BUSINESS FINANCE (FIN 312) Spring 2009

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1 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 get the answer for each calculation question to get full credit. You should make two copies. One copy to turn in for grading purposes, the other to study for the exam. The due date is Thursday April 0, 009. Late assignments will not be graded. Name(s): Student ID

2 Chapter 7 1. A semi-annual corporate bond has a face value of $1,000, a yield to maturity of 6.9 percent, and a coupon rate of 6.5 percent. The bond matures 8 years from today. This bond: 1. c a. pays interest payments of $34.50 every six months. b. sells at a premium. c. has a current yield that is greater than 6.5 percent. d. is currently quoted at a price of 97: / $1,000 $1,000 P = ; P = $ $ = $ Enter 8 6.9/ 65/ 1,000 N I/Y PV PMT FV Solve for Current yield = (.065 $1,000) $975.7 =.0666 = 6.66 percent. The price you receive when you sell a Treasury bond is the price. a. bid b. yield c. call d. asked. a You receive the bid price when you sell a Treasury bond. 3. Which one of the following bonds has the most interest rate risk? a. 5-year; 6 percent coupon b. 5-year; zero coupon c. 10-year; zero coupon d. 10-year; 6 percent coupon 3. c The longest term, lowest coupon bond is the most sensitive to interest rate changes. 4. Jenny earned 6.7 percent on her investments last year. What was her real rate of return if the inflation rate was 1.6 percent? (using the Fisher exact version) a. 5.0 percent b percent c percent d percent 4. a r = [( ) ( )] - 1 =.050 = 5.0 percent 5. Kiddy and Kat, Inc. has 9 percent semi-annual bonds outstanding with 13 years to maturity. The latest quote on these bonds is What is the yield to maturity? a percent b percent c. 6.9 percent d percent 5. d Enter 13 / / 1,000 N I/Y PV PMT FV Solve for 7.74

3 6. Black and White, Inc. offers a 7.5 percent bond with a yield to maturity of 6.65 percent. The bond pays interest annually and matures in 17 years. What is the market price of one of these bonds if the face value is $1,000? a. $1,046.0 b. $1, c. $1, d. $1, c P (.075 $1,000) 17 [ 1/ ( ) ] 1 + $1,000 = + ; P = $ $ = $1, ( ) 17 Enter ,000 N I/Y PV PMT FV Solve for -1, A zero coupon bond is currently priced to yield 5.87 percent if held to maturity 6.9 years from now. What is the current price of this bond if the face value is $1,000? a. $ b. $ c. $675.9 d. $ a $1,000 P = ; P = $ ( ) 6. 9 Enter ,000 N I/Y PV PMT FV Solve for The bonds of B&O, Inc. are currently quoted at 98.7 and have a 6.75 percent coupon. The bonds pay interest semi-annually and mature in 9 years. What is the current yield on these bonds? a. 6.8 percent b percent c percent d percent 8. b CY = $67.50 $987.0 = = 6.84 percent 9. A semi-annual, five-year bond is currently selling for $1, and has a yield to maturity of 5.94 percent. What is the coupon rate of this bond if the face value is $1,000? a percent b percent c percent d. 7.0 percent

4 9. c / 1 + C $1,000 $1,000 $1, = ; C =.0675 = 6.75% Enter / -1, ,000 N I/Y PV PMT FV Solve for Coupon rate = ($33.75 ) $1,000 =.0675 = 6.75% Current yield 10. Consider a $1,000 par value bond with a 7 percent annual coupon. The bond pays interest annually. There are 9 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10 percent? a % b. 8.46% c. 7.00% d. 8.5% e. 8.37% Answer: b Numerical solution: V B = $70((1-1/ )/0.10) + $1,000(1/ ) = $70(5.7590) + $1,000(0.441) = $ $44.10 = $87.3. Financial calculator solution: N = 9, I = 10, PMT = 70, FV = 1,000, and solve for PV =? = - $87.3. Current yield = $70/$87.3 = 8.46%. YIELD TO MATURITY 11. The bonds issued by Jensen & Son bear a 6 percent coupon, payable semiannually. The bond matures in 8 years and has a $1,000 face value. Currently, the bond sells at par. What is the yield to maturity? a percent b percent c percent d percent e percent

