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 number of periods, the valuation model is adjusted accordingly.

Assume that a $1,000,000 par value, semiannual coupon US Treasury note with four years to maturity has a coupon rate of 3%. The yield to maturity (YTM) of the bond is 11.00%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note:

a. $895,940.83

b. $746,617.36

c. $470,368.94

d. $634,624.76

Based on your calculations and understanding of semiannual coupon bonds, complete the following statement:

The T-note described in this problem is selling at a:

a. Premium

b. Discount

Answer 1

The value is computed as shown below:

The coupon payment is computed as follows:

= 3% / 2 x $ 1,000,000 (Since the payments are semi annually, hence divided by 2)

= $ 15,000

The YTM will be as follows:

= 11% / 2 (Since the payments are semi annually, hence divided by 2)

= 5.50% or 0.055

N will be as follows:

= 4 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 8

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 15,000 x [ [ (1 - 1 / (1 + 0.055)⁸ ] / 0.055 ] + $ 1,000,000 / 1.055⁸

= $ 15,000 x 6.334565988 + $ 651,598.8707

= $ 746,617.36 Approximately

Since the value of the bond is less than the par value, hence it is a discount bond.

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