经济类课件汇集_Module03 APPLICATION OF CAPM

FIN2101 BUSINESS FINANCE II MODULE 3-APPLICATION OF CAPM QUESTION 1 The three divisions of Bonza Ltd are engaged in leisure wear, graphics, and household paint The company has identified listed companies in each of these lines of business. On the basis of analysing the performance of the shares of those companies in relation to the market index, Bonza has estimated that the systematic risk of each of its three divisions is as follows Division Leisure wear 1.16 Graphics 164 Paint 0.70 The expected return on the market index is 13% in the foreseeable future, and the risk -free rate is currently 7%. The divisions are evaluating a number of independent projects which have the following expected returns Return Graphics 18% Paint 345678 Leisure wear 26% Leisure wear 13% 21% Graphics 16% Which projects should be accepted and which rejected? QUESTION 2 The risk-free rate is presently 5% and the expected return on the market portfolio is 10% The expected returns(based on market prices) for four (4)companies'ordinary shares are listed below, together with their expected betas Company Expected Return(ks Bet nc Corp Union Paint Co 9.5% 0.8 National Auto Co 10.5% 1.1 Parker Electronics Ltd 13.09 On the basis of these expectations, which shares are overvalued? Which are undervalued?

July 2003 FIN2101 BUSINESS FINANCE II MODULE 3 - APPLICATION OF CAPM QUESTION 1 The three divisions of Bonza Ltd are engaged in leisure wear, graphics, and household paint. The company has identified listed companies in each of these lines of business. On the basis of analysing the performance of the shares of those companies in relation to the market index, Bonza has estimated that the systematic risk of each of its three divisions is as follows: Division Beta Leisure wear 1.16 Graphics 1.64 Paint 0.70 The expected return on the market index is 13% in the foreseeable future, and the risk-free rate is currently 7%. The divisions are evaluating a number of independent projects which have the following expected returns: Project Division Return 1 Graphics 18% 2 Paint 12% 3 Paint 10% 4 Leisure wear 26% 5 Leisure wear 13% 6 Graphics 21% 7 Paint 14% 8 Graphics 16% Which projects should be accepted and which rejected? QUESTION 2 The risk-free rate is presently 5% and the expected return on the market portfolio is 10%. The expected returns (based on market prices) for four (4) companies' ordinary shares are listed below, together with their expected betas. Company Expected Return (ks) Beta Stillman Zinc Corp 12.0% 1.3 Union Paint Co 9.5% 0.8 National Auto Co 10.5% 1.1 Parker Electronics Ltd 13.0% 1.7 On the basis of these expectations, which shares are overvalued? Which are undervalued?

QUESTION 3 Sutton safes ltd has values)of 0.75(3: 4 ). Its debt funds is 10% before tax, and its marg inal tax rate is 30%. Sutton Safes is considering entry into the automated -teller-machine business, a field that involves electronics and considerably different from its own, so that the company is looking for a proxy company which might prov ide it with a relevant discount rate. Peerless Machines Ltd, a listed company, produces only automated-teller equipment. Peerless Machines has a debt-to-equity ratio of 0.25(1: 4), a beta of 1. 15, and an effective tax rate of 30% a) If Sutton Safes wishes to enter the automated -teller-machine business, what systematic risk(beta) is involved if it intends to employ the same amount of leverage in the new venture as it presently employs? b) If the risk-free rate is expected to be 6% and the market risk premium 6%, what return should the company require for the project if it adopts a capital asset pricing model approach? QUESTION 4 Matthews-Lynch Ltd, a manufacturer of kicking machines, is currently contemplating manufacturing try scoring machines, an area in which it has no experience. It proposes to finance this project, which will cost $100 000 initially, by borrowing $40 000, the balance coming from equity sources. The project is expected to last at least twenty (20)years The present yield to maturity of 20-year Government bonds for investments of $20 000 and over is 8%, whilst the current debt finance rate for projects of this nature is 12%. Matthews- Lynch's financial advisor has ind icated that the market risk premium is approximately 6% An investigation of all current try scoring machine manufacturers reveals the following information Debt/Equity ratio B Bennett-Ikin Ltd 1:3(0.33) 1.20 Stuart-Fittler Ltd 1:4(0.2: Anderson-Kimmorley ltd 1400.25) 1.60 The corporate tax rate is 30 percent Former Bennett-lkin Ltd manager, Wally Langer, estimates that this investment would return annual after-tax net cash inflows of $15 000 over the 20-year life of the project but he has habit of disagreeing with himself from one day to the next Using the CAPM approach, advise Matthews-Lynch Ltd as to the acceptability of the project on the basis of the above information. Comment on the valid ity of the conclusions you have reached

