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1 Taken from: Foundations of Finance: The Logic and Practice of Financial Management, Fourth Edition by Arthur J. Keown, John D. Martin, J. William Petty, David F. Scott, Jr. Copyright 2003, 2001, 1998, 1994 by Pearson Education, Inc. Published by Pearson Prentice Hall Upper Saddle River, New Jersey All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. This special edition published in cooperation with Pearson Custom Publishing Printed in the United States of America ISBN BA BK Please visit our web site at PEARSON CUSTOM PUBLISHING 75 Arlington Street, Suite 300, Boston, MA A Pearson Education Company

2 Contents Appendix A... 1 Appendix B... 9 Appendix C Apendix D Appendix E Appendix F Glossary Index... 31

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4 Appendix A Using a Calculator As you prepare for a career in business, the ability to use a financial calculator is essential, whether you are in the finance division or the marketing department. For most positions, it will be assumed that you can use a calculator in making computations that at one time were simply not possible without extensive time and effort. The following examples let us see what is possible, but they represent only the beginning of using the calculator in finance. With just a little time and effort, you will be surprised at how much you can do with the calculator, such as calculating a stock s beta, or determining the value of a bond on a specific day given the exact date of maturity, or finding net present values and internal rates of return, or calculating the standard deviation. The list is almost endless. In demonstrating how calculators may make our work easier, we must first decide which calculator to use. The options are numerous and largely depend on personal preference. We have chosen the Texas Instruments BAII Plus. We will limit our discussion to the following issues: I. Introductory Comments II. An Important Starting Point III. Calculating Table Values for: A. Appendix B (Compound sum of $1) B. Appendix C (Present value of $1) C. Appendix D (Sum of an annuity of $1 for n periods) D. Appendix E (Present value of an annuity of $1 for n periods) IV. Calculating Present Values V. Calculating Future Values (Compound sum) VI. Calculating the Number of Payments or Receipts VII. Calculating the Payment Amount VIII. Calculating the Interest Rate IX. Bond Valuation A. Computing the value of a bond B. Calculating the yield to maturity of a bond X. Computing the Net Present Value and Internal Rate of Return A. Where future cash flows are equal amounts in each period (annuity) B. Where future cash flows are unequal amounts in each period I. Introductory Comments In the examples that follow, you are told (1) which keystrokes to use, (2) the resulting appearance of the calculator display, and (3) a supporting explanation. The keystrokes column tells you which keys to press. The keystrokes shown in a white box tell you to use one of the calculator s dedicated or hard keys. For example, if +/ is shown in the keystrokes instruction column, press that key on the keyboard of the calculator. To use a function printed in a shaded box above a dedicated key, always press the shaded key first, then the function key. Appendix A 1

5 II. An Important Starting Point Example: You want to display four numbers to the right of the decimal. Keystrokes Display Explanation FORMAT DEC= 4 ENTER DEC= Sets display to show four numbers to the right of the decimal CE/C CE/C Clears display Example: You want to display two payments per year to be paid at the end of each period. Keystrokes Display Explanation P/Y P/Y = 2 ENTER P/Y = Sets number of payments per year at 2 BGN END Sets timing of payment at the end of each period CE/C CE/C Clears display III. Calculating Table Values A. The compound sum of $1 (Appendix B) Example: What is the table value for the compound sum of $1 for 5 years at a 12 percent annual interest rate? Keystrokes Display Explanation P/Y P/Y = 1 ENTER P/Y = Sets number of payments per year at 1 BGN END Sets timing of payment at the end of each period CE/C CE/C Clears display CLR TVM Clears TVM variables 1 +/ PV = Stores initial $1 as a negative present value. PV Otherwise the answer will appear as negative. 5 N N = Stores number of periods 12 I/Y I/Y = Stores interest rate CPT FV FV = Table value B. The present value of $1 (Appendix C) Example: What is the table value for the present value of $1 for 8 years at a 10 percent annual interest rate? Keystrokes Display Explanation P/Y P/Y = 1 ENTER P/Y = Sets number of payments per year at 1 BGN END Sets timing of payment at the end of each period CE/C CE/C Clears display CLR TVM Clears TVM variables 1 +/ FV = Stores future amount as negative value FV 8 N N = Stores number of periods 10 I/Y I/Y = Stores interest rate CPT PV PV = Table value 2 Appendix A

