# GESTÃO FINANCEIRA II PROBLEM SET 2 - SOLUTIONS

Size: px
Start display at page:

Transcription

1 GESTÃO FINANCEIRA II PROBLEM SET - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER

2 Yield to Maturity Chapter 8 Valuing Bonds 8-3. The following table summarizes prices of various default-free, zero-coupon bonds (expressed as a percentage of face value): a. Compute the yield to maturity for each bond. b. Plot the zero-coupon yield curve (for the first five years). c. Is the yield curve upward sloping, downward sloping, or flat? a. Use the following equation. 1 YTM n FV P n 1/ n 1/1 1 YTM1 YTM1 4.70% 9.1 1/ 1 YTM1 YTM1 4.80% / 3 1 YTM3 YTM3.00% / 4 1 YTM4 YTM4.0% / 1 YTM YTM.0% 76.1 b. The yield curve is as shown below. Zero Coupon Yield Curve Maturity (Years) c. The yield curve is upward sloping.

3 8-. In the box in Section 8.1, Bloomberg.com reported that the three-month Treasury bill sold for a price of \$.006 per \$ face value. What is the yield to maturity of this bond, expressed as an EAR? % Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6%. You hold the bond for five years before selling it. a. If the bond s yield to maturity is 6% when you sell it, what is the internal rate of return of your investment? b. If the bond s yield to maturity is 7% when you sell it, what is the internal rate of return of your investment? c. If the bond s yield to maturity is % when you sell it, what is the internal rate of return of your investment? d. Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Explain. a. Purchase price = / = Sale price = / 1.06 = Return = (3.30 / 17.41) 1/ 1 = 6.00%. I.e., since YTM is the same at purchase and sale, IRR = YTM. b. Purchase price = / = Sale price = / 1.07 = Return = (18.4 / 17.41) 1/ 1 = 1.13%. I.e., since YTM rises, IRR < initial YTM. c. Purchase price = / = Sale price = / 1.0 = 9.3. Return = (9.3 / 17.41) 1/ 1 = 11.1%. I.e., since YTM falls, IRR > initial YTM. d. Even without default, if you sell prior to maturity, you are exposed to the risk that the YTM may change What is the price of a three-year, default-free security with a face value of \$0 and an annual coupon rate of 4%? What is the yield to maturity for this bond? The price of the bond is CPN CPN CPN FV P... \$ N 3 1 YTM1 (1 YTM ) (1 YTM N ) (1.04) (1.043) (1.04) The yield to maturity is CPN CPN CPN FV P... 1 YTM (1 YTM ) (1 YTM ) N \$986.8 YTM 4.488% 3 (1 YTM ) (1 YTM ) (1 YTM )

4 8-0. What is the maturity of a default-free security with annual coupon payments and a yield to maturity of 4%? Why? The maturity must be one year. If the maturity were longer than one year, there would be an arbitrage opportunity Prices of zero-coupon, default-free securities with face values of \$0 are summarized in the following table: Suppose you observe that a three-year, default-free security with an annual coupon rate of 10% and a face value of \$0 has a price today of \$ Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not? First, figure out if the price of the coupon bond is consistent with the zero coupon yields implied by the other securities YTM1 3.0% (1 YTM ) YTM 3.% (1 YTM ) YTM % (1 YTM 3) According to these zero coupon yields, the price of the coupon bond should be: 0 \$ (1.03) (1.03) (1.034) The price of the coupon bond is too low, so there is an arbitrage opportunity. To take advantage of it: Today 1 Year Years 3 Years Buy 10 Coupon Bonds ,000 Short Sell 1 One-Year Zero Short Sell 1 Two-Year Zero Short Sell 11 Three-Year Zeros Net Cash Flow Assume there are four default-free bonds with the following prices and future cash flows: Do these bonds present an arbitrage opportunity? If so, how would you take advantage of this opportunity? If not, why not? To determine whether these bonds present an arbitrage opportunity, check whether the pricing is internally consistent. Calculate the spot rates implied by Bonds A, B, and D (the zero coupon bonds), and use this to check Bond C. (You may alternatively compute the spot rates from Bonds A, B, and C, and check Bond D, or some other combination.)