July 2003 QUESTION 3 Sutton Safes Ltd has a debt-to-equity ratio (at market values) of 0.75 (3:4). Its present cost of debt funds is 10% before tax, and its marginal tax rate is 30%. Sutton Safes is considering entry into the automated-teller-machine business, a field that involves electronics and is considerably different from its own, so that the company is looking for a proxy company which might provide it with a relevant discount rate. Peerless Machines Ltd, a listed company, produces only automated-teller equipment. Peerless Machines has a debt-to-equity ratio of 0.25 (1:4), a beta of 1.15, and an effective tax rate of 30%. a) If Sutton Safes wishes to enter the automated-teller-machine business, what systematic risk (beta) is involved if it intends to employ the same amount of leverage in the new venture as it presently employs? b) If the risk-free rate is expected to be 6% and the market risk premium 6%, what return should the company require for the project if it adopts a capital asset pricing model approach? QUESTION 4 Matthews-Lynch Ltd, a manufacturer of kicking machines, is currently contemplating manufacturing try scoring machines, an area in which it has no experience. It proposes to finance this project, which will cost $100 000 initially, by borrowing $40 000, the balance coming from equity sources. The project is expected to last at least twenty (20) years. The present yield to maturity of 20-year Government bonds for investments of $20 000 and over is 8%, whilst the current debt finance rate for projects of this nature is 12%. Matthews￾Lynch’s financial advisor has indicated that the market risk premium is approximately 6%. An investigation of all current try scoring machine manufacturers reveals the following information: Company Debt/Equity Ratio Beta Bennett-Ikin Ltd 1:3 (0.33) 1.20 Stuart-Fittler Ltd 1:4 (0.25) 1.50 Anderson-Kimmorley Ltd 1:4 (0.25) 1.60 The corporate tax rate is 30 percent. Former Bennett-Ikin Ltd manager, Wally Langer, estimates that this investment would return annual after-tax net cash inflows of $15 000 over the 20-year life of the project but he has a habit of disagreeing with himself from one day to the next. Using the CAPM approach, advise Matthews-Lynch Ltd as to the acceptability of the project on the basis of the above information. Comment on the validity of the conclusions you have reached

QUESTION 5 The stockbroking firm Insider Trad ing Pty Ltd employs you as a trainee market analyst in its research department. After a short time you note that the risk-free rate is 8% the expected rate of return on the market portfolio is 14% the market risk premium is 6% the expected returns(based on market prices)and betas for two(2)companies ordinary hares are as follows Expected returns(k Beta 5.3% 140 24.2% Required a) Calculate the required returns on Share A and Share B, given their levels of systematic risk b) Plot both the expected and required returns for each share on a Security market Line c) Identify which of the shares is undervalued or overvalued, and briefly explain your answer d Describe the adjustment process required to return Shares a and b to the sml 29.07.03

July 2003 QUESTION 5 The stockbroking firm Insider Trading Pty Ltd employs you as a trainee market analyst in its research department. After a short time you note that: • the risk-free rate is 8%; • the expected rate of return on the market portfolio is 14%; • the market risk premium is 6%; • the expected returns (based on market prices) and betas for two (2) companies’ ordinary shares are as follows: Company Expected Returns (ks) Beta A 5.3% 1.40 B 24.2% 1.15 Required: a) Calculate the required returns on Share A and Share B, given their levels of systematic risk. b) Plot both the expected and required returns for each share on a Security Market Line. c) Identify which of the shares is undervalued or overvalued, and briefly explain your answer. d) Describe the adjustment process required to return Shares A and B to the SML. 29.07.03

FIN2101 BUSINESS FINANCE II SOLUTIONS TO TUTORIAL QUESTIONS MODULE 3-APPLICATION OF CAPM

July 2003 FIN2101 BUSINESS FINANCE II SOLUTIONS TO TUTORIAL QUESTIONS MODULE 3 - APPLICATION OF CAPM

QUESTION 1 First calculate the required return for each division and then compare the expected return for each project to the required return for the appropriate division. a project should be accep if its expected return is greater than the division's required return k =R +|b:×(k-R Leisu re w ear div isio n k:=0.07+1.16×(0.130.0 =0.070.0696 =0.1396rl3.96% Grap h ics div isio n k,=0.07[.64(0.130.0 =0.070.0984 =0.1686r16.84% P ain tDiv isio n k=0.07+[0.7(0.130.0 =0.07+0.042 0.11rl1.2% Accept projects 1, 2, 4, 6 and 7

