Question: ABC Company is planning to issue a 10 percent, semiannual couponbond w
ID: 2662182 • Letter: Q
Question
Question:ABC Company is planning to issue a 10 percent, semiannual couponbond with five years
remaining to maturity. The bond has been priced (Par value) as Rs.1,000. The bond has
yield to maturity of 10 percent. The company is interested inestimating the effects of
yield changes on the price of the bond.
Requirement:
Calculate the Modified Duration of the bond. Question:
ABC Company is planning to issue a 10 percent, semiannual couponbond with five years
remaining to maturity. The bond has been priced (Par value) as Rs.1,000. The bond has
yield to maturity of 10 percent. The company is interested inestimating the effects of
yield changes on the price of the bond.
Requirement:
Calculate the Modified Duration of the bond.
Explanation / Answer
Question Details:
Question:
ABC Company is planning toissue a 10 percent, semiannual coupon bond with five yearsremaining to maturity. The bond has been priced (Par value) as Rs.1,000. The bond has yield to maturity of 10 percent. The company isinterested in estimating the effects of yield changes on the priceof the bond.
Requirement:
Calculate the ModifiedDuration of the bond.
Answer:
Interest Rate (r) or YTM = 10% per year or 10%/2 = 5% per sixmonths
Time = 5 years (Semiannual coupon bond) or 10 periods
Par Value or Face Value (FV) = Rs. 1000
Coupon rate = 10% semiannually
Effects of yield changes on price =?
Modified duration of the bond =?
Coupon Payment (C) = Coupon rate * Par Value = 10% * 1000 = Rs.100 semiannually
First of all we will calculate the, present value of the bond,as computed below:
PV = [C * (1 – 1 / (1+r) t) / r] + [FV / (1+r)t]
PV = [100 * (1 – 1 / (1+0.05) 10) / 0.05] +[1000 / (1+0.05) 10]
PV = [100 * (1 – 1 / (1.05) 10) / 0.05] + [1000/ (1.05) 10]
PV = [100 * (1 – 1 / 1.628895) / 0.05] + [1000 /1.628895]
PV = [100 * (1 – 0.613913) / 0.05] + [613.913]
PV = [100 * (0.386087) / 0.05] + [613.913]
PV = [100 * 7.72174] + [613.913]
PV = [772.174] + [613.913]
PV = Rs. 1386.09
At this information, the bond is selling at premium (higherprice), above than par value, which shows that the coupon rate isgreater than interest rate or yield to maturity, i.e. coupon rateis 10% per six months and interest rate is 5% per six months.
Now, we consider the effect of yield changes on the price ofbond, as we know that if market interest rate goes up, the bondprice will go down, and interest rate and price of the bond areinversely proportional to each other, let’s examine by anexample, computed below:
After one year passed, the coupon rate remains same as 10%, andpayments made same as semiannually, but what changes is time whichwill become 4 years, and let’s say, market interest rate goesup to 15 percent per year compounded annually, so now what will bethe present value after one year, or price of the bond after oneyear, let’s see
(Price will be drop from Rs. 1386.09 previously calculated, asinterest rate goes up.)
Interest Rate (r) or YTM = 15% per year or 15%/2 = 7.5% per sixmonths
Time = 5 years (Semiannual coupon bond) or 10 periods
Par Value or Face Value (FV) = Rs. 1000
Coupon rate = 10% semiannually
Effects of yield changes on price =?
Modified duration of the bond = 4 years (Semiannualcoupon bond) or 8 periods
Coupon Payment (C) = Coupon rate * Par Value = 10% * 1000 = Rs.100 semiannually
PV = [C * (1 – 1 / (1+r) t) / r] + [FV / (1+r)t]
PV = [100 * (1 – 1 / (1+0.075) 8) / 0.075] +[1000 / (1+0.075) 8]
PV = [100 * (1 – 1 / (1.075) 8) / 0.075] +[1000 / (1.075) 8]
PV = [100 * (1 – 1 / 1.783478) / 0.075] + [1000 /1.783478]
PV = [100 * (1 – 0.560702) / 0.05] + [560.702]
PV = [100 * (0.439298) / 0.075] + [560.702]
PV = [100 * 5.857307] + [560.702]
PV = [585.7307] + [560.702]
PV = [585.7307] + [560.702]
PV = Rs. 1146.43
Conclusion:
So, we see that, when the market rate goes up, the price will godown, with the passage of time, the modified duration of the bondwill be 4 years, which will be changed from 5 years after one yearhas been passed, it is also known as time to maturity. Also, if thecoupon payments are not fixed, so when coupon rate goes up and noother thing will change, then market price will go up, as couponrate is directly proportional to market price.
Extra Knowledge:
When, Coupon Rate > Market Interest Rate
Then, Bond Price > Par Value
Bonds are called as Premium Bonds
When, Coupon Rate = Market Interest Rate
Then, Bond Price = Par Value
When, Coupon Rate < Market Interest Rate
Then, Bond Price < Par Value
Bonds are called as Discount Bonds
Terminology:
Market Rate, Interest Rate, YTM, Yield to Maturity, DiscountRate, Nominal Interest Rate, and Banks Rate, all are same andinterchangeable words.
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