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Real Risk-Free Rate
Current 30-day T-bills are yielding 3.5 percent. Your accountant provided you with these interest rate premiums:
IP = 1.5%
LP = 0.6%
MRP = 1.8%
DFP = 2.15%
What is the real risk-free rate of return based on this data?
The risk-free rate of return is the theoretical rate of return of an investment with zero risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time.
The so-called “real” risk-free rate can be calculated by subtracting the current inflation rate from the yield of the Treasury bond matching your investment duration.
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Default Risk Premium
A Treasury bond maturing in 5 years has a yield of 4 percent. A 5-year corporate bond has a yield of 7 percent. Consider that the liquidity premium on the corporate bond is 0.5 percent. If this is so, what is the default risk on the corporate bond?
A default risk premium is effectively the difference between a debt instrument’s interest rate and the risk-free rate. The premium exists to compensate investors for an entity’s likelihood of defaulting on their debt. It is an additional amount of interest rates paid by a borrower to lender/ investor as a compensation for the higher credit risk of the borrower assuming his failure to pay back the principal amount in future and can be mathematically described as the difference in between the interest rates payable on bond and risk free rate of return.
The premium is determined by Credit history, Liquidity and profitability, Asset ownership
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Expected Interest Rate
For this problem, examine Treasury securities. Considering the following numbers, what would the yield on 3-year Treasury securities be?
Real risk-free = 4%.
Inflation expected at 1.5% for this year and 2% for the next 2 years.
Maturity risk premium = 0.
Treasury Securities
Treasury securities—including Treasury bills, notes, and bonds—are debt obligations issued by the U.S. Department of the Treasury. Treasury securities are considered one of the safest investments because they are backed by the full faith and credit of the U.S. government. The income from Treasury securities may be exempt from state and local taxes, but not from federal taxes.
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Required Rate of Return
Stock R’s beta = 1.5
Stock S’s beta = 0.75
Consider that the required return on an average stock is 14 percent. The risk-free rate of return is 6 percent. If this is so, the required return on the riskier stock exceeds the required return on the less risky stock by how much?
The required rate of return (RRR) is the minimum return an investor will accept for owning a company’s stock, as compensation for a given level of risk associated with holding the stock. The RRR is also used in corporate finance to analyze the profitability of potential investment projects.
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Evaluating Returns and Cash Flow Streams
Overview
Solve nine problems addressing a range of issues related to valuation of stocks, bonds, annuities, and cash flow streams.
The result of a financial manager’s efforts is ultimately reflected in stock price; maximizing shareowner wealth is what finance is all about. This assessment examines the classic financial tradeoff of risk versus reward.
By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:
Competency 1. Maximize shareholder wealth.
Calculate the required return on a portfolio fund.
Calculate the required rate of return.
Compute the present values of ordinary annuities.
Competency 3. Evaluate capital expenditure investment projects.
Calculate bond evaluation.
Apply computations to explain yield to call.
Calculate yield to maturity using correct calculations.
Compute the after tax cost of debt.
Competency 5. Apply evaluation principles of various financial instruments.
Explain uneven cash flow streams.
Evaluating Returns and Cash Flow Streams
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Context
Stocks
Maximizing shareowner wealth is all about increasing the stock price. Risky investments require higher returns, so when financial managers take greater risks, the logical reaction of shareowners is to demand a higher return. How do they accomplish this? If you were a bondholder, you would require a higher interest payment, but as a shareowner, you get higher returns by lowering the stock price.
So it may appear that a business should be averse to risk because it runs counter to the notion of a higher stock price, but in fact, businesses must take risks to get those higher returns. When relatively risky ventures pay off, or when shareowners believe management can pull it off, the stock price can soar.
Bonds
It is important to examine the main categories of bonds, long-term instruments such as Treasury bonds, corporate bonds, municipal bonds, and foreign bonds. All bonds share certain common features such as face or par value, coupon rate, maturity date, and other provisions. Some bonds are sold at a deep discount and do not provide any coupon interest payments; these are called zero-coupon bonds.
Previously we have talked about the fact that the value of any financial asset should be based on the present value of its future cash flows. This holds true for the valuation of bonds as well. There are different numerical tools used in assessing and comparing different bonds such as yield-to-maturity, current yield, and yield-to-call for callable bonds.
Our analysis of bonds would certainly be incomplete if we did not consider the risks involved in purchasing different types of bonds. Interest rate, reinvestment rate, and default risks are all associated with the investment in bonds. One important observation regarding the bond markets is that they rely on several independent bond rating agencies providing continuous monitoring of the most important bond issuers.