5 YTM1 7.0% (1 YTM ) YTM 6.% (1 YTM ) YTM % (1 YTM 3) Given the spot rates implied by Bonds A, B, and D, the price of Bond C should be \$1,10.1. Its price really is \$1,118.1, so it is overpriced by \$13 per bond. Yes, there is an arbitrage opportunity. To take advantage of this opportunity, you want to (short) Sell Bond C (since it is overpriced). To match future cash flows, one strategy is to sell 10 Bond Cs (it is not the only effective strategy; any multiple of this strategy is also arbitrage). This complete strategy is summarized in the table below. Today 1 Year Years 3Years Sell Bond C 11, ,000 1,000 11,000 Buy Bond A , Buy Bond B ,000 0 Buy 11 Bond D 9, ,000 Net Cash Flow Notice that your arbitrage profit equals 10 times the mispricing on each bond (subject to rounding error). 8-. Suppose you are given the following information about the default-free, coupon-paying yield curve: a. Use arbitrage to determine the yield to maturity of a two-year, zero-coupon bond. b. What is the zero-coupon yield curve for years 1 through 4? a. We can construct a two-year zero coupon bond using the one and two-year coupon bonds as follows. Cash Flow in Year: Two-year coupon bond (\$0 Face Value) 1, Less: One-year bond (\$ Face Value) () Two-year zero (\$1 Face Value) - 1, 1 Now, Price(-year coupon bond) = \$111.0 Price(1-year bond) = \$ By the Law of One Price: Price( year zero) = Price( year coupon bond) Price(One-year bond) = = \$ Given this price per \$1 face value, the YTM for the -year zero is (Eq. 8.3)

6 1/ 1 YTM () % b. We already know YTM(1) = %, YTM() = 4%. We can construct a 3-year zero as follows: Cash Flow in Year: Three-year coupon bond (\$0 face value) ,060 Less: one-year zero (\$60 face value) (60) Less: two-year zero (\$60 face value) - (60) Three-year zero (\$1060 face value) - - 1, Now, Price(3-year coupon bond) = By the Law of One Price: \$4.9. Price(3-year zero) = Price(3-year coupon bond) Price(One-year zero) Price(Two-year zero) = Price(3-year coupon bond) PV(coupons in years 1 and ) = / / 1.04 = \$ Solving for the YTM: 1/ YTM (3) % Finally, we can do the same for the 4-year zero: Cash Flow in Year: Four-year coupon bond (\$0 face value) ,10 Less: one-year zero (\$10 face value) (10) Less: two-year zero (\$10 face value) (10) Less: three-year zero (\$10 face value) (10) Four-year zero (\$110 face value) 1, Now, Price(4-year coupon bond) = By the Law of One Price: Price(4-year zero) = Price(4-year coupon bond) PV(coupons in years 1 3) = / / / = \$ Solving for the YTM: \$ / YTM (4) %

7 Yield to Maturity Thus, we have computed the zero coupon yield curve as shown. 7% 6% % 4% 3% % 1% 0% Year HMK Enterprises would like to raise \$10 million to invest in capital expenditures. The company plans to issue five-year bonds with a face value of \$0 and a coupon rate of 6.% (annual payments). The following table summarizes the yield to maturity for five-year (annualpay) coupon corporate bonds of various ratings: a. Assuming the bonds will be rated AA, what will the price of the bonds be? b. How much total principal amount of these bonds must HMK issue to raise \$10 million today, assuming the bonds are AA rated? (Because HMK cannot issue a fraction of a bond, assume that all fractions are rounded to the nearest whole number.) c. What must the rating of the bonds be for them to sell at par? d. Suppose that when the bonds are issued, the price of each bond is \$99.4. What is the likely rating of the bonds? Are they junk bonds? a. The price will be P \$8.36. (1.063) (1.063) b. Each bond will raise \$8.36, so the firm must issue: \$10,000, bonds. \$8.36 This will correspond to a principle amount of 9918 \$0 \$9,918,000. c. For the bonds to sell at par, the coupon must equal the yield. Since the coupon is 6.%, the yield must also be 6.%, or A-rated. d. First, compute the yield on these bonds: YTM 7.%. (1 YTM ) (1 YTM ) Given a yield of 7.%, it is likely these bonds are BB rated. Yes, BB-rated bonds are junk bonds.

8 Chapter 9 Valuing Stocks 9-1. Assume Evco, Inc., has a current price of \$0 and will pay a \$ dividend in one year, and its equity cost of capital is 1%. What price must you expect it to sell for right after paying the dividend in one year in order to justify its current price? We can use Eq. (9.1) to solve for the price of the stock in one year given the current price of \$0.00, the \$ dividend, and the 1% cost of capital. X X.0 At a current price of \$0, we can expect Evco stock to sell for \$.0 immediately after the firm pays the dividend in one year. 9-. Anle Corporation has a current price of \$0, is expected to pay a dividend of \$1 in one year, and its expected price right after paying that dividend is \$. a. What is Anle s expected dividend yield? b. What is Anle s expected capital gain rate? c. What is Anle s equity cost of capital? a. Div yld = 1/0 = % b. Cap gain rate = (-0)/0 = 10% c. Equity cost of capital = % + 10% = 1% 9-6. Summit Systems will pay a dividend of \$1.0 this year. If you expect Summit s dividend to grow by 6% per year, what is its price per share if its equity cost of capital is 11%? P = 1.0 / (11% 6%) = \$ Dorpac Corporation has a dividend yield of 1.%. Dorpac s equity cost of capital is 8%, and its dividends are expected to grow at a constant rate. a. What is the expected growth rate of Dorpac s dividends? b. What is the expected growth rate of Dorpac s share price? a. Eq 9.7 implies r E = Div Yld + g, so 8% 1.% = g = 6.%. b. With constant dividend growth, share price is also expected to grow at rate g = 6.% (or we can solve this from Eq 9.).

