Inves tors want to earn returns that exceed the inflation rate, so the T-bill rate of return exceeds the inflation rate.
Inflation erodes the purchasing power of money.
If prices of most goods and services rise by 3% in a year, $1 buys about 3% fewer goods and services at the end of the year than at the beginning.
If investors want to increase their purchasing power over time, they need to earn higher returns than the inflation rate.
If you put $50 into an investment that pays 3% interest, at the end of the year you will have $51.50, which is the initial $50 plus a $1.50 return.
The 3% nominal return doesn't take into account the effects of inflation, so it doesn't mean that you are better off financially at the end of the year.
One bag of gro ceries costs $50 at the beginning of the year.
By the end of the year, one bag of groceries will cost $51.50.
At the beginning of the year, you could have used your $50 to buy one bag of groceries or make the investment that promised a 3% return.
If you invested your money instead of spending it on groceries, by the end of the year you would have had $51.50, still just enough to buy one bag of groceries.
Purchasing power did not increase during the year.
Even though the nominal rate of return is 3%, the real rate of return is zero.
By investing $50 you increased your wealth by 3%, but in terms of purchasing power you are no better off because you can only buy the same amount of goods that you could have bought before you made the investment.
The real rate of return is equal to the nominal rate of return minus the inflation rate.
If you have $50 today, you have to decide whether to spend it or invest it.
If you invest it, you believe that you can earn a nominal return of 10%, so after one year your money will grow to $55.
If you spend the money today, you will buy 20 lattes at your favorite coffee shop for $2.50 each.
A year later, you have $55, because you decided to save and invest your money.
You can afford to buy 21 lattes at the new price.
Your real return on the investment is 5% because it enabled you to buy 5% more than you could before you invested, and that extra latte represents an increase in your purchasing power of 5%.
The return that investors will require to make an investment depends on the risk associated with it.
The return is a kind of fore cast.
The investor will want to buy the investment if it is expected to earn a return greater than the required return.
The investor's required return can be vastly different from the return that an investment actually earns.
Although the historical average inflation rate in the United States has been close to 3.0%, investors' expectations may deviate from the norm.
Inflation forecasts for 2016 are projected to be low due to the effects of the global recession.
The rate of return can be earned on a risk-free investment, such as a short-term U.S. Treasury bill.
The formula for this rate is in Equation 4.2.
The issue and issuer factors contribute to the overall risk of an investment and cause investors to require a risk premium above the risk-free rate.
If investors expect 1% inflation, then the real required rate on Treasury bills issued by the U.S. will be higher.
The percentage of Nike is approximately 6%.
The government is almost risk between the risk premium and required returns.
The return on a one-year Treasury bill hovered in 2015.
25 basis points is what we look at.
The amount invested in a savings account does not change in value, even though the real return on T-bills was below average.
The amount invested in stocks, bonds, and mutual funds was further increased by the European Central Bank.
Hold periods of the same length should be used when comparing returns.
Define the holding period to avoid this problem.
The holding period is used as a standard to annualize.
Income and capital gains were identified earlier in the chapter.
Capital gains and losses are only realized when the investor sells an asset at the end of the investment period.
The capital gain return on an investment that increases in market value from $50 to $70 is $20.
You would sell the investment for $70 at the end of the year to realize the capital gain.
An investor who purchased the same investment but plans to hold it for another three years would not have realized the capital gain because he or she wouldn't have been able to collect the $20 profit in cash.
The capital gain must be included in the total return calculation.
The income and capital gains components can have a negative value.
An investment may have a negative income.
You may have to pay cash to meet certain obliga tions.
Any investment can suffer a capital loss.
Real estate, stocks, bonds, mutual funds, options, futures, and gold can all decline in value.
Analysts use the HPR with holding periods of less than a year.
The beginning investment value is the sum of income and capital gains achieved over the holding period.
The annual total returns are calculated in this way.
The HPR equation can be used to measure the total return earned or estimate the total return expected.
The key financial variables for four investments over the past year can be found in Table 4.6 summa.
The lines labeled (1) and (3) show the total income and capital gain during the investment period.
The total return over the year is calculated by adding the two sources of return.
The holding period return is given in line 5 when we divide the total return value by the beginning-of-year investment value.
The common stock had the highest HPR over the one-year holding period.
The savings account had a low percentage.
