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ECN 481 (3), Measuring Interest Rates

# ECN 481 (3), Measuring Interest Rates - Measuring Interest...

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Measuring Interest Rates Bond Interest Rate is more formally called its Yield to Maturity Yield to Maturity -- the interest rate which equates the present value of all future payments with the current bond price

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Present Value Present Value – an equation that converts future payments into their current dollar equivalent Example 1 – Find the present value of payment received one year from now. Given P dollars today, with interest rate i, how much will you have one year from now (F)?
Answer to Example 1 F = Repayment of principal + Payment of Interest F = (P) + (i)(P) = (P)(1 + i) To obtain the present value of the future payment, solve for P P = F/(1 + i) -- Present value of payment (F) received one year from now

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Example 2 -- Present Value of Fixed Payment (F) Received n Years From Now After One Year: F = P(1 + i) Two Years: F = [P(1 + i)](1 + i) F = P(1 + i) 2 Three Years: F = P(1 + i) 3 n Years: F = P(1 + i) n
Obtaining The Present Value To convert to current dollars, solve previous equation for P P = F/(1 + i) n Present Value of Payment Received n Years From Now

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Example 3 -- Present Value of Annual Stream of Payments Suppose one receives a payment of A 1 at the end of year 1, A 2 at the end of year 2, A 3 at the end of year 3, …, and A n at the end of year n. What is the present value (current dollar equivalent) of that series of payments?
Answer to Example 3 Present Value = Sum or the present values of each payment P = A 1 /(1 + i) + A 2 /(1 + i) 2 + A 3 /(1 + i) 3 + … + A n /(1 + i) n

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Present Value -- Applications Consider formula (for simplicity, let A 1 = A 2 = A 3 = … = A n = A) P = A/(1 + i) + A/(1 + i) 2 + A/(1 + i) 3 + … + A/(1 + i) n Given any 2 variables, we can solve for the third.
Application #1 -- Given A and i, Solve for P Examples -- Multiyear Contracts, Lottery Winnings Example -- You win \$100,000 for each of 3 years, i = 0.08.

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ECN 481 (3), Measuring Interest Rates - Measuring Interest...

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