Question: What is the formula to calculate the present value of semi-annual coupon on fixed rate bond?
Answer: Below is the complicated formula C*[(1-{1/(1+i)^n})/i] + M/(1+i)^n C= Semi-annual coupon payment in currency n= number of cycles (number of years *2) i=Fixed Interest rates (Annually interest rate/2) M=Maturity Value Example: 8% interest rate, 10 years to maturity and $1000 par value and required yield is 10% So C=$40 ($80/2)= Semi-annual coupon payment n=20 (10*2) periods i=required interest/2=5%=0.05 M=$1000 Which results in, if every value is put in the formula = $875.38 Hence, you can say that present value or price of the bond should be $875.38 for considering all the future cashflows. If you are expecting 10% yield on the bond. If you pay more than this your yield would reduce and if you get at lesser price, it means you would realize more yield if held till maturity. Now, let say you change your required yield to 7% then what is the present value of the bond. Only “i� would change to 0.035 Then bond price comes to = 1,071.06 It means it is fine even you pay more than $1000 for this bond to buy, because it can still give 7% yield or more of you buy at $1071 or less and keep till maturity. Note: This calculation is for the option free bond and various other factors are not considered.
Question: What is the relationship between yield and bond price?
Answer: As you have seen bond price would move in opposite direction of the required yield. If you need more yield then bond price should reduce and similarly if you reduce your required yield then bond price would increase. The only variable you can change is the bond price or required yield. Because Bond coupon and maturity remain fixed. Hence, f you create a graph between price and required yield it would create a convex shape.
Question: When you can say that price of the bond should be equal to par value?
Answer: When the required yield and coupon is same, then price of the bond should be equal to par value of the bond. (Applicable only on option free bonds)
Question: What do you mean by that bond is sold on discount?
Answer: Suppose yield on a bond increases above coupon rate at any point, so bond price has to adjust. To do that bond price would go below its par value. So whenever bond is sold below par value it is known as bond is available at discount.