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 semi-annual interest payment. The bond rate is 6.6% per year payable semi-annually. You plan to hold the bond for 4 years, selling the bond immediately after you receive the interest payment. If your desired nominal yield is 3% per year compounded semi-annually, what will be your minimum selling price for the bond?

Answer 1

Answer:

Minimum selling price for the bond = $11350.38

Explanation:

Given - 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 semi-annual interest payment. The bond rate is

             6.6% per year payable semi-annually. You plan to hold the bond for

             4 years, selling the bond immediately after you receive the interest

              payment. If your desired nominal yield is 3% per year compounded

              semi-annually.

To find - What will be your minimum selling price for the bond?

Proof -

Formula for Bond value is -

Bond value = $\frac{Coupon Amount}{( 1+ Interest rate)^{1} } + \frac{Coupon Amount}{( 1+ Interest rate)^{2} } + \frac{Coupon Amount}{( 1+ Interest rate)^{3} } + .....\frac{Coupon Amount}{( 1+ Interest rate)^{n} }$

As given,

Coupon Rate = 6.6%

⇒Coupon Rate for semi-annual = 3.3%

and hereby time period becomes double i.e 8 years.

Now,

Interest rate = 3%

For semi-annual , interest = 1.5%

Now,

Coupon amount = 10,000×3.3% = 330

Now,

Bond value = 330 ×PVIF(1.5% , 8) + 10,000×IVAF(1.5%, 8)

                   = 330×7.486 + 10,000×0.888

                   = 11350.38

∴ we get

Minimum selling price for the bond = $11350.38