Evaluating Returns and Cash Flow Streams
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Cash Flow
An asset’s value depends on the valuation of the after-tax cash flows this asset is expected to produce.
Questions to consider
To deepen your understanding, you are encouraged to consider the questions below and discuss them with a fellow learner, a work associate, an interested friend, or a member of the business community.
Analyze some of the most important elements of the current tax laws, such as the differences between the treatment of dividends and interest paid and interest and dividend income received. How can financial managers increase shareholder value through managing tax obligations?
Examine the company you work for (if your company is not publicly held, pick a company you are familiar with), and consider the following.
Would you consider this company to be relatively risky? Does the stock rise and fall faster than the market?
What things contribute to the riskiness or stability of the stock?
What is the CAPM and security market line, and how can they be used in assessing share price?
The time value of money is defined as the math of finance for which interest is earned over time by saving or investing money. Why does time value affect almost any financial decision? Under what situations might time value matter less?
Examine the importance of bond ratings and some of the criteria used to rate bonds. Differentiate between interest rate risk, reinvestment rate risk, and default risk. How would a financial manager use bond ratings to increase the value of the firm?
Examine what is meant by the statement that a preferred stock is a hybrid between a common stock and a bond. What factors determine the value of a share of preferred stock?
Identify some of the factors that would cause you to rely more on either NPV or IRR. Does MIRR solve all of IRR’s shortcomings?
Evaluating Returns and Cash Flow Streams
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Resources
The following optional resources are provided to support you in completing the assessment or to provide a helpful context. For additional resources, refer to the Research Resources and Supplemental Resources in the left navigation menu of your courseroom.
Brigham, E. F., & Houston, J. F. (2016). Fundamentals of financial management (14th ed.). Boston, MA: Cengage.
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Assessment instructions
For this assessment, complete Problems 1–9 to apply the necessary knowledge to assess returns and cash flow streams. You may solve the problems algebraically, or you may use a financial calculator or an Excel spreadsheet. In addition to your solution to each computational problem, you must show the supporting work leading to your solution to receive credit for your answer. Note the following:
You may need an HP 10B II business calculator.
You may use Word or Excel, but you will find Excel to be most helpful for creating spreadsheets.
If you choose to solve the problems algebraically, be sure to show your computations.
If you use a financial calculator, show your input values.
If you use an Excel spreadsheet, show your input values and formulas.
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Portfolio Required Return
You are the money manager of a $10 million investment fund, which consists of four stocks. This fund has the following investments and betas:
Stock
Investment
Beta
A
$3,000,000
1.50
B
$1,000,000
(0.50)
C
$2,000,000
1.25
D
$4,000,000
0.75
If the market’s required rate of return is 12 percent, and the risk-free rate is 4 percent, what is the fund’s required rate of return?
The required rate of return (RRR) is the minimum return an investor will accept for owning a company’s stock, as compensation for a given level of risk associated with holding the stock. The RRR is also used in corporate finance to analyze the profitability of potential investment projects
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Over the past 5 years, the realized rate of return has averaged 13.0 percent.
A principal advantage of CAPM is the objective nature of the estimated costs of equity that the model can yield. CAPM cannot be used in isolation because it necessarily simplifies the world of financial markets. But financial managers can use it to supplement other techniques and their own judgment in their attempts to develop realistic and useful cost of equity calculations.
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Bond Valuation
You have two bonds in your portfolio. Each bond has a face value of $1000 and pays an 8 percent annual coupon. Bond X matures in 1 year, and Bond Y matures in 15 years.
If the going interest rate is 4 percent, 9 percent, and 14 percent, what will the value of each bond be? Assume Bond X only has one more interest payment to be made at maturity. Assume there are 15 more payments to be made on Bond Y.
The longer-term bond’s price varies more than the shorter-term bond‘s price when interest rates change. Explain why.
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Yield to Maturity
XYZ Inc. bonds have 5 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 8 percent.
What is the yield to maturity at a current market price of (1) $800 and (2) $1,200?
If a “fair” market interest rate for such bonds was 12 percent—that is, is rd=12%—would you pay $800 for each bond? Why or why not?
YTM – otherwise referred to as redemption or book yield – is the speculative rate of return or interest rate of a fixed-rate security, such as a bond. The YTM is based on the belief or understanding that an investor purchases the security at the current market price and holds it until the security has matured (reached its full value), and that all interest and coupon payments are made in a timely fashion.
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