6 III. Calculating Table Values (continued) C. The sum of an annuity of $1 for n periods (Appendix D) Example: What is the table value for the compound sum of an annuity of $1 for 6 years at a 14 percent annual interest rate? Keystrokes Display Explanation P/Y P/Y = 1 ENTER P/Y = Sets number of payments per year at 1 BGN END Sets timing of payment at the end of each period CE/C CE/C Clears display CLR TVM Clears TVM variables 1 +/ PMT = Stores annual payment (annuity) as a negative number. PMT Otherwise the answer will appear as a negative. 6 N N = Stores number of periods 14 I/Y I/Y = Stores interest rate CPT FV FV = Table value D. The present value of an annuity of $1 for n periods (Appendix E) Example: What is the table value for the present value of an annuity of $1 for 12 years at 9 percent annual interest rate? Keystrokes Display Explanation P/Y P/Y = 1 ENTER P/Y = Sets number of payments per year at 1 BGN END Sets timing of payment at the end of each period CE/C CE/C Clears display CLR TVM Clears TVM variables 1 +/ PMT = Stores annual payment (annuity) as a negative number. PMT Otherwise the answer will appear as a negative. 12 N N = Stores number of periods 9 I/Y I/Y = Stores interest rate CPT PV PV = Table value IV. Calculating Present Values Example: You are considering the purchase of a franchise of quick oil-change locations, which you believe will provide an annual cash flow of $50,000. At the end of 10 years, you believe that you will be able to sell the franchise for an estimated $900,000. Calculate the maximum amount you should pay for the franchise (present value) in order to realize at least an 18 percent annual yield. Keystrokes Display Explanation BGN END Sets timing of payment at the end of each period CE/C CE/C Clears display CLR TVM Clears TVM variables 10 N N = Stores n, the holding period 18 I/Y I/Y = Stores i, the required rate of return 50,000 PMT PMT = 50, Stores PMT, the annual cash flow to be received 900,000 FV FV = 900, Stores FV, the cash flow to be received at the end of the project CPT PV PV = 396, The present value, given a required rate of return of 18 percent. (Note: the present value is displayed with a minus sign since it represents cash paid out.) Appendix A 3

7 V. Calculating Future Values (Compound Sum) Example: If you deposit $300 a month (at the beginning of each month) into a new account that pays 6.25 percent annual interest compounded monthly, how much will you have in the account after 5 years? Keystrokes Display Explanation BGN END Sets timing of payment at the end of each period SET BGN Sets timing of payments to beginning of each period P/Y P/Y = 12 ENTER P/Y = Sets 12 payments per year CE/C CE/C Clears display CLR TVM Clears TVM variables 60 N N = Stores n, the number of months for the investment 6.25 I/Y I/Y = Stores i, the annual rate 300 +/ PMT = Stores PMT, the monthly amount invested (with a PMT minus sign for cash paid out) CPT FV FV = 21, The future value after 5 years VI. Calculating the Number of Payments or Receipts Example: If you wish to retire with $500,000 saved, and can only afford payments of $500 each month, how long will you have to contribute toward your retirement if you can earn a 10 percent return on your contributions? Keystrokes Display Explanation BGN BGN Verifies timing of payment at the beginning of each period P/Y P/Y = ENTER P/Y = Sets 12 payments per year CE/C CE/C Clears display CLR TVM Clears TVM variables 10 I/Y I/Y = Stores i, the interest rate 500 +/ PMT = Stores PMT, the monthly amount invested (with a PMT minus sign for cash paid out) 500,000 FV = 500, The value we want to achieve FV CPT N N = Number of months (since we considered monthly payments) required to achieve our goal VII. Calculating the Payment Amount Example: Suppose your retirement needs were $750,000. If you are currently 25 years old and plan to retire at age 65, how much will you have to contribute each month for retirement if you can earn 12.5 percent on your savings? Keystrokes Display Explanation BGN BGN Verifies timing of payment at the beginning of each period P/Y P/Y = ENTER P/Y = Sets 12 payments per year 4 Appendix A

