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The Time Value of Money

Would you rather have a dollar today or a dollar next year? Present Value: The use of interest rates to compare the value of a dollar realized today with the value of a dollar realized later . $1 today @ 5% interest in savings account. The Time Value of Money. Defining Present Value.

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The Time Value of Money

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  1. Would you rather have a dollar today or a dollar next year? Present Value: The use of interest rates to compare the value of a dollar realized today with the value of a dollar realized later. $1 today @ 5% interest in savings account. The Time Value of Money

  2. Defining Present Value • FV = future value of $ • PV = present value of $ • r = real interest rate • n = # of years • The Simple Interest Formulas • FV = PV x ( 1 + r )n • PV = FV/ (1 + r)n

  3. Assume an original bond was a 20 year bond with a face value of $1,000 and the coupon rate was 5%. That means the owner was receiving $50 in interest payments each year and was planning on receiving the $1,000 back at the end of year 20. But what if the owner need cash and wants to sell the bond after owning it for 18 years and that current interest rates on bonds just like his are 7%. Keep in mind there are two more interest payments due (one next year and one two years from now) and the face value will be due at the date of maturity two years from now. What price can the owner sell the bond for now that current interest rates are higher? Practice #2

  4. PV = $50/(1.07)1 + $1,050/(1.07)2 = $46.73 + $917.11 = $963.84. Now assume interest rates for similar risk bonds are 3%. Now what price can the owner sell the bond? PV = $50/(1.03)1 + $1,050/(1.03)2 = $1,038.27 Note: Bond prices are inversely related to interest rates. Practice #2 Continued

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