9 9-1. Colgate-Palmolive Company has just paid an annual dividend of \$0.96. Analysts are predicting an 11% per year growth rate in earnings over the next five years. After then, Colgate s earnings are expected to grow at the current industry average of.% per year. If Colgate s equity cost of capital is 8.% per year and its dividend payout ratio remains constant, what price does the dividend-discount model predict Colgate stock should sell for? PV of the first dividends: PV first PV of the remaining dividends in year : PV remaining in year Discounting back to the present PV remaining Thus the price of Colgate is P PV first PV remaining Suppose Cisco Systems pays no dividends but spent \$ billion on share repurchases last year. If Cisco s equity cost of capital is 1%, and if the amount spent on repurchases is expected to grow by 8% per year, estimate Cisco s market capitalization. If Cisco has 6 billion shares outstanding, what stock price does this correspond to? Total payout next year = billion 1.08 = \$.4 billion Equity Value =.4 / (1% 8%) = \$13 billion Share price = 13 / 6 = \$ Benchmark Metrics, Inc. (BMI), an all-equity financed firm, just reported EPS of \$.00 per share for 008. Despite the economic downturn, BMI is confident regarding its current investment opportunities. But due to the financial crisis, BMI does not wish to fund these investments externally. The Board has therefore decided to suspend its stock repurchase plan and cut its dividend to \$1 per share (vs. almost \$ per share in 007), and retain these funds instead. The firm has just paid the 008 dividend, and BMI plans to keep its dividend at \$1 per share in 009 as well. In subsequent years, it expects its growth opportunities to slow, and it will still be able to fund its growth internally with a target 40% dividend payout ratio, and reinitiating its stock repurchase plan for a total payout rate of 60%. (All dividends and repurchases occur at the end of each year.) Suppose BMI s existing operations will continue to generate the current level of earnings per share in the future. Assume further that the return on new investment is 1%, and that reinvestments will account for all future earnings growth (if any). Finally, assume BMI s equity cost of capital is 10%. a. Estimate BMI s EPS in 009 and 010 (before any share repurchases). b. What is the value of a share of BMI at the start of 009? a. To calculate earnings growth, we can use the formula: g = (retention rate) RONI. In 008, BMI retains \$4 of its \$ in EPS, for a retention rate of 80%, and an earnings growth rate of 80% 1% = 1%. Thus, EPS009 = \$.00 (1.1) = \$.60.

10 In 009, BMI retains \$4.60 of its \$.60 in EPS, for a retention rate of 8.14% and an earnings growth rate of 8.14% 1% = 1.3%. So, EPS010 = \$.60 (1.13) = \$6.9. b. From 010 on, the firm plans to retain 40% of EPS, for a growth rate of 40% 1% = 6%. Total Payouts in 010 are 60% of EPS, or 60% \$6.9 = \$ Thus, the value of the stock at the end of 009 is, given the 6% future growth rate, P009 = \$3.77/(10% - 6%) = \$94.3. Given the \$1 dividend in 009, we get a share price in 008 of P008 = (\$ )/1.10 = \$ Heavy Metal Corporation is expected to generate the following free cash flows over the next five years: After then, the free cash flows are expected to grow at the industry average of 4% per year. Using the discounted free cash flow model and a weighted average cost of capital of 14%: a. Estimate the enterprise value of Heavy Metal. b. If Heavy Metal has no excess cash, debt of \$300 million, and 40 million shares outstanding, estimate its share price. a. V(4) = 8 / (14% 4%) = \$80 V(0) = 3 / / / (7 + 80) / =\$681 b. P = ( )/40 = \$ You notice that PepsiCo has a stock price of \$.66 and EPS of \$3.0. Its competitor, the Coca- Cola Company, has EPS of \$.49. Estimate the value of a share of Coca-Cola stock using only this data. PepsiCo P/E =.66/3.0 = 16.46x. Apply to Coca-Cola: \$ = \$ Suppose that in January 006, Kenneth Cole Productions had EPS of \$1.6 and a book value of equity of \$1.0 per share. a. Using the average P/E multiple in Table 9.1, estimate KCP s share price. b. What range of share prices do you estimate based on the highest and lowest P/E multiples in Table 9.1? c. Using the average price to book value multiple in Table 9.1, estimate KCP s share price. d. What range of share prices do you estimate based on the highest and lowest price to book value multiples in Table 9.1? a. Share price = Average P/E KCP EPS = 1.01 \$1.6 = \$4.77 b. Minimum = 8.66 \$1.6 = \$14.9, Maximum =.6 \$1.6 = \$37.3 c..84 \$1.0 = \$34. d. 1.1 \$1.0 = \$13.0, 8.11 \$1.0 = \$97.73