8 VII. Calculating the Payment Amount (continued) CE/C CE/C Clears display CLR TVM Clears TVM variables 12.5 I/Y I/Y = Stores i, the interest rate 480 N N = Stores n, the number of periods until we stop contributing (40 years 12 months/year = 480 months) 750,000 FV FV = 750, The value we want to achieve CPT PMT PMT = Monthly contribution required to achieve our ultimate goal (shown as negative since it represents cash paid out) VIII. Calculating the Interest Rate Example: If you invest $300 at the end of each month for 6 years (72 months) for a promised $30,000 return at the end, what interest rate are you earning on your investment? Keystrokes Display Explanation BGN BGN Sets timing of payments to beginning of each period SET END Sets timing of payments to end of each period P/Y P/Y = ENTER P/Y = Sets 12 payments per year CE/C CE/C Clears display CLR TVM Clears TVM variables 72 N N = Stores n, the number of deposits (investments) 300 +/ PMT = Stores PMT, the monthly amount invested (with a PMT minus sign for cash paid out) 30,000 FV FV = 30, Stores the future value to be received in 6 years CPT I/Y I/Y = The annual interest rate earned on the investment IX. Bond Valuation A. Computing the value of a bond Example: Assume the current date is January 1, 1993, and that you want to know the value of a bond that matures in 10 years and has a coupon rate of 9 percent (4.5 percent semiannually). Your required rate of return is 12 percent. Keystrokes Display Explanation BGN END Verifies timing of payments to end of each period P/Y P/Y = ENTER P/Y = Sets 2 payments per year; end mode (END) assumes cash flows are at the end of each 6-month period CE/C CE/C Clears display CLR TVM Clears TVM variables 20 N N = Stores the number of semiannual periods (10 years 2) 12 I/Y I/Y = Stores annual rate of return 45 PMT PMT = Stores the semiannual interest payment 1,000 FV FV = 1, Stores the bond s maturity or par value CPT PV PV = Value of the bond, expressed as a negative number Appendix A 5

9 IX. Bond Valuation (continued) SOLUTION Using the Bond Feature: CE/C CE/C Clears display BOND STD = (This will be the last date entered) CLR WORK STD = Clears BOND variables ENTER STD = Stores the current date (month, date, year) CPN = ENTER CPN = Stores the coupon interest rate RDT = (This will be the last date entered) ENTER RDT = Stores the maturity date in 10 years RV = Verifies bond maturity or par value ACT SET 360 Sets calculations to be based on 360-day year 2/Y Verifies semiannual compounding rate YLD = ENTER YLD = Stores the investor s required rate of return PRI = CPT PRI = Value of bond as a percent of par value; i.e., value of bond is $ B. Computing the yield to maturity of a bond Example: Assume the current date is January 1, 1994, and that you want to know your yield to maturity on a bond that matures in 8 years and has a coupon rate of 12 percent (6 percent semiannually). The bond is selling for $1,100. Keystrokes Display Explanation BGN END Verifies timing of payments to end of each period P/Y P/Y = ENTER P/Y = Sets 2 payments per year; end mode (END) assumes cash flows are at the end of each 6-month period CE/C CE/C Clears display CLR TVM Clears TVM variables 16 N N = Stores the number of semiannual periods (8 years 2) / PV = 1, Value of the bond, expressed as a negative PV number 60 PMT PMT = Stores the semiannual interest payments 1,000 FV FV = 1, Stores the bond s maturity or par value CPT I/Y I/Y = The yield to maturity, expressed on an annual basis SOLUTION Using the Bond Feature: CE/C CE/C Clears display Bond STD = (This will be the last date entered) CLR WORK STD = Clears BOND variables ENTER STD = Stores the current date (month, date, year) CPN = ENTER CPN = Stores the coupon interest rate RDT = (This will be the last date entered) ENTER RDT = Stores the maturity date in 8 years RV = Verifies bonds maturity or par value ACT 6 Appendix A

