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MANAGEMENT ADVISORY SERVICES RISKS PORTF0LIO MANAGEMENT Beta Portfolio Beta You invest $600 in security A with a beta of 1.2 and $400 in security B with a beta of -0.20 The beta of the resulting portfolio is (M) a 1.40 c 0.36 b 1.00 d 0.64 e 0.80 Bodie A company holds the following stock portfolio: Stock % of Total Portfolio W 20% X 40% Y 30% Z 10% The beta of the portfolio is (M) A 2.0 C .9 B 1.1 D .8 Beta Coefficient 1.0 2.0 The market value of the shares of AstroFields Corporation is currently $24 million, and their beta is 1.4 AstroFields has a nominal $6 million of 8% coupon debentures outstanding which mature in years These debentures have a beta of 0.1, and they currently yield 10% What is the beta of AstroFields' assets? (VD) A 0.82 C 2.5 B 0.75 D 1.16 Gleim CompuSolutions Inc stocks have a total market value of $50 million and a debt of $30 million The current Treasury bill rate is 6%, and the expected market risk premium is 9% A plot of the returns on the stock against the market returns shows a scatter of points through which a line can be fitted with a slope of 45° What is the beta of the company's assets? (D) A 1.25 C 1.375 B 0.625 D 1.667 Gleim Arizona Rock, an all-equity firm, currently has a beta of 1.25, k RF = percent, and kM = 14 percent Suppose the firm sells 10 percent of its assets with beta = 1.25 and purchases the same proportion of new assets with a beta of 1.1 What will be the firm’s new overall required rate of return, and what rate of return must the new assets produce in order to leave the stock price unchanged? (M) a 15.645%; 15.645% d 15.750%; 15.645% b 15.750%; 14.700% e 14.750%; 15.750% c 15.645%; 14.700% Brigham Gleim Beta of New Stock in the Portfolio You are managing a portfolio of five stocks that are held in equal amounts The current beta of the portfolio is 1.4, and the beta of Stock A is 1.5 If Stock A is sold, what would the beta of the replacement stock have to be to produce a new portfolio beta of 1.25? (D) A 0.75 C 1.25 B 0.90 D 1.40 Gleim Asset Beta 35 The beta of debt is 0.4 and beta of equity is 1.2 The debt-equity ratio is 0.8 Calculate the beta of the assets of the firm (Assume no taxes.) A 0.9 C 1.6 B 0.48 D None of the above B&M 36 A firm's equity beta is 0.8 and the debt beta is 0.3 If the market value of debt is $40 million and that of equity is $160 million, what is the beta of the assets of the firm? A 0.7 C 1.1 B 0.8 D None of the above B&M RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS Equity Beta 38 A firm's asset beta is 0.5 and debt beta is zero If the debt/equity ratio is 1.6, what is the equity beta of the given? A 0.8 C 1.0 B 1.3 D None of the above B&M 37 The Free-Float Company, a company in the 36% tax bracket, has riskless debt in its capital structure which makes up 40% of the total capital structure, and equity is the other 60% The beta of the assets for this business is 0.8 and the equity beta is: A 0.80 C 0.53 B 0.73 D 1.14 B&M Division Beta Sun State Mining Inc., an all-equity firm, is considering the formation of a new division that will increase the assets of the firm by 50 percent Sun State currently has a required rate of return Page of 65 MANAGEMENT ADVISORY SERVICES of 18 percent, U S Treasury bonds yield percent, and the market risk premium is percent If Sun State wants to reduce its required rate of return to 16 percent, what is the maximum beta coefficient the new division could have? (D) a 2.2 d 1.6 b 1.0 e 2.0 c 1.8 Brigham Given the Correlation Coefficient between the Stock and Market Portfolio 41 The correlation coefficient between stock A and the market portfolio is +0.6 The standard deviation of return of the stock is 30% and that of the market portfolio is 20% Calculate the beta of the stock A 0.9 C 1.1 B 1.0 D 0.6 B&M 42 The correlation coefficient between stock B and the market portfolio is 0.8 The standard deviation of the stock B is 35% and that of the market is 20% Calculate the beta of the stock A 1.0 C 0.8 B 1.4 D 0.7 B&M Given the Historical Nominal Return for the Stock & Market Portfolio 43 Historical nominal return for stock A is –8%, +10% and +22% The nominal return for the market portfolio is +6%, +18% and 24% Calculate the beta for stock A A 1.64 C 1.0 B 0.61 D None of the above B&M 44 The three year annual return for stock B comes out to be 0%, 10% and 26% Three year annual returns for the market portfolios are +6%, 18%, 24% Calculate the beta for the stock A 1.36 C B 0.74 D None of the above B&M Required Return H.G Pennypacker is interested in finding the appropriate discount rate for its new project for making blue, pink, and yellow widgets The average beta of a group of colored widget manufacturers is 1.4 and their average debt-equity ratio is 0.30 Pennypacker plans to have a debt-equity ratio of 0.20 If the risk-free rate is 6% and the expected risk premium on the market portfolio is 9%, what is the required return for the project? (D) A 9.72% C 16.08% B 7.08% D 15.72% Gleim RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS RISKS