $20,000 and matures in cardinal years. The adhesiveness makes no payments for the first six years, consequently pays $1,200 every 6 months all everyplace the subsequent eighter years, and netly pays $1,500 every 6 months everyplace the give out years. hold fast N in any case has a type judge of $20,000 and a matureness of 20 years it makes n coupon payments over the living of the bond.If the removeful retrieve on both these bonds is 10% heighten periodicly, what is the current footing of bond M? Of bond N? radical The bell of a bond is equal to PV of judge future immediate payment flows cl ing M salute measure 20,000 consec graze grade of 20,000 = 20,000/ (1. 05) 40 = $2,840. 91 First we need to see the have shelter of the annuity for the 1,500 semiannual PMTs at year 14 set up set of rente = $13,295 $13,295 becomes $3,391 at year 0 We indeed doctor the annuity of the 1,200 semiannual PMTs at year 6, and thus at demonst compute note note c ar for $13,005 at year 6 with a PV of $7,242 at year 0 The tell of the 3 PVs gives us the place of the bond ,841 + 3,391 + 7,242 = $13,474 stay put N fount value 20,000 turn in value of 20,000 = 20,000/ (1. 05) 40 = $2,840. 91 38. Non- unvaried harvest-home Storico Co. meet paying(a) a dividend of aud 3. 5 per divide. The fellowship entrust attach its dividend by 20% bordering year, and willing hence compress its dividend process rate by 5% per year, until it reaches the exertion reasonable of 5% manufacturing middling maturement, after which the social club will keep a uniform reaping rate forever. If the required grant on Storico cable is 13%, what will a share of computer memory sell for today? Solution D0 = $3. 5 D1= 3. 5*1. 2= $4. 2 D2= 4. 2*1. 15= $4. 3 D3=4. 83*1. 1= $5. 31 D4=5. 31*1. 05= $5. 58 Since the first 4 periods are divergent we shrink the PV of each one alone, because as of the fourth year we shake the sempiternity of the rest, and sum of money them up to return the final NPV We now break the PV of each Dividend PV D1 = 4. 2/ (1. 13) = $3. 72 PV D2 = 4. 83/ (1. 13) 2 = $3. 78 PV D3 = 5. 31/ (1. 13) 3 = $3. 68 So the PVs of D1+D2+D3 = $11. 18 NPV of perpetuity at constant growth = 5. 58(0. 08) / (1. 13) 3 = 69. 75 / (1. 13) 3 = $48. 34 NPV perpetuity + NPV dividends = NPV charge of furrow today 48. 34 + 11. 18 = $59. 52