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## Time Value of Money

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**Present Value**• a dollar today is worth more than a dollar tomorrow • PV = Present Value • FV = Future Value • r = interest rate • t = numbers of time periods • 1/(1+r)t = PVIF = PV interest factor**Given ; PV = 100 , i = 10% , t = 1 , FV = ?**110 100 100 100 Given ; PV = 100 , i = 10% , t = 2 , FV = ? 121 Given ; PV = 100 , i = 10% , t = 3 , FV = ? 133.1 100 x (1.10)1 100 x (1.10)2 100 x (1.10)3**A**A A A 1 2 n-1 n Calculating Annuity Present Value • It’s just a combination set of PV calculations i % PV1 PV2 PV n-1 PV n PV**Calculating Annuity Present Value**• Annuity Discount Factor = PVIA = PV = A x [ PVIA (r,n) ] = (A / r ) x [ 1 – ( 1/(1+r)n ) • A = PMT = Annuity**A**A A 100 = 100(1.1)0 110 = 100(1.1)1 121 = 100(1.1)2 248.68 = (100/0.1)x[1-(1/(1.1)3] 248.68 x 1.103 = 331 Calculating Annuity Present Value Given ; A = 100 , i = 10% , t = 3 , FV = ?, PV = ? • Example; P = (A/i)[1-1/(1+i)n] F = P(1+i)n**Calculating Bond’s Present Value**• Example; a Thai government bond (LB06DA), which will mature in 8 Dec 2006 , give 8% coupon. If we buy this bond on 8 Dec2002 (just after the coupon was paid),by using discount rate at 3%, how much we need to pay? • Remember that Govy bond’s features are 1.Par = 1,000 2.Pay coupon semi-annual**Calculating Bond’s Present Value**1,000 40 40 40 40 40 40 40 40 Bond’s price = PVIA(1.5%,8) + PVIF(1.5%,8) = (40/0.015)x[1-(1/(1.015)8] + 1000 / (1.015)8 = 299.437 + 887.711 = 1,187.148 Note ; In Excel, use function “PRICE” by input 1.Settlement date 2.Maturity date 3.Coupon 4.Yield 5.Redemption 6.Frequency 12/02 06/03 12/03 06/04 12/04 06/05 12/05 06/06 12/06 i = 1.5% per period Number of period = n = 8**Example Time Value**Q1) Joe’s plan You are an financial consultant for a farmer named Joe. He just celebrated his 35th birthday yesterday on 31Dec2000. After he retire himself at 65 year olds (31Dec2030),he plan to withdraw 100,000 per year starting from his 65th birthday until his last 100,000 withdrawal at his 85th year (31Dec2055). Joe can find a bank who gives fix rate 12% per year for him during his lifetime. With information above, he ask for your recommendation on how much he need to annually deposit his money in order to accomplish his goal? One more thing, he ready to make the first deposit on his next birthday and will make the last deposit on his 65th birthday.**Calculating Amortized Loans**• The process of providing for a loan to be paid off by making regular principal reduction**Calculating Amortized Loans**• Example 1 ; Anna take out a $5,000, five-year loan at 9%. She agreed to amortize $1,000 principle each year on her loan. How much she must pay in each year?**Calculating Amortized Loans**• Example 2; Mary take out a $5,000, five-year loan at 9%. She agreed to pay $1,000 each year until the loan expired. How many years she will pay off all the loan she took? And how much for the last payment? 5000 =(1000/0.09)*[1-(1/(1.09)^6.9375)]