Question

Calculate a dirty price of 3-year bond with a face of 1,000,000 PLN, coupons paid each 4M with a rate of 9% pa., YTM 10% if there are 11 months till maturity date. Assume practical method of calculating dirty price.

Answer 1

Answer:

Dirty price = Clean price + Accrued interest

Clean price = C/(1+r) + C/(1+r)^2 + C/(1+r)^3 + ..... + (C+F)/(1+r)^n

C = Coupon payment = (9% of 1000000) / 3 = 30000 PLN

r = YTM = 10% per annum = (10/3)% per 4 month period

n = 11 months till maturity, hence 3 coupon payments remaining

Clean price = C/(1+r) + C/(1+r)^2 + (C+F)/(1+r)^3

= 30000/(1.033) + 30000/(1.033)^2 + (1030000)/(1.033)^3 = 990640.71 PLN

Accrued interest = F * (C/n) * (D/t)

F = 1000000 PLN

C = Annual coupon rate = 9%

n = Payment frequency = 3

D = Days since last payment = 30 days

T = Days between payments = 365/3 = 121.67

Accrued interest = 1000000 * (0.09/3) * (31/121.67) = 7643.63 PLN

Dirty price = 990640.71 PLN + 7643.63 PLN = 998284.34 PLN