Question

If you purchase a $1,000 face value, 4% annual coupon bond with 6 years to maturity when the going interest rate (or yield) is 3%, then you would pay $1,054.17 for the bond.

a) What is your expected rate of return on the bond assuming interest rates do not change and you hold the bond to maturity?

b) Suppose that you sell it a year later at which time the going interest rate has risen to 3.5%. What is your rate of return on the bond?

c) What is your expected rate of return on the bond assuming interest rates do not change and you sell the bond one year later?

Answer 1

a)

If you do not sell and hold the bond till maturity, expected rate of return will be equal to interest rate

Therefore, expected rate of return = 3%

b)

Annual coupon = 4% of 1000 = 40

Value in 1 year = Coupon * [1 - 1 / (1 + r)^n] /r + FV / (1 + r)^n

Value in 1 year = 40 * [1 - 1 / (1 + 0.035)^5] /0.035 + 1000 / (1 + 0.035)^5

Value in 1 year = 40 * [1 - 0.841973] / 0.035 + 841.973167

Value in 1 year = 40 * 4.515052 + 841.973167

Value in 1 year = 1,022.575262

Rate of return = [(Ending value + coupon - beginning value) / beginning value] * 100

Rate of return = [(1,022.575262 + 40 - 1,054.17) / 1,054.17] * 100

Rate of return = 0.80%

c)

Annual coupon = 4% of 1000 = 40

Value in 1 year = Coupon * [1 - 1 / (1 + r)^n] /r + FV / (1 + r)^n

Value in 1 year = 40 * [1 - 1 / (1 + 0.03)^5] /0.03 + 1000 / (1 + 0.03)^5

Value in 1 year = 40 * [1 - 0.862609] / 0.03 + 862.608784

Value in 1 year = 40 * 4.579707 + 862.608784

Value in 1 year = 1,045.797072

Rate of return = [(Ending value + coupon - beginning value) / beginning value] * 100

Rate of return = [(1,045.797072 + 40 - 1,054.17) / 1,054.17] * 100

Rate of return = 3%