Question

7) Suppose that a bond is purchased between coupon periods. The days between the settlement date and the next coupon period are 90. There are 182 days in the coupon period. Suppose that the bond purchased has a coupon rate of 6.8% and there are 8 semiannual coupon payments remaining. The par value of the bond is $100.

a. What is the full price for this bond if a 6.4% annual discount rate is used? b. What is the accrued interest for this bond?
c. What is the clean price of the bond?

Answer 1

No of periods = 8 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Par value

Coupon per period = (6.8% / 2) * $100

Coupon per period = $3.4

Bond Price = Coupon / (1 + annual discount rate / 2)^period + Par value / (1 + annual discount rate / 2)^period

Bond Price = $3.4 / (1 + 6.4% / 2)¹ + $3.4 / (1 + 6.4% / 2)² + ...+ $3.4 / (1 + 6.4% / 2)⁸ + $100 / (1 + 6.4% / 2)⁸

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $3.4 * (1 - (1 + 6.4% / 2)^-8) / (6.4% / 2) + $100 / (1 + 6.4% / 2)⁸

Bond Price = $101.3922

Days between the settlement date and the next coupon period = 90 days

Days in the coupon period = 182 days

Full Bond price = Bond price * (1 + annual discount rate / 2)^{(Days in the coupon period -Days between the settlement date and the next coupon period / Days in the coupon period)}

Full Bond price =  $101.3922 * (1 + 6.4% / 2)^{(182 - 90 / 182)}

Full Bond price = $103.0195

Accrued Interest = Coupon per period * (Days in the coupon period - Days between the settlement date and the next coupon period / Days in the coupon period)

Accrued Interest = $3.4 * (182 - 90 / 182)

Accrued Interest = $1.7187

Flat (Clean) Bond Price = Full Bond price - Accrued Interest

Flat (Clean) Bond Price = $103.0195 - $1.7187

Flat (Clean) Bond Price = $101.3008