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Date: 14/11/2012 52. Annuities: You are saving for the faculty education of your two children. They are really two years aside in grow older, one will begin college 12-15 years by today and the other will start 17 years from today.

You calculate your kids college bills to be $23, 000 per year per kid, payable at the start of each school year. The annual interest level is your five. 5 percent. How much cash must you put in in account each year to finance your little one’s education? The deposits start one year coming from today. You are going to make your last deposit when your oldest child enters university. Assume four years of college

Solution: Expense of 1 year for university = 23, 000 N=4 I=5. 5% PMT=23, 000 CPT PV sama dengan 80, 618. 45 For the initial child the PV sama dengan 80, 618. 45/ (1. 055) ^14 = $38, 097. 81 For the second child the PV sama dengan 80, 618. 45/ (1. 055) ^16 = $34, 229. ’07 Therefore the total cost today of your kids college price will be the addition of the 2 = $72, 326. 88 This is the present value of my annual savings, that are an pension, so to get the amount I actually am supposed to save every year would be: PV=72, 326. 88 N=15 I=5. 5 CPT PMT sama dengan 7, 205. 6 57. Calculating Annuity Values: Bilbo Baggins would like to save money to satisfy three goals.

First, he’d like to be able to retire 30 years from now with retirement salary of $25, 000 monthly for twenty years, with the 1st payment received 30 years and 1 month by now. Second, he would want to purchase a vacation cabin in Rivendell in 10 years at an believed cost of $350, 000. Third, after he passes upon at the end with the 20 years of withdrawals, he would like to leave an gift of money of $750, 000 to his nephew Frodo. They can afford just to save $2, 100 per month for 10 years. In the event he can generate an 10 percent EAR before this individual retires and an 8 percent EAR CANAL after this individual retires, simply how much will he have to save each month in years 14 through 31? Solution:

Initial we get the FV with the 2, 100 savings more than 10 years Bilbo Baggins have enough money to save $2, 100 us dollars per month for the next 10 years therefore at ten years he would have saved: PMT = a couple of, 100 I = 10. 48 / 12 = 0. 873 N sama dengan 10 back button 12 sama dengan 120 CPT FV = $442, 201. 15 Thus after a decade he would manage to purchase his yacht on the price of $350, 1000, and he would be left with a balance of $92, 201. 15 This kind of $92, 201. 15 will be our current PV at year 10. At 12 months 30, the entire year when Bilbo retires, the $92, 201. 15 will become 80, 201. 15*(1. 11) ^20 = $620, 283. twenty three Second we must find out how very much the inheritance of 750, 000 can be at season 30: 750, 000/1. 8^20= $160, emmergency 911. 16 Third In order for him to be able to withdraw a quantity of 25, 000 each month for the next 20 years after his retirement, we have to now estimate this annuity’s present value: N= twenty x 12 = 240 I= six. 72 / 12 = 0. 643 PMT= twenty-five, 000 CPT PV = $3, 052, 135. twenty six Adding up the PV’s with the $750, 1000 and the annuity, we will get $3, 213, 046. 32 We will subtract the near future value for year 31 of the $92, 201. 12-15 ($620, 283. 23) which usually we salvaged at 12 months 10 coming from $3, 213, 046. 32 to get $2, 592, 763. 2009 We are right now left with an annuity that pays $2, 592, 763. 09 for year 35, and a time period of two decades (yr11-30) To calculate the yearly PMT, we have

FV= $2, 592, 763. 2009 I= 10. 48 as well as 12 sama dengan 0. 873 N= twenty x doze = 240 CPT PMT = three or more, 207. 33 Therefore the month-to-month PMT Bilbo would have to save each month through years 11-30 would be = $3, 207. 33 34. Valuing bonds: Mallory Organization has two different a genuine, currently outstanding. Bond Meters has a encounter value of $20, 500 and matures in twenty years. The relationship makes simply no payments for the 1st six years, then will pay $1, 200 every 6 months over the subsequent eight years, and finally will pay $1, five-hundred every six months over the last years. Bond D also has a face benefit of $20, 000 and a maturity of 20 years, it makes n discount payments in the life with the bond.

In the event the required return on both these bonds is definitely 10% exponentially boosted semiannually, precisely what is the current selling price of connection M? Of bond And? Solution: The price tag on a connect is corresponding to PV of expected foreseeable future cash moves Bond M: Face worth 20, 000 Present benefit of 20, 000 sama dengan 20, 000/ (1. 05) ^40 sama dengan $2, 840. 91 Initially we need to find the present benefit of the annuity for the 1, five-hundred semiannual PMTs at 12 months 14 Present Value of Annuity = $13, 295 $13, 295 becomes $3, 391 for year 0 We then get the annuity of the 1, 200 semiannual PMTs in year 6th, and then at the moment Value $13, 005 by year six with a PV of $7, 242 in year zero The total of the several PV’s provides us the cost of the connection, 841 & 3, 391 + six, 242 sama dengan $13, 474 Bond In Face value 20, 500 Present value of twenty, 000 = 20, 000/ (1. 05) ^40 sama dengan $2, 840. 91 35. Non-constant expansion: Storico Company. just paid a dividend of aud 3. 5 per share. The company will increase its dividend by 20% next year, and can then decrease its dividend growth price by 5% per year, until it finally reaches the industry average of 5% industry average growth, after which it the company will keep a constant progress rate forever. If the required return in Storico share is 13%, what will a share of stock sell for today? Solution D0 sama dengan $3. 5 D1= three or more. 5*1. 2= $4. 2 D2= four. 2*1. 15= $4. several D3=4. 83*1. 1= $5. 31 D4=5. 31*1. 05= $5. 58 Since the initially 4 durations are different we have the PHOTO VOLTAIC of each one particular alone, then simply as of the 4th season we get the perpetuity with the rest, and sum these people up to get the final NPV We now find the PV of every Dividend PHOTO VOLTAIC D1 sama dengan 4. 2/ (1. 13) = $3. 72 PHOTOVOLTAIC D2 sama dengan 4. 83/ (1. 13) ^2 sama dengan $3. 78 PV D3 = five. 31/ (1. 13) ^3 = $3. 68 And so the PVs of D1+D2+D3 = $11. 18 NPV of perpetuity at constant development = 5. 58(0. 08) / (1. 13) ^3 = 69. 75 as well as (1. 13) ^3 sama dengan $48. thirty four NPV perpetuity + NPV dividends = NPV value of share today 48. 34 & 11. 18 = $59. 52

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