5 11. c r 8 1 1/(1 ).06 $1,000 + $1,000 $1,000 = + ; This can not be solved r r 8 (1 + ) directly, so it s easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that your answer is correct. Enter 8 / -1,000 60/ 1,000 N I/Y PV PMT FV Solve for 6 Answer is 6.00 percent Bond value - semiannual payment 1. Assume that you wish to purchase a 0-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40. If you require a 10 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? a. $619 b. $674 c. $761 d. $88 e. $90 Bond value - semiannual payment Answer: d Time Line: 0 5% month.. Periods PV =? FV = 1,000 Numerical solution: V B = $40((1-1/ )/0.05) + $1,000(1/ ) = $40( ) + $1,000(0.140) = $88.36 $88. Financial calculator solution: Inputs: N = 40; I = 5; PMT = 40; FV = 1,000. Output: PV = -$88.41; V B $88. Bond coupon rate 13. The current price of a 10-year, $1,000 par value bond is $1, Interest on this bond is paid every six months, and the nominal annual yield is 14 percent. Given these facts, what is the annual coupon rate on this bond?

6 a. 10% b. 1% c. 14% d. 17% e. 1% Bond coupon rate Answer: d Time Line: 0 rd/ = 7% month.... Periods PMT =? PMT PMT V B = 1, FV = 1,000 Numerical solution: $1, = PMT(PVIFA 7%,0 ) + $1,000(PVIF 7%,0 ) = PMT((1-1/ )/0.07) + $1,000(1/ ) = PMT( ) + $1,000(0.584) PMT = $900.51/ = $85. Annual coupon rate = ()($85)/$1,000 = 17%. Financial calculator solution: Inputs: N = 0; I = 7; PV = -1,158.91; FV = 1,000. Output: PMT = $85.00 (semiannual PMT). Annual coupon rate = $85()/$1,000 = 17.0%. TIME TO MATURITY OF COUPON BOND 14. The Lo Sun Corporation offers a 6 percent bond with a current market price of $ The yield to maturity is 7.34 percent. The face value is $1,000. Interest is paid semiannually. How many years is it until this bond matures? a. 16 years b. 18 years c. 4 years d. 30 years e. 36 years.0734 t 1 1/(1 ).06 $1,000 + $1, $ = ; It s easiest way.0734 t (1 + ) to solve this problem is using a financial calculator. You can then use the calculator answer as the time period in the formula just to verify that your answer is correct. Enter 7.34/ / 1,000 N I/Y PV PMT FV Solve for 3 The number of six-month periods is 3. The number of years is 16.

7 TREASURY BOND QUOTE 15. A Treasury bond is quoted at a price of 106:13. What is the market price of this bond if the face value is $1,000? a. $ b. $1, c. $1, d. $1, e. $1, b 106:13 = 106 and 13/3% = ; Market price = $1,000 = $1, (rounded) FISHER EFFECT 16. A bond that pays interest annually yields a 7.5 percent rate of return. The inflation rate for the same period is 3.5 percent. What is the real rate of return on this bond? (using Fisher exact version) a percent b percent c. 3.6 percent d. 3.7 percent e percent 16. ( ) = (1 + r) ( ); r = 3.6 percent Current yield and yield to maturity 17. A bond matures in 1 years, and pays an 8 percent annual coupon. The bond has a face value of $1,000, and currently sells for $985. What is the bond s current yield and yield to maturity? a. Current yield = 8.00%; yield to maturity = 7.9%. b. Current yield = 8.1%; yield to maturity = 8.0%. c. Current yield = 8.0%; yield to maturity = 8.37%. d. Current yield = 8.1%; yield to maturity = 8.37%. e. Current yield = 8.1%; yield to maturity = 7.9%. Current yield and yield to maturity Answer: b N = 1 PV = -985 PMT = 80 FV = 1,000 Solve for I/YR (YTM) = 8.0%. Current yield is calculated as: $80/$985 = 8.1%.

