Question

5‐year bond is issued with a 5% coupon. After 1 year and 40 days from its issue, the owner decides to sell it. Calculate the price at which the buyer sells the bond (clean price) and the actual price received by the seller. Consider an interest rate of 3%.

Clean price: Answer % (rounded to the second decimal)

Price paid by the buyer: Answer % (rounded to the second decimal)

Use 1 year=365 days for calculations

Answer 1

Coupon Rate = 5% effective

Remaining Time Period immediately after First Coupon Payment= 4 Years

Redemption Value = @ par = $1,000(Assume)

Interest Rate = 3%

Computation of Price of Bond Immediately after First Coupon Payment: (Clean Price)

Price of Bond = Present Value of all future expected Reciepts

Price of Bond = Present Value of all Coupon payments + Present Value of Redemtion proceeds

Price of Bond = [($ 1,000*5%)* PVAF(3%, 4 years)] + [$1,000 * PV(3%, 4yr)]

Price of Bond = [$ 50* 3.7171] + [$1,000 * 0.8885]

Price of Bond = $ 185.85 + $ 888.49

Price of Bond(Clean Price) = $ 1074.34

Computation of Bond Price after 1 year and 40 days from its issue:

Bond Price = Price of Bond Immediately after First Coupon Payment + Interest Accrued for the Period of Balance 40 Days

Bond Price = $ 1074.34 ( 1 + 0.03(40/360))

Bond Price = $ 1074.34 ( 1 + 0.0033)

Price Paid by the Buyer = $ 1077.92

Present Value of Annuity = P[1- (1+i)^-(n)] / i

Present Value = 1/ (1+i)^n