Question

Bonds often pay a coupon twice a year. For the valuation of bonds that make semiannual payments, the number of periods doubles, whereas the amount of cash flow decreases by half. Using the values of cash flows and the number of periods, the valuation model is adjusted accordingly.

Assume that a $1,000,000 par value, semiannual coupon U.S. Treasury note with five years to maturity (YTM) has a coupon rate of 3%. The yield to maturity of the bond is 7.70%.
Using this information and ignoring the other involved, calculate the value of the Treasury note:
a) $509,016.47
b) $686,768.25
c) $969,555.18
d) $807,962.65.
Based on your calculations and understanding of semiannual coupon bonds, complete the following statement:
Assuming that interest rates remain constant, the T-note's price is expected to:___________.

Answer 1

1.

Bond Price or Present value = $807962.6540 rounded off to $807962.65

Option d is the correct answer

2.

Assuming that interest rates remain constant, the T-note's price is expected to increase.

Step-by-step explanation:

1.

To calculate the quote/price of the bond today, which is the present value of the bond, we will use the formula for the price of the bond. As the bond is a semi annual bond, the semi annual coupon payment, number of periods and semi annual YTM will be,

Coupon Payment (C) = 1000000 * 0.03 * 6/12 = $15000

Total periods (n) = 5 * 2 = 10

r or YTM = 7.7% * 6/12 = 3.85% or 0.0385

The formula to calculate the price of the bonds today is attached.

Bond Price = 15000 * [( 1 - (1+0.0385)^-10) / 0.0385] + 1000000 / (1+0.0385)^10

Bond Price or Present value = $807962.6540 rounded off to $807962.65

2.

Assuming the interest rates remain constant, the T-note's price is expected to increase as the T-note comes close to its maturity. The bonds that are issued at discount see an increase in price when interest rate remains constant and the time to their maturity decreases as they pay par value at maturity and discount is amortized.