10 IX. Bond Valuation (continued) SET 360 Sets calculations to be based on 360-day year Verifies semiannual compounding rate 2/Y YLD = PRI = ENTER PRI = Stores the bond value as a percentage of par value YLD = CPT YLD = Bond s yield to maturity X. Computing the Net Present Value and Internal Rate of Return A. Where future cash flows are equal amounts in each period (annuity) Example: The firm is considering a capital project that would cost $80,000. The firm s cost of capital is 12 percent. The project life is 10 years, during which time the firm expects to receive $15,000 per year. Calculate the NPV and the IRR. Keystrokes Display Explanation BGN END Verifies timing of payments to end of each period P/Y P/Y = ENTER P/Y = Sets 1 payment per year; end mode (END) assumes cash flows are at the end of each year CE/C CE/C Clears display CLR TVM Clears TVM variables 15,000 PMT PMT = Stores the annual cash flows of $15, N N = Stores the life of the project 12 I/Y I/Y = Stores the cost of capital CPT PV PV = 84, Calculates present value +/ PV = 84, Changes PV to positive 80,000 = 4, Calculates net present value by subtracting the cost of the project 80,000 +/ 80, PV PV = 80, CPT I/Y I/Y = Calculates the IRR B. Where future cash flows are unequal amounts in each period Example: The firm is considering a capital project that would cost $110,000. The firm s cost of capital is 15 percent. The project life is 5 years, with the following expected cash flows: $ 25,000, $50,000, $60,000, $60,000 and $70,000. In addition, you expect to receive $30,000 in the last year from the salvage value of the equipment. Calculate the NPV and IRR. Keystrokes Display Explanation CE/C CE/C Clears display CF CF 0 = CLR WORK CF 0 = Clears cash flow variables 110,000 +/ CF 0 = 110, Stores CF 0, the initial investment (with a minus sign for a negative cash flow) ENTER CO1 = Stores CF 1, the first year s cash flow (with a minus sign 25,000 +/ CO1 = 25, for a negative cash flow) ENTER FO1 = Stores the number of years CF 1 is repeated (in this case, 1 year only) ENTER Appendix A 7

11 X. Computing the Net Present Value and Internal Rate of Return (continued) CO2 = ,000 CO2 = 50, Stores CF 2 ENTER FO2 = ENTER FO2 = Stores the number of years CF 2 is repeated CO3 = ,000 CO3 = 60, Stores CF 3 ENTER FO3 = Stores the number of years CF 3 is repeated 2 ENTER (here, 2 years, so our response is 2 to the FO 3 prompt) CO4 = ,000 CO4 = 100, Stores CF 4, $70,000 plus expected $30,000 ENTER FO4 = Stores the number CF 4 ENTER QUIT Ends storage of individual cash flows NPV I = ENTER I = Stores interest rate NPV = CPT NPV = 29, Calculate the project s NPV at the stated interest rate IRR IRR = CPT IRR = Calculates the project s IRR 8 Appendix A

12 Appendix B Compound Sum of $1 n 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% n 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% Appendix B 9

13 Compound Sum of $1 (continued) n 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% n 31% 32% 33% 34% 35% 36% 37% 38% 39% 40% Appendix B

14 Appendix C Present Value of $1 n 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% n 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% Appendix C 11

15 Present Value of $1 (continued) n 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% n 31% 32% 33% 34% 35% 36% 37% 38% 39% 40% Appendix C

16 Appendix D Sum of an Annuity of $1 for n Periods n 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% n 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% Appendix D 13

17 Sum of an Annuity of $1 for n Periods (continued) n 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% n 31% 32% 33% 34% 35% 36% 37% 38% 39% 40% Appendix D

18 Appendix E Present Value of an Annuity of $1 for n Periods n 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% n 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% Appendix E 15

19 Present Value of an Annuity of $1 for n Periods (continued) n 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% n 31% 32% 33% 34% 35% 36% 37% 38% 39% 40% Appendix E