11 9-4. Suppose that in January 006, Kenneth Cole Productions had sales of \$18 million, EBITDA of \$.6 million, excess cash of \$ million, \$3 million of debt, and 1 million shares outstanding. a. Using the average enterprise value to sales multiple in Table 9.1, estimate KCP s share price. b. What range of share prices do you estimate based on the highest and lowest enterprise value to sales multiples in Table 9.1? c. Using the average enterprise value to EBITDA multiple in Table 9.1, estimate KCP s share price. d. What range of share prices do you estimate based on the highest and lowest enterprise value to EBITDA multiples in Table 9.1? a. Estimated enterprise value for KCP = Average EV/Sales KCP Sales = 1.06 \$18 million = \$49 million. Equity Value = EV Debt + Cash = \$ = \$646 million. Share price = Equity Value / Shares = \$646/ 1 = \$30.77 b. \$16.1 \$8.64 c. Est. enterprise value for KCP = Average EV/EBITDA KCP EBITDA = 8.49 \$.6 million = \$47 million. Share Price = (\$ )/1 = \$7.10 d. \$. \$ Consider the following data for the airline industry in early 009 (EV = enterprise value, BV = book value, NM = not meaningful because divisor is negative). Discuss the challenges of using multiples to value an airline. All the multiples show a great deal of variation across firms. This makes the use of multiples problematic because there is clearly more to valuation than the multiples reveal. Without a clear understanding of what drives the differences in multiples across airlines, it is unclear what the correct multiple to use is when trying to value a new airline.

### How To Value A Stock

Chapter 9 Valuing Stocks 9-1. Assume Evco, Inc., has a current price of \$50 and will pay a \$2 dividend in one year, and its equity cost of capital is 15%. What price must you expect it to sell for right

### Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices

196 Part Interest Rates and Valuing Cash Flows Chapter 6 APPENDIX B The Yield Curve and the Law of One Price Thus far, we have focused on the relationship between the price of an individual bond and its

### CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

Chapter - The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

### CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

### CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is

### LECTURE- 4. Valuing stocks Berk, De Marzo Chapter 9

1 LECTURE- 4 Valuing stocks Berk, De Marzo Chapter 9 2 The Dividend Discount Model A One-Year Investor Potential Cash Flows Dividend Sale of Stock Timeline for One-Year Investor Since the cash flows are

### Chapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.

Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10-year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity

### Chapter Nine Selected Solutions

Chapter Nine Selected Solutions 1. What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the

### Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage

Prof. Alex Shapiro Lecture Notes 12 Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage I. Readings and Suggested Practice Problems II. Bonds Prices and Yields (Revisited)

### CIS September 2012 Exam Diet. Examination Paper 2.2: Corporate Finance Equity Valuation and Analysis Fixed Income Valuation and Analysis

CIS September 2012 Exam Diet Examination Paper 2.2: Corporate Finance Equity Valuation and Analysis Fixed Income Valuation and Analysis Corporate Finance (1 13) 1. Assume a firm issues N1 billion in debt

### CHAPTER 5 HOW TO VALUE STOCKS AND BONDS

CHAPTER 5 HOW TO VALUE STOCKS AND BONDS Answers to Concepts Review and Critical Thinking Questions 1. Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are used

### Practice Set #2 and Solutions.

FIN-672 Securities Analysis & Portfolio Management Professor Michel A. Robe Practice Set #2 and Solutions. What to do with this practice set? To help MBA students prepare for the assignment and the exams,

### You just paid \$350,000 for a policy that will pay you and your heirs \$12,000 a year forever. What rate of return are you earning on this policy?

