Question

You bought a $1,000, 20-year 12% annual coupon bond at issue. Immediately thereafter the YTM had changed to 10%.

1)Find the total interest at the end of year 5. Express your answer in dollar and cents.

2)Find the interest-on-interest at the end of year 5. Express your answer in dollar and cents.

3)Find the capital gain at the end of year 5. Express your answer in dollar and cents.

4)Find the total income at the end of year 5. Express your answer in dollar and cents.

5)Find the realized return at the end of year 5. Express your answer as a percentage with 3 digits after the decimal point.

Please show the correct answer and explanation, Thanks!

Answer 1

Given details:

• FV of Bond = $1,000
• Coupon Rate = 12%
• YTM = 10%

1) Total interest at the end of year 5:

• Interest at the end of year 1 = $120
• Interest at the end of year 2 = $120
• Interest at the end of year 3 = $120
• Interest at the end of year 4 = $120
• Interest at the end of year 5 = $120

Hence, total interest at the end of year 5 = $600.00.

2) Interest-on-interest at the end of year 5

When the coupon rate is paid to the investor, there's no interest on interest paid to him.

3) Capital gain at the end of year 5

Bond value at the end of 5 years (15 years to maturity):

BV = $120/(1+YTM)^1 + $120/(1+YTM)^2 + ..... + ($120+$1,000)/(1+YTM)^15 = $1,152

Hence, capital gain = $1,152 - $1,000 = $152

4) Total income at the end of year 5

Total income = Realized gains + Unrealized gains = $600 + $152 = $752

5) Realized return at the end of year 5

Realized return = Only the income from interest received = $600