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Published byEmma Mosley Modified over 9 years ago
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Time Value of Money
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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 Present Value
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110 121 133.1 100 x (1.10) 1 100 x (1.10) 2 100 x (1.10) 3 100 Given ; PV = 100, i = 10%, t = 1, FV = ?Given ; PV = 100, i = 10%, t = 2, FV = ? 100 Given ; PV = 100, i = 10%, t = 3, FV = ? 100
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Calculating Annuity Present Value It ’ s just a combination set of PV calculations PV PV 1 PV 2 PV n-1 PV n i % AAAA 12 n-1n
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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
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Example; Calculating Annuity Present Value Given ; A = 100, i = 10%, t = 3, FV = ?, PV = ? AAA 110 = 100(1.1) 1 121 = 100(1.1) 2 100 = 100(1.1) 0 331 248.68 = (100/0.1)x[1-(1/(1.1) 3 ] F = P(1+i) n P = (A/i)[1-1/(1+i) n ] 248.68 x 1.10 3 =
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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
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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 Calculating Bond’s Present Value 12/ 02 12/ 06 12/ 03 12/ 04 12/ 05 06/ 03 06/ 04 06/ 05 06/ 06 40 1,000 Number of period = n = 8 i = 1.5% per period
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Example Time Value Q1) Joe ’ s plan You are an financial consultant for a farmer named Joe. He just celebrated his 35 th birthday yesterday on 31Dec2000. After he retire himself at 65 year olds (31Dec2030),he plan to withdraw 100,000 per year starting from his 65 th birthday until his last 100,000 withdrawal at his 85 th 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 65 th birthday.
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The process of providing for a loan to be paid off by making regular principal reduction Calculating Amortized Loans
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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?
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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)]
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