Question

A 7-year $1000 par value bond with 10% semiannual coupons was sold on April 1, 2000, which yields 8% convertible semiannually. The coupons were payable at the beginning of October and April after the purchase. On June 25, 2005, the owner wished to know the dirty and clean values of this bond. Use both theoretical method and practical method, with the “30/360” method for figuring day counts. (Answers: $1055.44, $1032.35 by theoretical method, $1055.64, $1032.31 by practical method). Please show all work and numerical equation.

Answer 1

The clean price of a bond is calculated as follows :-

were, YTM = Yield expected from the bond = 8% semiannual (given) = 4% (8%/2)

t = tenure left of the bond = from 25 June, 2005 to 1 April, 2007 = 645 days = 3.5342 half years (645/365*2)

Coupon = Face Value * Coupon Rate = 1000 * 10% * 1/2 = $50 every 6 months

Face Value = $ 1,000.

Theoretical Clean Price = 161.79 + 870.56

Theoretical Clean Price = 1032.35

Dirty Price = Clean Price + Accrued Interest

Accrued Interest = Face Value * Interest Rate * Number of days/365 days

Interest Rate = Coupon Rate = 10%

number of days = Accrued interest will be received 1 April, 2005 to 25 June, 2005 = 85 days

Accrued Interest = 1000 * 10% * 85/365

Accrued Interest = $ 23.09

Thus, Dirty price of bond = 1032.35 + 23.09 = $ 1055.44

Thus, theoretical clean price of bond is $ 1032.35 and theoretical dirty price of bond is $ 1055.44.

2. In practical approach we use 360 days instead of 365 days format.

were, YTM = Yield expected from the bond = 8% semiannual (given) = 4% (8%/2)

t = tenure left of the bond = from 25 June, 2005 to 1 April, 2007 = 635 days (5+30*9+360)

= 635/360*2 = 3.5277 half years

Coupon = Face Value * Coupon Rate = 1000 * 10% * 1/2 = $50 every 6 months

Face Value = $ 1,000.

Practical Clean Price = 161.52 + 870.79

Practical Clean Price = 1032.31

Dirty Price = Clean Price + Accrued Interest

Accrued Interest = Face Value * Interest Rate * Number of days/360 days

Interest Rate = Coupon Rate = 10%

number of days = Accrued interest will be received 1 April, 2005 to 25 June, 2005 = 84 days(24+30*2)

Accrued Interest = 1000 * 10% * 84/360

Accrued Interest = $ 23.33

Thus, Dirty price of bond = 1032.31 + 23.33 = $ 1055.64

Thus, practical clean price of bond is $ 1032.31 and practical dirty price of bond is $ 1055.64.