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Chapter 21: Problem 15

Distinguish the nominal rate of return from the real rate of return.

Short Answer

Expert verified
The nominal rate of return is the percentage increase in an investment's value over a period without considering inflation, while the real rate of return adjusts for inflation and represents the actual gain or loss in purchasing power. The main difference between the two is inflation adjustment. To compare investments accurately, it's crucial to evaluate their real rates of return, as this considers the change in purchasing power over time.

Step by step solution

01

Definition of Nominal Rate of Return

The nominal rate of return is the percentage increase in the value of an investment over a specific period, not considering the impact of inflation. It represents the raw growth that the investment has experienced during the time frame.
02

Definition of Real Rate of Return

The real rate of return takes into account the effect of inflation on the investment value, thus providing the actual gain or loss in purchasing power. It represents the increase or decrease in the value of an investment after adjusting for inflation.
03

Calculating the Real Rate of Return

To calculate the real rate of return, we can use the Fisher equation: \[ 1 + R_{real} = \frac{1 + R_{nominal}}{1 + R_{inflation}} \] Where \(R_{real}\) stands for the real rate of return, \(R_{nominal}\) is the nominal rate of return, and \(R_{inflation}\) represents the inflation rate.
04

Difference between Nominal and Real Rate of Return

1. Inflation Adjustment: The significant difference between the nominal and real rate of return is the adjustment for inflation. The nominal rate does not take inflation into account, while the real rate does and reflects the change in purchasing power. 2. Interpretation: A higher nominal rate might not necessarily mean that the investment has performed better, as one must also consider the inflation rate. When comparing the performance of different investments, it's essential to evaluate their real rates of return to take into account the effect of inflation. 3. Application: Nominal rates of return are typically used for short term investments and simple cash flow estimations. Real rates of return are more useful for long term investments and assessing the actual growth, as they consider the change in purchasing power. In conclusion, to distinguish the nominal rate of return from the real rate of return, it is important to understand how inflation impacts their calculations and their interpretations in terms of investment performance.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Nominal Rate of Return
The nominal rate of return reflects the simple percentage increase in the value of an investment over a given period. This rate does not account for any external factors like inflation. It essentially shows the raw growth of investment without any adjustments. For example, if you invest $1,000 and it grows to $1,100 over a year, the nominal rate of return is 10%. This rate is straightforward and is often used to quickly assess the apparent growth of an investment.
However, the nominal rate might not paint the full picture of an investment's performance since inflation could erode the actual purchasing power gained from the investment during that period. It is most applicable in stable or short-term investment contexts where inflation is assumed to be negligible.
Real Rate of Return
The real rate of return reveals the actual increase in the purchasing power derived from an investment. Unlike the nominal rate, it adjusts for inflation, providing a clearer picture of an investment's value growth in real terms. If inflation is significant, an investment may show a positive nominal return but could result in a negative real return, meaning your purchasing power is actually decreasing.
To calculate the real rate of return, you need to adjust the nominal rate using the Fisher equation: \( 1 + R_{\text{real}} = \frac{1 + R_{\text{nominal}}}{1 + R_{\text{inflation}}} \). Here, \( R_{\text{real}} \) is the real rate of return, \( R_{\text{nominal}} \) is the nominal rate, and \( R_{\text{inflation}} \) is the inflation rate. This formula highlights the importance of considering inflation to understand the genuine benefits of an investment.
Investment Performance
Investment performance is often assessed through the lens of both nominal and real rates of return. These measures help investors understand how well their investments are doing not just in sheer growth, but in actual financial benefit after accounting for inflation.
  • Nominal rates are suitable for quick evaluations but require context to understand their implications fully.
  • Real rates give a deeper insight into an investment's effectiveness, particularly over the long term. They help investors assess if they truly gained or lost purchasing power.
When evaluating investment performance, it is crucial to interpret both types of rates. A high nominal rate could be misleading if inflation rates are substantial, making the real rate more favorable in understanding the genuine financial outcome.
Inflation Adjustment
Inflation adjustment is crucial in converting nominal returns into real returns, reflecting the true economic impact on the investment's value. Inflation erodes the purchasing power of money, which means the same amount of money buys less over time.
Inflation adjustment is crucial for long-term investments. Using just the nominal rate can mislead investors about the actual benefit from an investment. Adjusting for inflation gives a more realistic assessment of whether the investment truly added value or if its gains were merely due to increased prices in the economy.
  • For short-term evaluations, nominal rates might suffice if inflation is minimal.
  • For meaningful insights, especially over long durations, adjusting for inflation is a necessity.
Understanding inflation adjustment helps investors maintain clear expectations about their financial growth and helps avoid overestimating potential gains.

