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# Topic 2_2_student - Topic 2 The Time Value of Money...

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Topic 2 The Time Value of Money Readings: Chap 4 (4.1-4.4)

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PV of multiple cash flows How to deal with multiple cash flows? A nice property of present values is that they can be summed. Suppose that you will receive \$10,000 in one year and \$20,000 in three years. The interest rate is 6% compounded annually. What amount of money today will make you as happy as receiving the two cash flows in the future? 3 10,000 20,000 26,226.35 (1 6%) (1 6%) + = + +
Annuity An annuity is a series of identical fixed cash flows to be made for a specified number of years. What’re examples of annuities? What is the PV of \$100 to be received every year for 10 years starting in year one? Assuming the interest rate is 10% compounded annually. 10 ) 1 . 1 ( 1 100 ... 2 ) 1 . 1 ( 1 100 1 ) 1 . 1 ( 1 100 + + + = PV

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An easier way to value annuity 1 1 ( ) (1 ) n PV Annuity CF r r r = - + A nnuities starting one year from today and interest rate is compounded annually . 10 1 1 100 614.46 10% 10%(1 10%) PV = - = +
What if the compounding interval is not annual? * 1 1 ( ) / (1 ) n m PV Annuity CF r r r m m m = - + Instead of receiving \$100 every month for 10 years, how much should you get today to be just as happy? The discount rate (or interest rate, or required rate of return) is 10%. Assuming monthly compounding. 10*12 1 1 100 7,567.12 10% 10% 10% /12 (1 ) 12 12 PV = - = +

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Example You want to buy a car with financing. The dealer offers you a loan with \$199 payment every month for 5 years. The APR of the loan is 5%. If you were paying cash today instead, what amount would you be willing to pay?
Suppose that you get a mortgage for \$30,000 and plan to pay it off in 5 years with equal monthly payments. How much will your monthly payments be if the APR of your mortgage is 5% compounded monthly? 5*12 1 1 30,000 ( ) 5% 5% 5% *(1 ) 12 12 12 CF = - + 566.14 CF =

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Understanding Annuities What does that \$614.46 tell us? Your parents tell you that they need cash now. So they would prefer \$614.46 today to \$100 a year for 10 years. Assume that there is a bank that you can lend and borrow money at 10% annual interest rate, how can you convert \$100 a year for 10 years to \$614.46 today.
How do you do it?

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