Question

7. Valuing semiannual coupon bonds 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 five years to maturity has a coupon rate of 6%. The yield to maturity (YTM) of the bond is 9.90%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note: $849,059.88 $721,700.90 $534,907.72 $1,018,871.86 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 .

Answer 1

The value of the Treasury note is $849,059.88 and this is selling at a discount.

The value of a treasury note depends on different factors such as:

• The initial value
• The coupon rate
• The value of the yield to maturity

Considering these aspects, let's calculate the value of the treasury note

Initial value: $1,000,000

$1,000,000 x 6% (coupon rate) =  $60,000

$60,000 / 2 (the coupon pays twice a year) = $30,000 - This value refers to the payment per period

Let's consider now the number of periods and the yield to maturity

Number of periods: 5 x 2 (the number of periods double) = 10 periods

Yield to maturity or rate: 9.90% / 2 (cash flow decreases by half) = 4.95%

Finally, you can use the PV formula to calculate the value:

PV (4.95%,10,-30000,-1000000) - This part is done in excel program as the original formula is quite complex

PV =$849,059.88

Based on this, the value of the note is $849,059.88, and you can conclude this is selling at a discount because this value is lower than the initial value of 1,000,000.

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