The beginning-of-period and end-of-period investment values are needed to find the HPR.
If the current income and capital gain values were drawn from a 6-month period instead of a one-year period, the HPR values would have been the same.
The holding period return can be negative or positive.
You can use historical data or forecast data to calculate HPRs.
The holding period return can be used to make investment decisions.
It makes it easier to compare the performance of investments that may differ greatly in terms of the amount of money required from an investor, because it measures an investment's return (including both the income and capital gains components) relative to the investment's initial cost.
If we only look at the total returns in dollars calculated for each of the investments, the real estate investment appears to have the highest total return.
The real estate investment requires the largest dollar outlay.
Common stock has the highest return per invested dollar at 12.05%.
For holding periods of one year or less, the HPR provides a method for evaluating and comparing investment returns because the return per invested dollar reflects the efficiency of the investment.
An alternative way to define a satisfactory investment is in terms of the annual rate of return it earns.
The HPR calculation doesn't fully account for the time value of money, and the HPRs for competing investments are not always compa rable.
The discount rate is the amount of the investment's cost to the present value of the benefits that it provides for the investor.
You can decide if an investment is worth it once you know the IRR.
The investment is acceptable if the IRR is equal to or greater than the required return.
It is unacceptable to invest below the required return.
It is easy to calculate the IRR on an investment that provides a single future cash flow.
More complex calculations are involved in the IRR on an investment.
These calculations can be simplified with a hand-held financial calculator.
U.S. savings bonds, zero-coupon bonds, and stocks with no dividends are some of the investments that do not provide periodic income.
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If you want to find the IRR on an investment that costs $1,000 today, you can get it for $1,400 in five years.
To calculate the IRR for this investment on a financial calculator, you have to consider the investment's cost as a present value, the payoff as a future value, and the present value as a future value.
If you want to calculate an unknown IRR, most calculators require you to enter the negative number.
You can verify the IRR using the inputs shown at the left.
An income stream can be provided by investments such as income-oriented stocks and bonds.
The discount rate that equates the present value of the investment's cash flows to its current price is the IRR on an investment that pays income periodically.
The investment is presented in Table 4.5.
The present value of the investment's cash flows is shown in the table.
8% is the internal rate of return if the market price of the investment is the same as the present value.
The price of this investment could fall to $1,100.
The present value of the investment's cash flows is $1,117.75 if we discount them at 9%.
The IRR must be above 9% to be above the investment's market price.
At a 10% discount rate, the present value of the cash flows is $1,063.40, so the investment's IRR must be below 10%.
You need to keep looking for the exact discount rate at which the investment's cash flows equal $1,100.
You can use a financial calculator to do that.
The following spreadsheet shows the IRR for a stream of income.
The IRR calculation contains a subtle assumption, but it is a measure of the return that an investment provides.
The assumption is that if the investor reinvested all of the income, they would get the same return on the original investment.
An example can be used to illustrate this concept.
If you buy a $1,000 U.S. Treasury bond, it will pay 8% annual interest for 20 years.
You get the $1,000 principal back when you receive $80 each year.
To earn an 8% IRR on this investment, you must be able to use the $80 annual interest income for the remaining 20-year life at the same annual rate of return.
The elements of return are shown in Figure 4.1.
At the end of 20 years, you'll have $2,600, the $1,000 principal and $1,600 in interest.
You will have $4,661 at the end of the 20-year life of the bond if you reinvested each $80 annual interest payment, and if those reinvest ment payments earn an 8% return from the time that they are received until the end of the bond's 20-year life.
If you want an 8% rate of return on an investment that makes periodic cash payments, you must earn that same rate of return when you invest in the full amount.
You can invest $1,000 today and have the same amount for 20 years.
You must be able to earn interest on interest at the same 8% rate if you want to achieve the IRR of 8%.
The rate of return is earned on interest or other income.
You'll earn the rate of return you set out to earn if you put your income to work at this rate.
Your return will decline if you must invest income at a lower rate.
It means that the IRR calculation accounts for the fact that you earn a higher return on an investment when you can use your cash flows.
A lot of income is involved in an investment program that involves interest.
You have to invest income.
The continued reinvestment of income plays an important role in investment success.
A simple technique for estimating growth rates using a financial calculator and an excel spreadsheet can be found here.
Imagine if you wanted to determine the rate at ExxonMobil Corp.