1 You estimate that you will have \$24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each

### 1. What are the three types of business organizations? Define them

Written Exam Ticket 1 1. What is Finance? What do financial managers try to maximize, and what is their second objective? 2. How do you compare cash flows at different points in time? 3. Write the formulas

### Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates

Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment

### Mid-Term Exam Practice Set and Solutions.

FIN-469 Investments Analysis Professor Michel A. Robe Mid-Term Exam Practice Set and Solutions. What to do with this practice set? To help students prepare for the mid-term exam, two practice sets with

### BUSINESS FINANCE (FIN 312) Spring 2009

BUSINESS FINANCE (FIN 31) Spring 009 Assignment Instructions: please read carefully You can either do the assignment by yourself or work in a group of no more than two. You should show your work how to

### CHAPTER 8 INTEREST RATES AND BOND VALUATION

CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are

### Practice Questions for Midterm II

Finance 333 Investments Practice Questions for Midterm II Winter 2004 Professor Yan 1. The market portfolio has a beta of a. 0. *b. 1. c. -1. d. 0.5. By definition, the beta of the market portfolio is

### Primary Market - Place where the sale of new stock first occurs. Initial Public Offering (IPO) - First offering of stock to the general public.

Stock Valuation Primary Market - Place where the sale of new stock first occurs. Initial Public Offering (IPO) - First offering of stock to the general public. Seasoned Issue - Sale of new shares by a

### CHAPTER 8 STOCK VALUATION

CHAPTER 8 STOCK VALUATION Answers to Concepts Review and Critical Thinking Questions 5. The common stock probably has a higher price because the dividend can grow, whereas it is fixed on the preferred.

### Bond valuation and bond yields

RELEVANT TO ACCA QUALIFICATION PAPER P4 AND PERFORMANCE OBJECTIVES 15 AND 16 Bond valuation and bond yields Bonds and their variants such as loan notes, debentures and loan stock, are IOUs issued by governments

### Yield to Maturity Outline and Suggested Reading

Yield to Maturity Outline Outline and Suggested Reading Yield to maturity on bonds Coupon effects Par rates Buzzwords Internal rate of return, Yield curve Term structure of interest rates Suggested reading

### Examination II. Fixed income valuation and analysis. Economics

Examination II Fixed income valuation and analysis Economics Questions Foundation examination March 2008 FIRST PART: Multiple Choice Questions (48 points) Hereafter you must answer all 12 multiple choice

### The Term Structure of Interest Rates CHAPTER 13

The Term Structure of Interest Rates CHAPTER 13 Chapter Summary Objective: To explore the pattern of interest rates for different-term assets. The term structure under certainty Forward rates Theories

### CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS

1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries

### How To Calculate The Cost Of Capital Of A Firm

Sample Problems Chapter 10 Title: Cost of Debt 1. Costly Corporation plans a new issue of bonds with a par value of \$1,000, a maturity of 28 years, and an annual coupon rate of 16.0%. Flotation costs associated

### Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk

Bond Valuation 1 Topics in Chapter Key features of bonds Bond valuation Measuring yield Assessing risk 2 Determinants of Intrinsic Value: The Cost of Debt Net operating profit after taxes Free cash flow

### Chapter 4 Valuing Bonds

Chapter 4 Valuing Bonds MULTIPLE CHOICE 1. A 15 year, 8%, \$1000 face value bond is currently trading at \$958. The yield to maturity of this bond must be a. less than 8%. b. equal to 8%. c. greater than

### Exam 1 Morning Session

91. A high yield bond fund states that through active management, the fund s return has outperformed an index of Treasury securities by 4% on average over the past five years. As a performance benchmark

### Chapter Review Problems

Chapter Review Problems State all stock and bond prices in dollars and cents. Unit 14.1 Stocks 1. When a corporation earns a profit, the board of directors is obligated by law to immediately distribute

Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation

### Estimating Beta. Aswath Damodaran

Estimating Beta The standard procedure for estimating betas is to regress stock returns (R j ) against market returns (R m ) - R j = a + b R m where a is the intercept and b is the slope of the regression.

### LOS 56.a: Explain steps in the bond valuation process.

The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction

### Duration and convexity

Duration and convexity Prepared by Pamela Peterson Drake, Ph.D., CFA Contents 1. Overview... 1 A. Calculating the yield on a bond... 4 B. The yield curve... 6 C. Option-like features... 8 D. Bond ratings...

### 2. Determine the appropriate discount rate based on the risk of the security

Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the

### Exercise. Exam Aid: All calculators are allowed but empty memory. Paper dictionaries are allowed. No other aids allowed in the exam room.

