You have just purchased a municipal bond with a $10,000 par value for $9,500. Yo

Question

You have just purchased a municipal bond with a $10,000 par value for $9,500. You purchased it immediately after the previous owner received a semiannual interest payment. The bond rate is 6.6% per year payable semiannually. You plan to hold the bond for 3 years, selling the bond immediately after you receive the interest payment. If your desired nominal yield is 7.5% per year compounded semiannually, what will be your minimum selling price for the bond? You have just purchased a municipal bond with a $10,000 par value for $9,500. You purchased it immediately after the previous owner received a semiannual interest payment. The bond rate is 6.6% per year payable semiannually. You plan to hold the bond for 3 years, selling the bond immediately after you receive the interest payment. If your desired nominal yield is 7.5% per year compounded semiannually, what will be your minimum selling price for the bond?

Explanation / Answer

Current price of bond is the present value of cash flows expected in future from the bond. Here, the purchase price of $9,500 is the present value of interest payment for next 3 years and the expected selling price discounted using the required return.

Semi-annual interest payment = $10,000*6.6%*1/2 = $330

Interest payments in 3 years = 3 years * 2 = 6

Semi-annual required rate of return = 7.5%/2 = 3.75% = 0.0375

Present value of annuity = Annuity * {1 – (1+r)-n}/r

Present value of annuity of 6 interest payments = $330*(1-1.0375-6)/0.0375 = $330*5.2851 = $1,744.08

Let the selling price after 3 years be S.

Present value of selling price = S/1.03756 = S*0.8018

$9,500 = $1,744.08 + S*0.8018

S*0.8018 = $9,500-$1,744.08 = $7,755.92

S = $7,755.92/0.8018 = $9,673.14

Hence Answer is $9,673.14

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