8 Chapter 8 STOCK VALUE 18. Michael s, Inc. just paid $1.40 to their shareholders as the annual dividend. Simultaneously, the company announced that future dividends will be increasing by 4.5 percent. If you require an 8 percent rate of return, how much are you willing to pay to purchase one share of Michael s stock? a. $31.11 b. $3.51 c. $40.00 d. $41.80 e. $43.68 $1.40 ( ) 18.d P 0 = ; P 0 = $ STOCK VALUE 19. Lee Hong Imports paid a $1.00 per share annual dividend last week. Dividends are expected to increase by 5 percent annually. What is one share of this stock worth to you today if the appropriate discount rate is 14 percent? a. $7.14 b. $7.50 c. $11.11 d. $11.67 e. $1.5 $1.00 (1 +.05) 19.d P 0 = ; P 0 = $ REQUIRED RETURN 0. The common stock of Eddie s Engines, Inc. sells for $5.71 a share. The stock is expected to pay $1.80 per share next month when the annual dividend is distributed. Eddie s has established a pattern of increasing their dividends by 4 percent annually and expects to continue doing so. What is the market rate of return on this stock? a. 7 percent b. 9 percent c. 11 percent d. 13 percent e. 15 percent 1.c $1.80 $5.71 = ; R = percent R.04

9 DIVIDEND YIELD VS. CAPITAL GAINS YIELD 1. Shares of common stock of the Samson Co. offer an expected total return of 1 percent. The dividend is increasing at a constant 8 percent per year. The dividend yield must be: a. - 4 percent. b. 4 percent. c. 8 percent. d. 1 percent. e. 0 percent. D.b.1 = ; Dividend yield = 4 percent P 0 DIVIDEND AMOUNT. The common stock of Energizer s pays an annual dividend that is expected to increase by 10 percent annually. The stock commands a market rate of return of 1 percent and sells for $60.50 a share. What is the expected amount of the next dividend to be paid on Energizer s common stock? a. $.90 b. $1.00 c. $1.10 d. $1.1 e. $1.33. D = ; D 1 = $ $ 1 GROWTH DIVIDEND 3. B&K Enterprises will pay an annual dividend of $.08 a share on their common stock next week. Last year, the company paid a dividend of $.00 a share. The company adheres to a constant rate of growth dividend policy. What will one share of B&K common stock be worth ten years from now if the applicable discount rate is 8 percent? a. $71.16 b. $74.01 c. $76.97 d. $80.05 e. $ $.08 $.00 $.08 (1 +.04) 3.c g = ; g =.04; D10 = ; D 10 = $76.97 $

10 SUPERNORMAL GROWTH 4. The Bell Weather Co. is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 0 percent a year for the next four years and then decreasing the growth rate to 5 percent per year. The company just paid its annual dividend in the amount of $1.00 per share. What is the current value of one share of this stock if the required rate of return is 9.5 percent? a. $35.63 b. $38.19 c. $41.05 d. $43.19 e. $ Dividends for the first 4 years are: $1.0, $1.44, $1.78, and $ $.0736 (1 +.05) P 4 = ;P 4 = $ $1.0 $1.44 $1.78 $.0736 $ P 0 = ; P = $41.05 (1.095) (1.095) (1.095) (1.095) (1.095) 4. The common stock of Neal s Metal Works sells for $3.89 a share. The company recently paid their annual dividend of $1.80 per share and expects to increase this dividend by.5 percent annually. What is the rate of return on this stock? a percent b percent c percent d percent $1.80 (1 +.05) $ d r = +.05 =.0811 = 8.11percent 5. Mertyle, Inc. recently announced that their annual dividend will be increasing to $.0 a share for next year with annual increases in the dividend amount of 1.75 percent thereafter. You require a 14.5 percent rate of return on this relatively risky security. How much are you willing to pay for one share of this stock? a. $16.48 b. $16.95 c. $17.5 d. $17.56 $ c P 0 = = $17. 5

