In: Finance
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?
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