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 U.S. Treasury note with five years to maturity (YTM) has a coupon rate of 3%. The yield to maturity of the bond is 11.00%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note:

Answer 1

Value of treasury Note =$698,494.97

Step-by-step explanation:

The value of the notes is the present value of the future cash inflows discounted at its YTM of 11%

Value of Notes = PV of interest + PV of RV

The value of Note can be worked out as follows:

Step 1 :Calculate the PV of Interest payment

Present value of the interest payment

PV = Interest payment × (1- (1+r)^(-n))/r

r-Yield to Maturity, n- number of years

Interest payment = 3% × $1,000,000 × 1/2= $15,000 .

Semi-annual interest yield = 11%/2 =5.5%

PV = 15,000 × (1 - (1.055)^(-5×2)/0.055) = 113,064.3874

Step 2 :PV of redemption Value

PV of RV = RV × (1+r)^(-n)

= 1000,000 × (1.055)^(-5×2)

= 585,430.57

Step 3

Calculate Value of the Notes

=113,064.3874 + 585,430.57

= $698,494.96

Value of treasury Note =$698,494.97