11 6. The Ol Tech Co. last paid a $.40 annual dividend. The market rate of return on this security is 13 percent and the market price is $8.70 a share. What is the expected growth rate of Ol Tech? a percent b. 4.8 percent c percent d percent $.40 (1 + g) $ b. 13 = + g ; g = 4.8 percent 7. The common stock of the Zing Co. is selling for $5.40 a share and offers an 8.7 percent rate of return. If the dividend growth rate is constant at 3 percent, what is the amount of the last annual dividend paid? a. $.8 b. $.86 c. $.90 d. $ c D (1 +.03) 5.40 = ; D 0 = $ $ 0 STOCK QUOTE 8. A stock listing contains the following information: P/E 17.5, closing price 33.10, dividend.80, YTD % chg 3.4, and a net chg of Which of the following statements are correct given this information? I. The stock price has increased by 3.4 percent during the current year. II. The closing price on the previous trading day was $3.60. III. The earnings per share are approximately $1.89. IV. The current yield is 17.5 percent. a. I and II only b. I and III only c. II and III only d. III and IV only e. I, III, and IV only 8.b STOCK MARKET REPORTING 9. The closing price of a stock is quoted at.87, with a P/E of 6 and a net change of 1.4. Based on this information, which one of the following statements is correct? a. The closing price on the previous day was $1.4 higher than today s closing price. b. A dealer will buy the stock at $.87 and sell it at $6 a share. c. The stock increased in value between yesterday s close and today s close by $.014. d. The earnings per share are equal to 1/6 th of $.87. e. The earnings per share have increased by $1.4 this year. 9.d

12 Chapter 9 Use the following information to answer questions 30 through 33. You are analyzing a proposed project and have compiled the following information: Year Cash flow 0 -$135,000 1 $ 8,600 $ 65,500 3 $ 71,900 Required payback period 3 years Required return 8.50 percent 30. What is the net present value of the proposed project? a. $3,89.86 b. $3,313.9 c. $4,89.06 d. $4, a $8,600 $65,500 $71,900 NPV = $135, ; NPV = $3, ( ) ( ) ( ) CF 0 -$135,000 C0 1 $8,600 F0 1 1 C0 $65,500 F0 1 C0 3 $71,900 F0 3 1 I = 8.5 NPV CPT $3, What is the discounted payback period? a..57 years b..64 years c..87 years d..94 years 3. d Year Cash flow Discounted cash flow 1 $8,600 $6, $65,500 $55, $71,900 $56,91.09 $135,000 $6, $55,639.3 Discounted payback = + =.94 years $56,91.09

13 3. Should the project be accepted based on the internal rate of return (IRR)? Why or why not? a. yes; The project IRR is greater than the required return. b. yes; The project IRR is equal to zero. c. no; The project IRR is greater than the required return. d. no; The project IRR is greater than zero. 3. a CF 0 -$135,000 C0 1 $8,600 F0 1 1 C0 $65,500 F0 1 C0 3 $71,900 F0 3 1 I = 8.5 IRR CPT 9.69 percent The project should be accepted because the IRR of 9.69 percent is greater than the required return of 8.5 percent. 33. Should the proposed project be accepted based on the profitability index (PI)? Why or why not? a. yes; The PI is less than 1.0. b. yes; The PI is greater than 1.0. c. no; The PI is less than 1.0. d. no; The PI is greater than b CF 0 $0 C0 1 $8,600 F0 1 1 C0 $65,500 F0 1 C0 3 $71,900 F0 3 1 I = 8.5 NPV CPT $138,89.86 $138,89.86 PI = = 1.0 $135,000 The project should be accepted because the PI of 1.0 is greater than 1.0.