Exercise Exam Aid: All calculators are allowed but empty memory. Paper dictionaries are allowed. No other aids allowed in the exam room. Note: No formula sheets are allowed in the exam. Exercise: 01 Exercise

### Bond Valuation. What is a bond?

Lecture: III 1 What is a bond? Bond Valuation When a corporation wishes to borrow money from the public on a long-term basis, it usually does so by issuing or selling debt securities called bonds. A bond

### FNCE 301, Financial Management H Guy Williams, 2006

REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including

### Caput Derivatives: October 30, 2003

Caput Derivatives: October 30, 2003 Exam + Answers Total time: 2 hours and 30 minutes. Note 1: You are allowed to use books, course notes, and a calculator. Question 1. [20 points] Consider an investor

### M5.1 Forecasting from Traded Price-to-Book Ratios: Cisco Systems Inc.

M5.1 Forecasting from Traded Price-to-Book Ratios: Cisco Systems Inc. Price = \$21 Required equity return = 12% Forward P/E = \$21/\$0.89 = 23.60 Book value per share = \$25,826/6,735 = \$3.835 P/B = \$21/3.835

### Modified dividend payout ratio =

15 Modifying the model to include stock buybacks In recent years, firms in the United States have increasingly turned to stock buybacks as a way of returning cash to stockholders. Figure 13.3 presents

### ANSWERS TO END-OF-CHAPTER PROBLEMS WITHOUT ASTERISKS

Part III Answers to End-of-Chapter Problems 97 CHAPTER 1 ANSWERS TO END-OF-CHAPTER PROBLEMS WITHOUT ASTERISKS Why Study Money, Banking, and Financial Markets? 7. The basic activity of banks is to accept

### GESTÃO FINANCEIRA II PROBLEM SET 3 - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE

GESTÃO FINANCEIRA II PROBLEM SET 3 - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 010-011 Chapter 10 Capital Markets and the Pricing of Risk 10-1.

### Bond Valuation. Capital Budgeting and Corporate Objectives

Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What

### CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING

CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING Answers to Concepts Review and Critical Thinking Questions 1. No. The cost of capital depends on the risk of the project, not the source of the money.

### Solutions 2. 1. For the benchmark maturity sectors in the United States Treasury bill markets,

FIN 472 Professor Robert Hauswald Fixed-Income Securities Kogod School of Business, AU Solutions 2 1. For the benchmark maturity sectors in the United States Treasury bill markets, Bloomberg reported the

### CHAPTER FOUR Cash Accounting, Accrual Accounting, and Discounted Cash Flow Valuation

CHAPTER FOUR Cash Accounting, Accrual Accounting, and Discounted Cash Flow Valuation Concept Questions C4.1. There are difficulties in comparing multiples of earnings and book values - the old techniques

### Bond Valuation. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Bond Valuation: An Overview

Bond Valuation FINANCE 350 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University 1 Bond Valuation: An Overview Bond Markets What are they? How big? How important? Valuation

### Estimating Risk free Rates. Aswath Damodaran. Stern School of Business. 44 West Fourth Street. New York, NY 10012. Adamodar@stern.nyu.

Estimating Risk free Rates Aswath Damodaran Stern School of Business 44 West Fourth Street New York, NY 10012 Adamodar@stern.nyu.edu Estimating Risk free Rates Models of risk and return in finance start

### Key Concepts and Skills Chapter 8 Stock Valuation

Key Concepts and Skills Chapter 8 Stock Valuation Konan Chan Financial Management, Spring 2016 Understand how stock prices depend on future dividends and dividend growth Be able to compute stock prices

### FNCE 301, Financial Management H Guy Williams, 2006

Stock Valuation Stock characteristics Stocks are the other major traded security (stocks & bonds). Options are another traded security but not as big as these two. - Ownership Stockholders are the owner

### Bond Pricing Fundamentals

Bond Pricing Fundamentals Valuation What determines the price of a bond? Contract features: coupon, face value (FV), maturity Risk-free interest rates in the economy (US treasury yield curve) Credit risk

### Term Structure of Interest Rates

Appendix 8B Term Structure of Interest Rates To explain the process of estimating the impact of an unexpected shock in short-term interest rates on the entire term structure of interest rates, FIs use

### Use the table for the questions 18 and 19 below.

Use the table for the questions 18 and 19 below. The following table summarizes prices of various default-free zero-coupon bonds (expressed as a percentage of face value): Maturity (years) 1 3 4 5 Price

### Fixed Income: Practice Problems with Solutions

Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.

### Investments 320 Dr. Ahmed Y. Dashti Chapter 3 Interactive Qustions

Investments 320 Dr. Ahmed Y. Dashti Chapter 3 Interactive Qustions 3-1. A primary asset is an initial offering sold by a business, or government, to raise funds. A) True B) False 3-2. Money market instruments

### GESTÃO FINANCEIRA II PROBLEM SET 5 SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE

GESTÃO FINANCEIRA II PROBLEM SET 5 SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 2010-2011 Chapter 18 Capital Budgeting and Valuation with Leverage

### Coupon Bonds and Zeroes

Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zero-coupon bonds Bond replication No-arbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semi-annual compounding

### The Marginal Cost of Capital and the Optimal Capital Budget

WEB EXTENSION12B The Marginal Cost of Capital and the Optimal Capital Budget If the capital budget is so large that a company must issue new equity, then the cost of capital for the company increases.

