Bob bought an 8.5% annual coupon bond at par. One year later, he sold the bond at a quoted price of 98. During the year, market interest rates rose and inflation was 3%. What real rate of return did Bob earn on this investment?
To find the real rate of return, we need to adjust the nominal rate of return for inflation.
Step 1: Calculate the nominal rate of return:
To find the nominal rate of return, we subtract the purchase price from the selling price and divide by the purchase price.
Nominal Rate of Return = (Selling Price - Purchase Price) / Purchase Price
Given:
Purchase Price = Par value = 100 (since Bob bought the bond at par)
Selling Price = 98
Nominal Rate of Return = (98 - 100) / 100 = -2 / 100 = -0.02 or -2%
Step 2: Calculate the inflation-adjusted rate of return:
To adjust the nominal rate of return for inflation, we add the inflation rate to 1 and multiply by it.
Inflation-adjusted rate of return = (1 + Nominal Rate of Return) * (1 + Inflation Rate) - 1
Given:
Inflation Rate = 3% or 0.03
Inflation-adjusted rate of return = (1 + (-0.02)) * (1 + 0.03) - 1
= (0.98) * (1.03) - 1
= 1.0294 - 1
= 0.0294 or 2.94%
Therefore, Bob earned a real rate of return of approximately 2.94% on this investment after adjusting for inflation.
To calculate the real rate of return Bob earned on this investment, we need to consider the effects of inflation. The real rate of return is the nominal rate of return minus the inflation rate.
First, let's calculate the nominal rate of return. Bob bought the bond at par, which means he paid 100% of its face value. The bond had an 8.5% annual coupon rate, so he received 8.5% of the face value as interest over the year. This amounts to 8.5/100 * 100 = 8.5.
Since Bob sold the bond at a quoted price of 98, he received 98% of its face value. Therefore, his gain from selling the bond is 98 - 100 = -2.
Next, we need to calculate the interest he received on the bond. The interest he received was the coupon payment of 8.5, which is 8.5/100 * 100 = 8.5.
Finally, we can calculate the nominal rate of return using the formula:
Nominal Rate of Return = (Gain from selling the bond + Coupon payment) / Initial investment
Nominal Rate of Return = (-2 + 8.5) / 100 = 6.5%
Now, let's calculate the real rate of return. We know the inflation rate was 3%, so we subtract this from the nominal rate of return:
Real Rate of Return = Nominal Rate of Return - Inflation Rate
Real Rate of Return = 6.5% - 3% = 3.5%
Therefore, Bob earned a real rate of return of 3.5% on this investment.