20 Appendix F Check Figures for Selected End-of-Chapter Study Problems CHAPTER Taxable income = $526,800 Tax liability = $179, Taxable income = $365,000 Tax liability = $124, Taxable income = ($38,000) Tax liability = $ Taxable income = $153,600 Tax liability = $43, Taxable income = $370,000 Tax liability = $125, Taxable income = $1,813,000 Tax liability = $616,420 CHAPTER Inferred real rate on Treasury bills: 1.56% Inferred real rate on Treasury bonds: 4.55% % % 2-5. a. The logic here is based on the expectations theory of the term structure of interest rates. CHAPTER $120, No numerical solution 3-5. Free cash flow ($8) 3-7. Free cash flow $53,800 CHAPTER $500, a. Total assets turnover = 2 b. Sales = $17.5m Percentage increase = 75% c. For last year, OIROI = 20% Projected OIROI = 35% 4-5. RATIO 2000 Current ratio 4.0x Acid-test (quick) ratio 1.92x Average collection period 107 days Inventory turnover 1.36x Operating income return on investment 13.8% Operating profit margin 24.8% Total asset turnover.56x Inventory turnover 1.36x Fixed asset turnover 1.04x Debt ratio 34.6% Times interest earned 5.63x Return on common equity 10.5% 4-7. a. Current ratio = 1.84 Acid-test ratio =.72 Debt ratio =.55 Times interest earned = 8 Inventory turnover = 5.48 Fixed asset turnover = 2.22 Return on equity = 23.4% CHAPTER a. $12,970 c. $3, a. n = 15 years 5-3. b. 5% c. 9% 5-4. b. PV = $ a. $6,289 c. $ c. $1, a. FV 1 = $10,600 FV 5 = $13,380 FV 15 = $23, a. $6,690 b. Semiannual: $6,720 Bimonthly: $6, Year 1: 18,000 books Year 2: 21,600 books Year 3: 25,920 books $6, % $658, b. $8, $6, % $6, a. $1, $15,912 CHAPTER k = 985. %; σ = 643. %; σ = 254. % 6-3. A: 2 k = 16. 7%; σ = %; σ = % B: 2 k = 92. %; σ = %; σ = 3. 57% 6-5. The beta is approximately 0.5. Appendix F 17

21 % 6-9. a. Jazmon: For time = 4, 30%; Solomon for time = 3, 14.29% a. 15.8% b CHAPTER $ % semiannually 9.8% compounded annually % 7-7. a. $ b. Market value $ when required rate of return is 15% Market value $1, when required rate of return is 8% 7-9. $513 CHAPTER $ a. 8.5% b. $ a. 18.9% b. $ % 8-9. $ a % b. $ $50 CHAPTER a. IRR = 7% b. IRR = 17% 9-3. a. IRR = approximately 19% 9-5. a. payback period = 4 years 9-7. a. Project A: Payback period = 2.5 years a. NPV A = $ NPV B = $455 b. PI A = PI B = 1.09 c. IRR A = 40% IRR B = 20% a. Payback A = years Payback B = years b. NPV A = $8,743 NPV B = $11,615 c. IRR A = 40% IRR B = 30% CHAPTER a. $6,800 b. $3,400 c. No taxes d. $1, a years b. $10, a. $560,000 b. Cash Flow AFTER TAX= $116, d. NPV a = $8025 NPV b = $10,112 CHAPTER a. k d (1 t) = 6.53% b. k nc = 14.37% c. k c = 15.14% d. k p = 8.77% e. k d (1 t) = 7.92% k nc = 12.06% k p = 9.23% k p = 14.29% a. k c = 17.59% b. k nc = 18.25% P 0 = $ NP 0 = $ Number of bonds = 597 k d (1 t) = 7.08% a. Incentive Compensation CEO $540,000 $675,000 $810,000 b. CEO $405,000 $1,012,500 CHAPTER a times b times c times a times b times c times d. $18,326, e. (25%) (1.85) = 46.25% a. F = $780,000 b. S B = $1,560, a. P = $6.875 (selling price per unit) a. 1,200 units b. $600,000 c. $1.316 times d % a. EBIT = $2,000,000 b. EPS will be $1.00 for each plan d. Plan B CHAPTER ,238 shares; $11,428, Value before and after dividend: $ a. Year Dividend 1 $ $0.93 b. Target dividend: $ ,743 shares; $15,555,556 CHAPTER Rate = 13.79% a. Rate = 36.73% b. Rate = 74.23% a. Rate = 16.27% a. APR = 10% b. APR = 11.76% c. APR = 12.5% 80% 100% 120% 60% 150% 18 Appendix F