### C(t) (1 + y) 4. t=1. For the 4 year bond considered above, assume that the price today is 900\$. The yield to maturity will then be the y that solves

Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of long-term fixed income securities are federal government bonds, corporate

### 1. Present Value. 2. Bonds. 3. Stocks

Stocks and Bonds 1. Present Value 2. Bonds 3. Stocks 1 Present Value = today s value of income at a future date Income at one future date value today of X dollars in one year V t = X t+1 (1 + i t ) where

### CHAPTER 8. Problems and Questions

CHAPTER 8 Problems and Questions 1. Plastico, a manufacturer of consumer plastic products, is evaluating its capital structure. The balance sheet of the company is as follows (in millions): Assets Liabilities

### CIS September 2013 Exam Diet Examination Paper 2.2: Corporate Finance Equity Valuation and Analysis Fixed Income Valuation and Analysis Level 2

CIS September 2013 Exam Diet Examination Paper 2.2: Corporate Finance Equity Valuation and Analysis Fixed Income Valuation and Analysis Level 2 SECTION A: MULTIPLE CHOICE QUESTIONS Corporate Finance (1

### Econ 330 Exam 1 Name ID Section Number

Econ 330 Exam 1 Name ID Section Number MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If during the past decade the average rate of monetary growth

### Chapter 5: Valuing Bonds

FIN 302 Class Notes Chapter 5: Valuing Bonds What is a bond? A long-term debt instrument A contract where a borrower agrees to make interest and principal payments on specific dates Corporate Bond Quotations

### Econ 121 Money and Banking Fall 2009 Instructor: Chao Wei. Midterm. Answer Key

Econ 121 Money and Banking Fall 2009 Instructor: Chao Wei Midterm Answer Key Provide a BRIEF and CONCISE answer to each question. Clearly label each answer. There are 25 points on the exam. I. Formulas

### Equity Valuation. Lecture Notes # 8. 3 Choice of the Appropriate Discount Rate 2. 4 Future Cash Flows: the Dividend Discount Model (DDM) 3

Equity Valuation Lecture Notes # 8 Contents About Valuation 2 2 Present-Values 2 3 Choice of the Appropriate Discount Rate 2 4 Future Cash Flows: the Dividend Discount Model (DDM) 3 5 The Two-Stage Dividend-Growth

### Chapter 11. Bond Pricing - 1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions.

Bond Pricing - 1 Chapter 11 Several Assumptions: To simplify the analysis, we make the following assumptions. 1. The coupon payments are made every six months. 2. The next coupon payment for the bond is

Chapter Two Determinants of Interest Rates Interest Rate Fundamentals Nominal interest rates - the interest rate actually observed in financial markets directly affect the value (price) of most securities

### How To Invest In Stocks And Bonds

Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation

Relative value analysis: calculating bond spreads Moorad Choudhry January 2006 Relative value analysis: bond spreads Moorad Choudhry Investors measure the perceived market value, or relative value, of

### Practice Problems for FE 486B Thursday, February 2, 2012. a) Which choice should you make if the interest rate is 3 percent? If it is 6 percent?

Practice Problems for FE 486B Thursday, February 2, 2012 1) Suppose you win the lottery. You have a choice between receiving \$100,000 a year for twenty years or an immediate payment of \$1,200,000. a) Which

### Chapter 3 Fixed Income Securities

Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixed-income securities. Stocks. Real assets (capital budgeting). Part C Determination

### FIN 472 Fixed-Income Securities Forward Rates

FIN 472 Fixed-Income Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU Interest-Rate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward

### Bonds and Yield to Maturity

Bonds and Yield to Maturity Bonds A bond is a debt instrument requiring the issuer to repay to the lender/investor the amount borrowed (par or face value) plus interest over a specified period of time.

