Question

Information on two bonds is presented in the table. Each bond has a face value of $100. Coupons are paid annually.

... See table below ...

a.) Compute the percentage change in the price of each bond if its YTM were to increase by 1 percentage point, for example, from 2% to 3%.

b.) If you think the bond yields will increase in the next 3 months, which bond would you prefer to own now? Briefly explain.

Information on two bonds is presented in the table. Each bond has a face value of $100. Coupons are paid annualy Bond Maturity (Years) Coupon Rate YTM 4% 6% А 8 7% 6% В 10 a.) Compute the percentage change in the price of each bond if its YTM were to increase by 1 percentage point, for example, from 2% to 3%. b.) If you think the bond yields will increase in the next 3 months, which bond would you prefer to own now? Briefly explain.

Answer 1

Given:

Bond 1; Fave Value (FV) = $100; Coupon (C1) = 4%, Yield To Maturity (YTM1) = 6%; Maturity (M1) = 8 yrs

Bond 2; Fave Value (FV) = $100; Coupon (C2) = 6%, Yield To Maturity (YTM2) = 7%; Maturity (M2) = 10 yrs

Now we know that the coupon on a bond is always calculate on the face value of the bond, So the value of the coupons is

C1 = (.04) * (100) = $4

C2 = (.06) * (100) = $6

Also YTM or yield to maturity means what will be the yield on the bond if it is held till maturity or YTM is the annualised return % on a bond if the bond is held till maurity. This return component includes the return in the form of coupon which the subscriber of the bond gets and the capital gains//losses on the bond.

We find the value of a bond by discounting the cash flows which a subscriber of a bond get while holding the bond. Thus to value the bond we will have to discount the coupon payments which will be made on an annual basis and the Face value of the bond which will be paid at the maturity of the bond. The discounting of all these cash flows is done at YTM rate of that bond because we assume that the bond is held till maturity and all the reinvetments of are made at YTM only.

Thus the cash flows will look like as shown below for bond Bond 1:

Time	Cash Flow ($)
0	0
1	4
2	4
3	4
4	4
5	4
6	4
7	4
8	104

As shown above each cash flow consists of the coupon received by the boldholder, except in the last year when the bondholder recieves the face value of the bond in addition to the coupon payment as well.

Thus we calculate the value of bond by discounting all these cash flows at YTM1 = 6%. This process is done as follows:

Value of bond1 = 0 + 4/((1+.06)^1) + 4/((1+.06)^2) + 4/((1+.06)^3) ..... + 104/((1+.06)^8)

The above formula discounts each cash flow by calculating the present value of the future cash flow using the formula Present Value = Future Value / ((1 + Discount rate )^Time)

value of bond 1 calculated from above, B1 = $87.58

Similarly, value of bond 2, B2 = $92.98. Cash flows for bond 2 are as shown below:

Time	Cash Flow ($)
0	0
1	6
2	6
3	6
4	6
5	6
6	6
7	6
8	6
9	6
10	106

Now if the YTM increases by 1% point the discount rate will increase which will reduce the value of the bond.

Bond 1: YTM increases from 6% to 7%. The new value of the bond 1 is $82.09. This is calculated using the same method mentioned earlier, i.e., by discounting the cash flows. Please note that when the YTM increases, only the discount rate will change from 6% to 7% and there will be no change in the cash flows.

Bond 2:YTM increases from 7% to %. The new value of the bond 2 is $86.57. This is calculated using the same method mentioned earlier, i.e., by discounting the cash flows. Please note that when the YTM increases, only the discount rate will change from 7% to 8% and there will be no change in the cash flows.

% change in value = 100 * (Final Value - Initial Value)/Initial Value

Thus change in value of bond 1 = 100 * (82.09-87.58)/87.58 = -6.27%

And change in value of bond 2 = 100 * (86.57-92.98)/92.98 = -6.87%

Thus % change in value of bond 1 if YTM increases by 1% is -6.27% or decrease by 6.27%

and % change in value of bond 2 if YTM increases by 1% is -6.87% or decrease by 6.87%

PART B:

If the bond yield increase the discount rate used to discount the bonds will increase. This means that each cash flow will now be divided by a higher number resulting in an decrease in value of the bonds. Now the value of both bonds will decrease but we would like to choose that bond whose value will decrease to a lower extent than the other.

As seen in part a, the value of bond 1 decreased by 6.27% while the value of bond 2 decreased by 6.87% when YTM increased by 1%. From this we can infer that the % decrease in value of bond 2 is higher than bond 1 ( bond 2 is more sensitive than bond 1) and thus given everything else equal, we would prefer to hold bond 1 over bond 2 because in future the worth of bond 1 in the market would have reduced to a lesser extent than bond 2 if we expect yield to increase in future.