Question

A Chinese steel producer has issued a 3-year, 8 percent coupon bond with face value RMB 1,000,000. i) How much is this bond worth to you if the interest rate is 8%? ii) How much is this bond worth to you if the interest rate is 10%? iii) Suppose you buy this bond at par and hold it for one year. When you sell the bond, after the coupon for the first year having been paid, the interest rate is 5%. What is the price of the bond when you sell it? What is your holding period yield?

Answer 1

i) If the coupon rate and interest rate is same, then the price trades at par. In this case, both rates are at 8%, the bond is worth of RMB1,000,000 (trades at par value)

ii) If interest rate is 10%, the present value of the bond can be calculated by=(coupon1/(1+10%))+(coupon2/(1+10%)^2)+(Coupon3+face value)/(1+10%)^3

Bond worth=(80,000/1.1)+(80,000/1.1^2)+(1080000/1.1^3)=950,262.96

iii) If interest rates fall to 5% after 1 year

bond value after one year=(80,000/1.05)+(1080000/1.05^2)=1,055,782

Gain in the value=1055782-1000000=55782

Holding period return=55782/1000000=5.58%