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Quiz #3 7/11/13 Econ 173A

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Scenario What would you pay for a U.S. Treasury Bond with the following features? Matures 7/11/23 Coupon rate 6.75% paid annually Desired yield 2.65%

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Security Prices The fair market value, “price”, of a financial security is the Present Value of it’s Cash Flows. To calculate this we need: a) Cash Flows in Dollar$ b) Time of the cash flows, “t” periods and “T” the years to the final cash flow, called the “term”. c) A discount rate “r”.

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Scenario redux The subject scenario translates into this: Cash flows: The Bond’s Face $1,000 due in 10 years The Coupons of $ 67.50 annually for 10 years. A discount rate: 2.65%, which is your desired yield.

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The Set-up To calculate the Present Value of the Bond’s two cash flows we need to calculate: The PV of $1,000 10 years from now, and The PV of the (coupons) Annuity of $ 67.50 for 10 years. Add them.

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Present Value of the Face PV(Face) = F x PVF (r,t) = 1,000 x (1 + r) -t = 1,000 x ( 1+ 0.0265 ) -10 = 1,000 x 0.77 = $ 777.00

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Present Value of the Coupons PV(Coupons) = C x PVFA (r,t) = 67.50 x {[ 1- PVF(r, t)] / r } = 67.50 x [ 1- ( 1.0265 ) -10 ] / 0.0265 = 67.50 x 8.67 = $ 585.22

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The Price of the Bond Is equal to the PV of both Cash flows: = F x PVF (r,t) + C x PVFA (r,t) = 1,000 x 0.77 + 67.50 x 8.67 = $ 777.00 + $ 585.22 = $ 1,362.22

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Do you want to improve your Quiz score? Demonstrate that this is the correct price, i.e. if you pay that amount today and receive the Coupons and reinvest them at “r”, include the last Coupon plus the Face then you will achieve the 2.65 percent EAR or yield you bid for. Use Excel® and print-out your Table of calculations and Values. Turn-in Monday.

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