### Bonds, Preferred Stock, and Common Stock

Bonds, Preferred Stock, and Common Stock I. Bonds 1. An investor has a required rate of return of 4% on a 1-year discount bond with a \$100 face value. What is the most the investor would pay for 2. An

Econ 121 Money and Banking Instructor: Chao Wei Answer Key to Midterm Provide a brief and concise answer to each question. Clearly label each answer. There are 50 points on the exam. 1. (10 points, 3 points

### YIELD CURVE GENERATION

1 YIELD CURVE GENERATION Dr Philip Symes Agenda 2 I. INTRODUCTION II. YIELD CURVES III. TYPES OF YIELD CURVES IV. USES OF YIELD CURVES V. YIELD TO MATURITY VI. BOND PRICING & VALUATION Introduction 3 A

### TIP If you do not understand something,

Valuing common stocks Application of the DCF approach TIP If you do not understand something, ask me! The plan of the lecture Review what we have accomplished in the last lecture Some terms about stocks

### Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value

Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations

### Chapter 14 Capital Structure in a Perfect Market

Chapter 14 Capital Structure in a Perfect Market 14-1. Consider a project with free cash flows in one year of \$130,000 or \$180,000, with each outcome being equally likely. The initial investment required

### Lecture 12/13 Bond Pricing and the Term Structure of Interest Rates

1 Lecture 1/13 Bond Pricing and the Term Structure of Interest Rates Alexander K. Koch Department of Economics, Royal Holloway, University of London January 14 and 1, 008 In addition to learning the material

### Problems and Solutions

Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixed-coupon bond whose features are the following: face value: \$,000 coupon rate: 8% coupon frequency: semiannual

FINC 3630: Advanced Business Finance Additional Practice Problems Accounting For Financial Management 1. Calculate free cash flow for Home Depot for the fiscal year-ended February 1, 2015 (the 2014 fiscal

### CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING

CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING Topic One: Bond Pricing Principles 1. Present Value. A. The present-value calculation is used to estimate how much an investor should pay for a bond;

### 1.2 Structured notes

1.2 Structured notes Structured notes are financial products that appear to be fixed income instruments, but contain embedded options and do not necessarily reflect the risk of the issuing credit. Used

### SAMPLE FACT EXAM (You must score 70% to successfully clear FACT)

SAMPLE FACT EXAM (You must score 70% to successfully clear FACT) 1. What is the present value (PV) of \$100,000 received five years from now, assuming the interest rate is 8% per year? a. \$600,000.00 b.

### Financial-Institutions Management. Solutions 1. 6. A financial institution has the following market value balance sheet structure:

FIN 683 Professor Robert Hauswald Financial-Institutions Management Kogod School of Business, AU Solutions 1 Chapter 7: Bank Risks - Interest Rate Risks 6. A financial institution has the following market

### Executive Summary of Finance 430 Professor Vissing-Jørgensen Finance 430-62/63/64, Winter 2011

Executive Summary of Finance 430 Professor Vissing-Jørgensen Finance 430-62/63/64, Winter 2011 Weekly Topics: 1. Present and Future Values, Annuities and Perpetuities 2. More on NPV 3. Capital Budgeting

### FIN 3710. First (Practice) Midterm Exam 03/09/06

FIN 3710 Investment Analysis Zicklin School of Business Baruch College Spring 2006 FIN 3710 First (Practice) Midterm Exam 03/09/06 NAME: (Please print your name here) PLEDGE: (Sign your name here) Instructions:

### Interest Rates and Bond Valuation

Interest Rates and Bond Valuation Chapter 6 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean

### ENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure

ENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure Chapter 9 Valuation Questions and Problems 1. You are considering purchasing shares of DeltaCad Inc. for \$40/share. Your analysis of the company

### Chapter 6 Valuing Bonds. (1) coupon payment - interest payment (coupon rate * principal) - usually paid every 6 months.

Chapter 6 Valuing Bonds Bond Valuation - value the cash flows (1) coupon payment - interest payment (coupon rate * principal) - usually paid every 6 months. (2) maturity value = principal or par value

### Untangling F9 terminology

Untangling F9 terminology Welcome! This is not a textbook and we are certainly not trying to replace yours! However, we do know that some students find some of the terminology used in F9 difficult to understand.

### STUDENT CAN HAVE ONE LETTER SIZE FORMULA SHEET PREPARED BY STUDENT HIM/HERSELF. FINANCIAL CALCULATOR/TI-83 OR THEIR EQUIVALENCES ARE ALLOWED.

Test III-FINN3120-090 Fall 2009 (2.5 PTS PER QUESTION. MAX 100 PTS) Type A Name ID PRINT YOUR NAME AND ID ON THE TEST, ANSWER SHEET AND FORMULA SHEET. TURN IN THE TEST, OPSCAN ANSWER SHEET AND FORMULA

### Professional Level Skills Module, Paper P4

Answers Professional Level Skills Module, Paper P4 Advanced Financial Management December 2011 Answers 1 Up to 4 professional marks are available for the presentation of the answer, which should be in

Answers to Review Questions 1. The real rate of interest is the rate that creates an equilibrium between the supply of savings and demand for investment funds. The nominal rate of interest is the actual