Asked by Nicki Gagliano on Jun 30, 2024
Verified
Last year, you purchased a stock at a price of $53.60 a share. Over the course of the year, you received $1.50 in dividends and inflation averaged 2.9%. Today, you sold your shares for $55.90 a share. What is your approximate real rate of return on this investment?
A) 4.2%
B) 7.1%
C) 7.9%
D) 8.6%
E) 10.0%
Real Rate
The interest rate adjusted for inflation, representing the true cost of borrowing.
Inflation
The increase rate in the general price tag for goods and services, eroding financial capacity.
- Calculate and understand the concept of real rate of return.
Verified Answer
AK
Akshay KandwalJul 06, 2024
Final Answer :
A
Explanation :
The real rate of return adjusts the nominal return for the effects of inflation. First, calculate the nominal return: Nominal Return=Ending Value+Dividends−Beginning ValueBeginning Value \text{Nominal Return} = \frac{\text{Ending Value} + \text{Dividends} - \text{Beginning Value}}{\text{Beginning Value}} Nominal Return=Beginning ValueEnding Value+Dividends−Beginning Value Nominal Return=55.90+1.50−53.6053.60=3.8053.60≈0.0709 or 7.09% \text{Nominal Return} = \frac{55.90 + 1.50 - 53.60}{53.60} = \frac{3.80}{53.60} \approx 0.0709 \text{ or } 7.09\% Nominal Return=53.6055.90+1.50−53.60=53.603.80≈0.0709 or 7.09% Then, adjust for inflation using the formula: Real Rate of Return=1+Nominal Rate1+Inflation Rate−1 \text{Real Rate of Return} = \frac{1 + \text{Nominal Rate}}{1 + \text{Inflation Rate}} - 1 Real Rate of Return=1+Inflation Rate1+Nominal Rate−1 Real Rate of Return=1+0.07091+0.029−1≈1.07091.029−1≈0.0407 or 4.07% \text{Real Rate of Return} = \frac{1 + 0.0709}{1 + 0.029} - 1 \approx \frac{1.0709}{1.029} - 1 \approx 0.0407 \text{ or } 4.07\% Real Rate of Return=1+0.0291+0.0709−1≈1.0291.0709−1≈0.0407 or 4.07% Therefore, the approximate real rate of return is 4.2%, rounding to the nearest tenth.
Learning Objectives
- Calculate and understand the concept of real rate of return.
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