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Most popular questions from this chapter

How can sensitivity analysis be incorporated in DCF analysis?

A company should accept for investment all positive NPV investment alternatives when which of the following conditions is true? a. The company has extremely limited resources for capital investment. b. The company has excess cash on its balance sheet. c. The company has virtually unlimited resources for capital investment. d. The company has limited resources for capital investment but is planning to issue new equity to finance additional capital investment.

What is the payback method? What are its main strengths and weaknesses?

\((\mathrm{CMA},\) adapted) The Kuhl Brothers own a frozen custard ice cream shop. The brothers currently are using a machine that has been in use for the last 4 years. \(0 n\) January \(1,2017,\) the \(\mathrm{Kuhl}\) Brothers are considering buying a new machine to make their frozen custard. The Kuhl Brothers have two options: (1) continue using the old freezing machine or (2) sell the old machine and purchase a new freezing machine. The seller of the new machine is not interested in a tradein of Kuhl's old machine. The following information has been obtained: The Kuhl Brothers are subject to a \(25 \%\) income tax rate. Any gain or loss on the sale of machines is treated as an ordinary tax item and will affect the taxes paid by the Kuhl Brothers in the year in which it occurs. The Kuhl Brothers have an after-tax required rate of return of \(8 \%\). Assume all cash flows occur at year-end except for initial investment amounts. 1\. The Kuhl Brothers ask you whether they should buy the new machine. To help in your analysis, calculate the following: a. One-time after-tax cash effect of disposing of the old machine on January 1,2017 b. Annual recurring after-tax cash operating savings from using the new machine (variable and fixed) c. Cash tax savings due to differences in annual depreciation of the old machine and the new machine d. Difference in after-tax cash flow from terminal disposal of new machine and old machine 2\. Use your calculations in requirement 1 and the net present value method to determine whether the Kuhl Brothers should continue to use the old machine or acquire the new machine. 3\. How much more or less would the recurring after-tax cash operating savings of the new machine need to be for the Kuhl Brothers to earn exactly the \(8 \%\) after-tax required rate of return? Assume that all other data about the investment do not change.

Johnny Buster owns Entertainment World, a place that combines fast food, innovative beverages, and arcade games. Worried about the shifting tastes of younger audiences, Johnny contemplates bringing in new simulators and virtual reality games to maintain customer interest. As part of this overhaul, Johnny is also looking at replacing his old Guitar Hero equipment with a Rock Band Pro machine. The Guitar Hero setup was purchased for 25,200 dollar and has accumulated depreciation of 23,000 dollar, with a current trade-in value of 2,700 dollar.It currently costs Johnny 600 dollar per month in utilities and another 5,000 dollar a year in maintenance to run the Guitar Hero equipment. Johnny feels that the equipment could be kept in service for another 11 years, after which it would have no salvage value. The Rock Band Pro machine is more energy efficient and durable. It would reduce the utilities costs by \(30 \%\) and cut the maintenance cost in half. The Rock Band Pro costs 49,000 dollar and has an expected disposal value of 5,000 at the end of its useful life of 11 years. Johnny charges an entrance fee of 5 dollar per hour for customers to play an unlimited number of games. He does not believe that replacing Guitar Hero with Rock Band Pro will have an impact on this charge or materially change the number of customers who will visit Entertainment World. 1\. Johnny wants to evaluate the Rock Band Pro purchase using capital budgeting techniques. To help him, read through the problem and separate the cash flows into four groups: (1) net initial investment cash flows, (2) cash flow savings from operations, (3) cash flows from terminal disposal of investment, and (4) cash flows not relevant to the capital budgeting problem. 2\. Assuming a tax rate of \(40 \%\), a required rate of return of \(8 \%\), and straight-line depreciation over the remaining useful life of equipment, should Johnny purchase Rock Band Pro?
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