One bond has a coupon rate of 70 another a coupon rate of 90

One bond has a coupon rate of 7.0%, another a coupon rate of 9.0%. Both bonds pay interest annually, have 5-year maturities, and sell at a yield to maturity of 8.0%.

a. If their yields to maturity next year are still 8.0%, what is the rate of return on each bond? (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.)

b. Does the higher-coupon bond give a higher rate of return over this period?

Yes No

Solution

a) STEP 1: CALCUATION OF PRICE OF THE BOND AT YEAR 1 AND YEAR 2.

b) STEP 2: Difference in price at year 1 and 2 is the gain/loss and the coupon of 1year is the income. so we have 2 income in this. 1 from coupon and other from the difference in price.

c) STEP 3: calculation of rate of return will be as Income / Purchase price * 100. So income can be denominated as {Coupon of 1 year + (Sale Price at year 2 - Purchase Price at year 1)}.

Bond A:-

Year 1 Price = Coupon * PVaf(i,n) + FV * PVif(i,n)

= 70 * PVaf(8%, 5) + 1000 * PVif(8%,5)

= (70 * 3.9927) + (1000 * 0.6806)

= 960.07

Year 2 Price = Coupon * PVaf(i,n) + FV * PVif(i,n)

= 70 * PVaf(8%, 4) + 1000 * PVif(8%,4)

= (70 * 3.3121) + (1000 * 0.7350)

= 966.88

Rate of Return = { 70 + (966.88 - 960.07) } / 960.07

= 0.079998 i.e. 8% approx.

Bond B:-

Year 1 Price = Coupon * PVaf(i,n) + FV * PVif(i,n)

= 90 * PVaf(8%, 5) + 1000 * PVif(8%,5)

= (90 * 3.9927) + (1000 * 0.6806)

= 1039.93

Year 2 Price = Coupon * PVaf(i,n) + FV * PVif(i,n)

= 90 * PVaf(8%, 4) + 1000 * PVif(8%,4)

= (90 * 3.3121) + (1000 * 0.7350)

= 1033.12

Rate of Return = { 90 + (1033.12 - 1039.93) } / 1039.93

= 0.079998 i.e. 8% approx.

b) No, both the bond has given same rate of return i.e. 8%

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