Expected Return 28 Stock A has an expected return of 10% per year and stock B has an expected return of 20% If 55% of the funds are invested in stock B, what is the expected return on the portfolio of stock A and stock B? A 10% C 14.5% B 20% D None of the above B&M 18 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% If FC and MC are combined in a portfolio with 50% of the funds invested in each, calculate the expected return on the portfolio A 10% C 16% B 13% D None of the above B&M 16 The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:- 24%, 0%, 24%, Market Portfolios:- 10%, 12%, 20% Calculate the expected return for Stock B and the market portfolio A Stock B 16%, Market Portfolio: 14% C Stock B 24%, Market Portfolio: 12% B Stock B 14%, Market Portfolio: 16% D None of the above B&M The historical returns data for the past three years for Company A's stock is -6.0%, 15%, 15% and that of the market portfolio is 10%, 10% and 16% Calculate the expected return for the stocks and the market portfolio A RA=8% RM= 12% C RA=10% RM=15% B RA= 12% RM=8% D None of the above B&M Mr Wilson recently bought a computer and decided to invest $100,000 using an online trading account He analyzed the stock of five different companies as follows: Expected Return Standard Deviation R and X Pharmaceuticals 10% 12% Walden Automotive 16% 15% YMOC Industrials 17% 16% Trustshield Banks 13% 13% Waterstone Tires 22% 18% Page of 65 MANAGEMENT ADVISORY SERVICES RISKS Mr Wilson decides to invest $35,000 in R and X Pharmaceuticals, $35,000 in Trustshield Banks, and $10,000 in each of the other three stocks Based on this information, what should Mr Wilson assume to be his portfolio's expected return? A 8.37% C 14.80% B 13.55% D 15.60% Gleim Risk-Adjusted Rate of Return 10 Dandy Product’s overall weighted average required rate of return is 10 percent Its yogurt division is riskier than average, its fresh produce division has average risk, and its institutional foods division has below-average risk Dandy adjusts for both divisional and project risk by adding or subtracting percentage points Thus, the maximum adjustment is percentage points What is the risk-adjusted required rate of return for a low-risk project in the yogurt division? (E) a 6% d 12% b 8% e 14% c 10% Brigham Portfolio Variance 17 The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:- 24%, 0%, 24%, Market Portfolios:- 10%, 12%, 20% Calculate the variance in the market A 192 C 128 B 28 D None of the above B&M 19 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% If FC and MC are combined in a portfolio with 50% of the funds invested in each, what is the variance of the portfolio with 50% of the funds invested in FC and 50% in MC (approximately)? A 208 C 188 B 325 D None of the above B&M Portfolio Standard Deviation 11 What is the standard deviation of the following two-stock portfolio? (VD) Weighting Standard Deviation Stock A 60% 11% Stock B 40% 14% A 11.25% C 12.50% B 12.20% D 126.66% RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS Correlation CFM Sample Q2-9 30 Stock X has a standard deviation of return of 10% Stock Y has a standard deviation of return of 20% The correlation coefficient between stocks is 0.5 If you invest 60% of the funds in stock X and 40% in stock Y, what is the standard deviation of a portfolio? A 10% C 12.2% B 20% D None of the above B&M 20 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% If FC and MC are combined in a portfolio with 50% of the funds invested in each, what is the standard deviation of the portfolio with 50% of the funds invested in FC and 50% in MC? A 14.4% C 13% B 18% D None of the above B&M Minimum Portfolio Risk Proportion of Investment Stock A has an expected return of 20% and Stock B has an expected return of 12% The riskiness of stock A as measured by the variance is three times that of stock B If the correlation coefficient between the two stocks is zero, what proportion of investment in each stock gives the minimum portfolio variance (minimum risk)? A 50% in Stock A and 50% in Stock B B 25% in Stock A and 75% in Stock B C 75% in Stock A and 25% in Stock B D None of the above B&M Stock X has an expected return of 20% and Stock Y has an expected return of 10% The riskiness of Stock X as measured by the standard deviation of returns is twice that of Stock Y If the correlation coefficient between the two stocks is zero, what proportion of the investment in each stock gives the least portfolio risk (minimum portfolio risk)? A 50% in X and 50% in Y C 20% in X and 80% in Y B 25% in X and 75% in Y D None of the above B&M Minimum Variance Portfolio Proportion of Investment 21 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% What is the proportion of funds to be invested in FC and MC to achieve the minimum variance portfolio? Page of 65 MANAGEMENT ADVISORY SERVICES A FC: 50% MC: 50% B FC: 25% MC: 75% RISKS C FC: 20% MC: 80% D None of the above B&M Variance 23 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% What is the variance of the minimum variance portfolio of FC and MC? A 188 C 208 B 196 