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A bond with a face value of $1,000 was purchased last year for $985 and sold today for $1.120. The coupon rate on the bond is 7% and inflation this past year was 3%.

a. What is the income yield?
b. What is the capital gain yield?
c. What was the total return on investment?
d. What was the real rate of return?

1 Answer

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Final answer:

The income yield of the bond is 7.11%, the capital gain yield is 13.65%, the total return on investment is 20.76%, and the real rate of return is 17.76%.

Step-by-step explanation:

The income yield of a bond refers to the annual income generated by the bond relative to its purchase price. To calculate the income yield, we need to calculate the interest payment received and divide it by the purchase price of the bond. In this case, the interest payment received is 7% of the face value, which is $70. The income yield is therefore $70 / $985 = 0.0711 or 7.11%.

The capital gain yield of a bond refers to the change in price of the bond relative to its purchase price. To calculate the capital gain yield, we need to calculate the difference between the selling price and the purchase price of the bond, and divide it by the purchase price. In this case, the capital gain yield is ($1,120 - $985) / $985 = 0.1365 or 13.65%.

The total return on investment is calculated by summing the income yield and the capital gain yield. In this case, the total return is 7.11% + 13.65% = 20.76%.

The real rate of return takes into account inflation and measures the purchasing power of the investment. To calculate the real rate of return, we subtract the inflation rate from the total return. In this case, the real rate of return is 20.76% - 3% = 17.76%.

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