14 NET PRESENT VALUE 34. What is the net present value of a project with the following cash flows and a required return of 1 percent? a. -$87. b. -$177.6 c. $177.6 d. $04.36 e. $87. Year Cash Flow 0 -$8,900 1 $1,450 $19,630 3 $,750 $1,450 $19,630 $, NPV = $8, ; NPV = -$177.6 (negative) 1 3 (1 +.1) (1 +.1) (1 +.1) CF 0 -$8,900 C0 1 $1,450 F0 1 1 C0 $19,630 F0 1 C0 3 $,750 F0 3 1 I = 1% NPV CPT -$177.6 INTERNAL RATE OF RETURN 35. What is the internal rate of return on an investment with the following cash flows? a percent b percent c percent d percent e percent Year Cash Flow 0 -$13,400 1 $ 36,00 $ 54,800 3 $ 48, CF 0 -$13,400 C0 1 $ 36,00 F0 1 1 C0 $ 54,800 F0 1

15 C0 3 $ 48,100 F0 3 1 IRR CPT 5.96% PAYBACK PERIOD 36. It will cost $,600 to acquire a small ice cream cart. Cart sales are expected to be $1,400 a year for three years. After the three years, the cart is expected to be worthless as that is the expected remaining life of the cooling system. What is the payback period of the ice cream cart? a..86 years b years c years d..46 years e..86 years 36. Payback period $,600 $1,400 = 1+ = 1.86 years $1,400 DISCOUNTED PAYBACK PERIOD 37. A project has an initial cost of $8,500 and produces cash inflows of $,600, $4,900, and $1,500 over the next three years, respectively. What is the discounted payback period if the required rate of return is 7 percent? a..13 years b..33 years c..67 years d..91 years e. never 37. The project never pays back on a discounted basis. $,600 $4,900 $1,500 DCF = + + ; DCF = $7,934.0, which is less than the 1 3 (1 +.07) (1 +.07) (1 +.07) initial cost of $8,500 CROSSOVER RATE 38. You are analyzing the following two mutually exclusive projects and have developed the following information. What is the crossover rate? Project A Project B Year Cash Flow Cash Flow 0 -$84,500 -$76,900 1 $9,000 $5,000 $40,000 $35,000 3 $7,000 $6,000

16 a percent b percent c percent d percent e percent 1. Year Project A Cash Flow Project B Cash Flow Difference 0 -$84,500 -$76,900 -$7,600 1 $9,000 $5,000 $4,000 $40,000 $35,000 $5,000 3 $7,000 $6,000 $1,000 CF 0 -$7,600 C0 1 $4,000 F0 1 1 C0 $5,000 F0 1 C0 3 $1,000 F0 3 1 IRR CPT percent 39. A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below: The company's required rate of return is 1 percent. What is the IRR of the better project? (Hint: Note that the better project may or may not be the one with the higher IRR.) a % b. 1.00% c % d % e. 1.53% Financial calculator solution: Calculate the NPV and IRR of each project then select the IRR of the higher NPV project.

17 Project S: Inputs: Output: NPV S = 4.53; IRR S = 13.88% Project L: Inputs: Output: NPV L = 35.4; IRR L = 13.09% Project L has the higher NPV and its IRR = 13.09%. INTERNAL RATE OF RETURN AND NET PRESENT VALUE 40. You are considering two independent projects with the following cash flows. The required return for both projects is 10 percent. Given this information, which one of the following statements is correct? Year Project A Project B 0 -$950,000 -$15,000 1 $330,000 $ 55,000 $400,000 $ 50,000 3 $450,000 $ 50,000 a. You should accept project B since it has the higher IRR and reject project A because you can not accept both projects. b. You should accept project A because it has the lower NPV and reject project B. c. You should accept project A because it has the higher NPV and you can not accept both projects. d. You should accept project B because it has the higher IRR and reject project A. e. You should accept both projects if the funds are available to do so. 40. e Project A: Project B: CF 0 -$950,000 CF 0 -$15,000 C0 1 $330,000 C0 1 $ 55,000 F0 1 1 F0 1 1 C0 $400,000 C0 $ 50,000 F0 1 F0 C0 3 $450,000 F0 3 1 IRR CPT IRR CPT percent percent I = 10 I = 10 NPV CPT NPV CPT $18, $3, Since these are independent projects and both the IRR and NPV rules say accept, you should accept both projects if there are sufficient funds to do so.

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