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Q: 2 quick questions ( Answered ,   1 Comment )
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 Subject: 2 quick questions Category: Business and Money > Finance Asked by: donothavetime-ga List Price: \$10.00 Posted: 29 Oct 2005 12:10 PDT Expires: 28 Nov 2005 11:10 PST Question ID: 586443
 ```1. The State Lottery Commission has proclaimed you the winner of a so-called \$2 million prize. But, what you will really et is \$100,000 today, plus 19 future payments of \$100,000 per year for a total of 20 years. Assuming a discount rate of 8%, what is the real value of this prize? 2. Today you purchase a \$1,000 par value bond with an annual coupon of \$65. The bond matures in 15 years from today. You paid the market price for this bond which was \$1,240. You also received your first coupon payment of \$65. today as your purchased the bond. What is the bond's yield to maturity?```
 Subject: Re: 2 quick questions Answered By: elmarto-ga on 29 Oct 2005 13:47 PDT Rated:
 ```Hello! Here are the answers to your questions. Question 1 The "real value" of this prize is the present value of the described flow of payments. Following is a link that gives a good description and formulae for calculating the present value of a stream of payments: Calculating the Present and Future Value of Annuities http://www.investopedia.com/articles/03/101503.asp [check under the section "Calculating the Present Value of an Annuity Due"] Given that the discount rate is 8%, the present value of the lottery prize would be (in thousands): PV = 100 + 100/(1.08)^1 + 100/(1.08)^2 + 100/(1.08)^3 + ... + 100/(1.08)^19 Fortunately, the same result can be achieved using a simpler formula, which is mentioned in the link I gave above, under the section "Calculating the Present Value of an Annuity Due". Applying this formula, we get that the present value of the lottery prize is: PV = 100*[1 - 1.08^(-20)]*1.08/0.08 = 1,060.36 Thefore, the "real value" of the prize is \$1,060,360 rather than 2 million. Question 2 In this question, we must again make use of the formula for present value. The yield to maturity (YTM) is the discount rate that is implied in the price of the bond. The value of a bond is the present value of its flow of payments. The bond from this question gives you \$65 every year for 15 years, and then gives you \$1,000 (it's par value) at the end of the 15th year. Therefore, letting "i" be the discount rate, the value of this bond is: PV = 65 + 65/(1+i)^1 + 65/(1+i)^2 + ... + 65/(1+i)^14 + 1000/(1+i)^15 Now, we also know that the market price of this bond is \$1,240. Therefore, the present value of the bond is also \$1,240. So we get the equation: 1240 = 65 + 65/(1+i)^1 + 65/(1+i)^2 + ... + 65/(1+i)^15 + 1000/(1+i)^15 From this equation, we should be able to find the discount rate "i". The value we find for "i" will be the yield to maturity. That is, the YTM is simply the discount rate that makes the market price be what it is. Since the above equation cannot be solved analytically, we will use a bond calculator. You can find an online one at the following link: Bond Yield Calculator http://www.moneychimp.com/calculator/bond_yield_calculator.htm A small caveat is that this calculator (and all of the online calculators I could find) assume that the first coupon payment occurs one year from now instead of today. So, in order to be able to use them, we just have to rearrange the equation like this: 1240 - 65 = 65/(1+i)^1 + 65/(1+i)^2 + ... + 65/(1+i)^15 + 1000/(1+i)^15 1175 = 65/(1+i)^1 + 65/(1+i)^2 + ... + 65/(1+i)^15 + 1000/(1+i)^15 Notice that since you received \$65 the same day you bought it for \$1,240, then this is equivalent as paying \$1,175 and receiving the first coupon payment one year from today. So now we can use the calculator. Enter the following data into it: Current price: 1175 Par Value: 1000 Coupon Rate: 6.5 (because \$65 -the coupon value- is 6.5% of the par value) Years to Maturity: 15 Now click on "Calculate". We get from the calcualtor that the YTM is 4.833% Google search terms: "present value" ://www.google.com.ar/search?hl=es&q=%22present+value%22&meta= yield to maturity ://www.google.com.ar/search?hl=es&q=yield+to+maturity&meta= bond price calculator ://www.google.com.ar/search?hl=es&q=bond+price+calculator&meta= I hope this helps! If you have any questions regarding my answer,please don't hesitate to request a clarification. Otherwise I await your rating and final comments. Best wishes! elmarto```
 donothavetime-ga rated this answer: `Answers were well thought out and posted quickly. Thank You! Highly recommended.`

 Subject: Re: 2 quick questions From: research_help-ga on 31 Oct 2005 07:05 PST
 ```elmarto, you may wish to review the terms of service regarding answering questions that are obviously school homework assignments. You don't appear to be that new to the service so one would assume that you have already reviewed the terms.```