Calculate the market value of a 20-year, $100,000 City of New York bond that has six years remaining to maturity, a coupon rate of 11% and is trading today at a yield rate of 8.2% (compounded semiannually).

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Quizplus · Accepted Answer

To calculate the market value of the bond, we use the formula for the present value of the bond's cash flows, which include the semiannual interest payments and the principal repayment at maturity. The bond has a face value of $100,000, a coupon rate of 11% (which means an annual interest of $11,000), and there are 6 years left until maturity, so there are 12 periods (since interest is compounded semiannually). The yield rate is 8.2% annually, but since compounding is semiannual, the semiannual yield rate is 4.1%.The present value (PV) of the bond's cash flows can be calculated as the sum of the present value of the annuity (the semiannual interest payments) and the present value of the face value (the lump sum payment at maturity). The formula for the present value of an annuity is $PV_{annuity} = PMT \times \left(1 - \frac{1}{(1 + r)^n}\right) / r$, where PMT is the payment per period, r is the interest rate per period, and n is the total number of periods. The formula for the present value of a lump sum is $PV_{lumpsum} = FV / (1 + r)^n$, where FV is the future value or lump sum amount.Given:- PMT = $11,000 / 2 = $5,500 (since payments are semiannual)- r = 8.2% / 2 = 4.1% = 0.041 (semiannual yield rate)- n = 6 years * 2 = 12 periodsCalculating the present value of the annuity (interest payments):$PV_{annuity} = $5,500 \times \left(1 - \frac{1}{(1 + 0.041)^{12}}\right) / 0.041$Calculating the present value of the lump sum (principal repayment):$PV_{lumpsum} = $100,000 / (1 + 0.041)^{12}$Adding these two components gives the total present value of the bond, which is the market value. When you perform these calculations, you find that the market value of the bond is closest to the value given in option C, $113,063.

Calculate the Market Value of a 20-Year, $100,000 City of New