Question

Valulng semiannual coupon bonds Bonds often pay a coupon twice a yeac. For the valuation of bonds that make semlannual payments, the number of periods doubles, whereas the amount of cash flow decreases by half. Using the values of cash flows and number of periods, the valuation model is adjusted accordingly. Assume that a 51,000,000 par value, semiannual coupon US Treasury note with three years to maturity has a coupon rate of 3%. The yleld to maturity (YTM) of the bond is 7.70\%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note:

a) $552,009.74
b) $876,205.93
c) $1,051,447.12
d) $744,775.04
Based on your caiculations and understanding of semiannual coupon bonds, complete the foliowing statement: The T-note described in this problem is selling at a ____.

Answer 1

The value of the US Treasury note with semiannual payments is calculated using the present value of annuity and lump sum formulas, factoring in the bond's coupon rate, YTM, and number of periods. Since the YTM is greater than the coupon rate, the bond would be trading at a discount.

Step-by-step explanation:

To calculate the value of a semiannual coupon US Treasury note, we must adjust the valuation model to account for the semiannual payments. The given US Treasury note has a par value of $1,000,000, a semiannual coupon rate of 1.5% (since 3% annual coupon rate divided by 2), and a maturity of three years. With six periods (two per year for three years), and a yield to maturity (YTM) of 7.70%, which is the market's required return, we need to find the present value of the coupon payments and the par value at maturity.

The semiannual coupon payment will be $1,000,000 * 1.5% = $15,000. Each of these payments, as well as the par value to be received at the end, needs to be discounted back to their present value at the yield-to-maturity rate. The YTM for semiannual periods will be 7.70% / 2 = 3.85%.

Using the formula for the present value of an annuity and the present value of a lump sum, we can calculate the present value of the bond. However, we do not have enough information to compute the precise valuation here; it would depend on the methodology and calculator used.

As for the bond's trading status, if the bond's calculated market price is less than the par value, it is trading at a discount; if it is over the par value, at a premium. Given the YTM is higher than the coupon rate, we can infer the bond will be selling at a discount.