Question

On 15 January, 2021, you bought a Government bond, with a face value of $1,000; a term to maturity of 5 years; a coupon rate of 6% per annum payable yearly, and a yield to maturity of 5% per annum. You paid the market price of $1,043.76 for the bond. On 15 January, 2022, you sold the bond to Jill, providing her with a yield to maturity of 4% per annum. [NOTE: You bought and sold the bond immediately after payment of the interest coupon due on 15 January each year – that is, the interest payments due on 15 January in 2021 and 2022 are not included in the bond prices.]

REQUIRED:

i. What price would Jill have paid for the bond? [Show answer correct to the nearer cent.]

ii. What is your holding period return for holding the bond for one year, receiving the January, 2022 interest coupon, then selling the bond? [Show answer as a percentage, correct to 2 decimal places.]

Answer 1

i. 

Amount paid by the Jill is the selling price of bond. We will calculate price of bond after 1 year that will be the selling price of bond for us as well as amount paid by Jill

 

Original term to maturity is 5 years.

 

Bond is sold after 1 year of holding. So years to maturity (n)=4

 

Face value of bond = 1000

 

Coupon rate =6% annual

 

Annual coupon amount = Face value * coupon rate

                                           = 1000*6%

                                           = 60

 

Yield to maturity at that time (i)=4%

 

Price of bond will be calculated using bond price formula.

 

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i    + face value/(1+i)^n

                                    = (60*(1-(1/(1+4%)^4))/4%)  +  (1000/(1+4%)^4)

                                   =1072.597904

 

So price paid by Jill is $1072.60

 

ii.

Purchase price of bond = 1043.76 

 

Sales price of bond = 1072.60

 

One year coupon received = $60

 

Holding period return formula = (Sales price - Purchase price + Coupon interest )/ Purchase price

                                                       = (1072.60-1043.76 +60)/1043.76 

                                                       = 0.08511535219 or 8.51%

 

So holding period return of bond is 8.51%.

i. The price paid by Jill is $1072.60

ii. The holding period return of bond is 8.51%.