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.
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.
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.
An asset’s value depends on the valuation of the after-tax cash flows this asset is expected to produce.
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.
Problem 1: 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:
StockInvestmentBetaA$3,000,0001.50B$1,000,000(0.50)C$2,000,0001.25D$4,000,0000.75If 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?
Problem 2: 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?
Problem 3: CAPM and Required Return
Calculate the required rate of return for XYZ Inc. using the following information:
The investors expect a 3.0 percent rate of inflation.
The real risk-free rate is 2.0 percent.
The market risk premium is 6.0 percent.
XYZ Inc. has a beta of 1.7.
Over the past 5 years, the realized rate of return has averaged 13.0 percent.
Problem 4: 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.
Problem 5: Yield to Call
Five years ago, XYZ Inc. issued 20-year bonds with a 12 percent annual coupon rate at their $1,000 par value. The bonds had 5 years of call protection and an 8 percent call premium. Yesterday, XYZ Inc. called the bonds.
For this problem, imagine that the investor who purchased the bonds when they were issued held them until they were called. Considering this, compute the realized rate of return. Should the investor be happy with XYZ Inc. calling the bonds? Why or why not?
Problem 6: 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?
Problem 7: After-Tax Cost of Debt
The XYZ Inc.’s currently outstanding bonds have a 10 percent yield to maturity and an 8 percent coupon. It can issue new bonds at par that would provide a similar yield to maturity. If its marginal tax rate is 40 percent, what is XYZ’s after-tax cost of debt?
Problem 8: Present Value of an Annuity
Find the present values of the following ordinary annuities if discounting occurs once a year:
$300 per year for 10 years at 10 percent.
$150 per year for 5 years at 5 percent.
$350 per year for 5 years at 0 percent.
Problem 9: Uneven Cash Flow Stream
Use the table below to answer the following:
What are the present values of the following cash flow streams if they are compounded at 5 percent annually?
What are the PVs of the streams at 0 percent compounded annually?
012345Stream A$0$100$400$400$400$300Stream B$0$300$400$400$400$100Competencies Measured
By successfully completing this assessment, you will demonstrate your proficiency in the course competencies through the following assessment scoring guide 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.