July 2003 QUESTION 1 First calculate the required return for each division and then compare the expected return for each project to the required return for the appropriate division. A project should be accepted if its expected return is greater than the division’s required return. k = R + b (k - R ) j F j  m F  ( )  ( )  ( ) = 0 .1 1 2o r 1 1 .2 % = 0 .0 7+ 0 .0 4 2 k = 0 .0 7+ 0 .7 0 .1 3- 0 .0 7 P ain t Div isio n = 0 .1 6 8 4o r 1 6 .8 4 % = 0 .0 7+ 0 .0 9 8 4 k = 0 .0 7+ 1 .6 4 0 .1 3- 0 .0 7 Grap h icsDiv isio n = 0 .1 3 9 6o r 1 3 .9 6 % = 0 .0 7+ 0 .0 6 9 6 k = 0 .0 7+ 1 .1 6 0 .1 3- 0 .0 7 L eisu re W ear Div isio n j j j    Accept projects 1, 2, 4, 6 and 7

QUESTION 2 R R Stillman k=0.05[3×(0.100.0列 =0.050.065 0.116rl 1 5%<12%. UNDERVALUED) Un ion k=0.05D0.8(0.100.0别 =0.050.04 0.0% r9%(<9.5%: UNDERVALUED) Natio n alau to k:=0.051.(0.100.0 0.05-0.05 0. 105r105%=10.5%CORRECTLY PRICED Park er k;=0,.05[1.7×(0.100.0引 =0.050.085 =0.13613.5%13.0%OVERⅤ ALUED) A share is OVERVALUED or OVERPRICED when its required rate of return k;is greater than its expected rate of return based on market price ks. Conversely, a share is UNDERVALUED or UNDERPRICED when its required return is less than the expected return based on market price

July 2003 QUESTION 2 k = R + b (k - R ) j F j  m F  ( ) ( )  ( ) ( )  ( ) ( )  ( ) = 0 .1 3 5o r 1 3 .5 %(> 1 3 .0 % OVERVALUED ) = 0 .0 5+ 0 .0 8 5 k = 0 .0 5+ 1 .7 0 .1 0- 0 .0 5 P ark er = 0 .1 0 5o r 1 0 .5 %= 1 0 .5 % CORRECTLY P RICED = 0 .0 5+ 0 .0 5 5 k = 0 .0 5+ 1 .1 0 .1 0- 0 .0 5 Natio n alAu to = 0 .0 9o r 9 % < 9 .5 % UNDERVALUE D = 0 .0 5+ 0 .0 4 k = 0 .0 5+ 0 .8 0 .1 0- 0 .0 5 Un io n = 0 .1 1 5o r 1 1 .5 %< 12% UNDERVALUE D = 0 .0 5+ 0 .0 6 5 k = 0 .0 5+ 1 .3 0 .1 0- 0 .0 5 S tillman j j j j         A share is OVERVALUED or OVERPRICED when its required rate of return kj is greater than its expected rate of return based on market price ks. Conversely, a share is UNDERVALUED or UNDERPRICED when its required return is less than the expected return based on market price

QUESTION 3 (a) Step 1-Degear Levered Proxy beta 1+0.25 0.92 Step 2-Regear Unlevered Proxy beta 0.921+0.7 1.61 (b) 0.06[1.6k(00 0.1566r15.66% kd=109giⅳa k2|+ka(.T) 0.15 +0.101-0 0.1196rl1.95%

July 2003 QUESTION 3 (a) Step 1 - Degear Levered Proxy Beta 0 . 9 2 1 0 . 2 5 1 . 1 5 E D 1 b b p p LP UP = + =         + = Step 2 - Regear Unlevered Proxy Beta   = 1 .6 1 = 0 .9 21 + 0 .7 5 E D b = b 1 + j j j UP         (b)  ( )  ( ) = 0 .1 5 6 6o r 1 5 .6 6 % = 0 .0 6+ 1 .6 1 0 .0 6 k j = R F + b j k m - R F   k =10%(g iv en) d ( ) ( ) = 0 .1 1 9 5o r 1 1 .9 5 % = 0 .0 8 9 5+ 0 .0 3 7 3 + 0 .1 01 - 0 .3 7 4 = 0 .1 5 6 6 V D + k 1 - T V E k = k j j d j j j                            

QUESTION 4 Step 1-Calculate Industry Average Data 1.2+1.5+1.6 33+0.25+0.2 b D 1+0.28 1.1172 Step 3-Regear Unlevered Proxy beta Note: The project's debt-to-equity ratio is $40000: $60 000 or 2: 3(0.67) E 1.117+0.6 18657241.86

July 2003 QUESTION 4 Step 1 - Calculate Industry Average Data 1 . 4 3 3 1 . 2 1 . 5 1 . 6 b LP = + + = 0 . 2 7 6o r 0 . 2 8 3 0 . 3 3 0 . 2 5 0 . 2 5 D p - E p = + + = Step 2 - Degear Levered Proxy Beta 1 . 1 1 7 2 1 0 . 2 8 1 . 4 3 E D 1 b b p p LP UP = + =         + = Step 3 - Regear Unlevered Proxy Beta Note: The project’s debt-to-equity ratio is $40 000:$60 000 or 2:3 (0.67).   = 1 .8 6 5 7 2 4o r 1 .8 6 6 = 1 .1 1 7 21 + 0 .6 7 E D b = b 1 + j j j UP        

QUESTION 4 (Continued) Step 4- Calculate the cost of Equity capital b, x(km-R) 0.08[18660.14008 0.080.11196 =0.1919r19.196% Step 5-Calculate the Cost of Debt Step 6- Calculate the Cost of capital ka(1-T 0.191 60000 +0.1x1-0.3 40000 00000 100000 0.1151760.0336 0.1487715% Step 7-Evaluate the project NPV=$1s00VHFA0.15,2d10⑩00 (S10×625}$10000 9385$10000 6l15 Conclusion: The project is unacceptable as it has a negative NPV. However, given t projects long life and the uncertainty about the cash inflows, we might do further research before making a final decision to reject the project

July 2003 QUESTION 4 (Continued) Step 4 - Calculate the Cost of Equity Capital  ( )  ( ) = 0 .1 9 1 9 6o r 1 9 .1 9 6 % = 0 .0 8+ 0 .1 1 1 9 6 = 0 .0 8+ 1 .8 6 6 0 .1 4- 0 .0 8 k j = R F + b j k m - R F   Step 5 - Calculate the Cost of Debt k =12%(g iv en) d Step 6 - Calculate the Cost of Capital ( ) ( ) = 0 .1 4 8 7 7 6o r 15% = 0 .1 1 5 1 7 6+ 0 .0 3 3 6 100000 4 0000 + 0 .1 21 - 0 .3 100000 6 0000 = 0 .1 9 1 9 6 V D + k 1 - T V E k = k j j d j j j                             Step 7 - Evaluate the Project ( ) = - $ 61 1 5 = $ 9 38 8 5- $ 1 0 00 0 0 = $ 1 50 0 0 6 .2 5 9- $ 1 0 00 0 0 NP V = $ 1 50 0 0P VIF A - $ 1 0 00 0 0 0 . 1 5 , 2 0  Conclusion: The project is unacceptable as it has a negative NPV. However, given the project’s long life and the uncertainty about the cash inflows, we might do further research before making a final decision to reject the project

QUESTION 5 R:+b,×(m-R1 kA=0.08[14×(0.140.08 =0.08+0.084 0.164r16.4% kB=0.08[1.15(0.140.08 0.080.069 0.14r14.9% 5.3%when a share of its level of systematic risk should be giving a retum or 10. 4 yL Share a is OVERVALUED- it is giv ing a return(at its current market price)of onl Share B is UNDERVALUED-it is giving a return(at its current market price)of 24.2% compared with a required return(given its systematic risk)of 14.9% No one will buy Share A as it is overpriced. Eventually its market price will drop so as to provide the investor with a return that is commensurate with its level of risk On the other hand, demand for Share B will be high as it is giving an excess return This demand will push the share price up. With the market price increasing, the return will drop to 14.9%so that the share will again plot on the SML 05.08.02

July 2003 QUESTION 5 a)  ( ) j F j m R F k = R + b  k -  ( )  ( ) = 0 .1 4 9o r 1 4 .9 % = 0 .0 8+ 0 .0 6 9 k = 0 .0 8+ 1 .1 5 0 .1 4- 0 .0 8 = 0 .1 6 4o r 1 6 .4 % = 0 .0 8+ 0 .0 8 4 k = 0 .0 8+ 1 .4 0 .1 4- 0 .0 8 B A   c) Share A is OVERVALUED - it is giving a return (at its current market price) of only 5.3% when a share of its level of systematic risk should be giving a return of 16.4%. Share B is UNDERVALUED - it is giving a return (at its current market price) of 24.2% compared with a required return (given its systematic risk) of 14.9%. d) No one will buy Share A as it is overpriced. Eventually its market price will drop so as to provide the investor with a return that is commensurate with its level of risk. On the other hand, demand for Share B will be high as it is giving an excess return. This demand will push the share price up. With the market price increasing, the return will drop to 14.9% so that the share will again plot on the SML. 05.08.02