D None of the above B&M Expected Return Stock A has an expected return of 20% and Stock B has an expected return of 12% The riskiness of Stock A as measured by the variance is three times that of Stock B If the correlation coefficient between the two stocks is zero, what is the expected return on the minimum variance portfolio? A 16% C 12% B 14% D 20% B&M Stock X has an expected return of 20% and stock Y has 10% The riskiness of Stock X as measured by the standard deviation of the return is twice that of Stock Y If the correlation coefficient between the two stocks is zero, what is the expected return on the portfolio with minimum risk (minimum variance portfolio)? A 20% C 12% B 15% D 10% B&M 22 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% What is the expected return on the minimum variance portfolio? A 14.8% C 10% B 16% D None of the above B&M Stock & Market Portfolio Standard and Poor's 500 Index is a: A Portfolio of common stocks B Portfolio of corporate bonds C Portfolio of government bonds D A and B above RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS B&M Market Variance 10 The historical returns data for the past three years for Company A's stock is -6.0%, 15%, 15% and that of the market portfolio is 10%, 10% and 16% Calculate the variance of the market A C 147 B 12 D None of the above B&M Variance due to Market Risk 25 Telecompute Company's variance of return is 400 If the R-squared of the regression between the company's return and the market return is 0.6, calculate the variance that is due to the market risk for the company A 240 C 600 B 160 D More information is needed B&M Covariance 11 The historical returns data for the past three years for Company A's stock is -6.0%, 15%, 15% and that of the market portfolio is 10%, 10% and 16% Calculate the covariance between the stock return and the market return A 21 C 14 B 42 D None of the above B&M 18 The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:- 24%, 0%, 24%, Market Portfolios:- 10%, 12%, 20% Calculate the covariance of returns between Stock B and the market portfolio A 24 C 292 B 28 D None of the above B&M Stock Beta 12 The historical returns data for the past three years for Company A's stock is -6.0%, 15%, 15% and that of the market portfolio is 10%, 10% and 16% Calculate the beta for Stock A A 1.0 C 0.57 B 1.75 D None of the above B&M 19 The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:- 24%, 0%, 24%, Market Portfolios:- 10%, 12%, 20% Calculate the beta for Stock B A 1.0 C 0.125 B 0.86 D None of the above B&M Page of 65 MANAGEMENT ADVISORY SERVICES 24 Computer Company's variance of returns is 900 If the R-squared of the regression between the company's returns and the market return is 0.4, calculate the unique risk for the company A 540 C 900 B 360 D More information is needed B&M Market Risk Premium 20 The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:- 24%, 0%, 24%, Market Portfolios:- 10%, 12%, 20% If the risk-free rate is 4%, calculate the market risk premium A 10% C 18.1% B 14% D None of the above B&M Required Rate of Return 21 The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:- 24%, 0%, 24%, Market Portfolios:- 10%, 12%, 20% Calculate the required rate of return (cost of equity) for Stock B using CAPM A 12.5% C 14.3% B 8.6% D None of the above B&M Two-Stock Portfolio Variances of Return 14 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% Calculate the variances of return for FC and MC A FC: 100 MC: 256 C FC: 216 MC: 130 B FC: 325 MC: 196 D None of the above B&M Standard Deviation 15 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% Calculate the standard deviation of return for FC and MC A FC:10% MC: 16% C FC: 18% MC: 14% B FC: 18% MC: 16% D None of the above B&M Covariance 10 If the covariance of Stock A with Stock B is –100, what is the covariance of Stock B with Stock A? A +100 C 1/100 RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS RISKS B –100 D Need additional information B&M 16 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% Calculate the covariance between the returns of FC and MC A 155 (0.01555) C 252 (0.0252) B 103 (0.01333) D None of the above B&M 31 Stock M and Stock N have had returns for the past three years of –12% 10%, 22% and 6%, 15%, 24% respectively Calculate the covariance between the two securities A +198 C +132 B –198 D None of the above B&M 32 Stock P and stock Q have had annual returns of -10%, 12%, 28% and 8%, 13%, 24% respectively Calculate the covariance of return between the securities A 149 C 100 B –149 D None of the above B&M 34 If the correlation coefficient between stock C and stock D is +1.0% and the standard deviation of return for stock C is 15% and that for stock D is 30%, calculate the covariance between stock C and stock D A +45 C –45 B +450 D None of the above B&M Correlation Coefficient – Given Covariance and Standard Deviation 33 If the covariance between stock A and stock B is 100, the standard deviation of stock A is 10% and that of stock B is 20%, calculate the correlation coefficient between the two securities A +0.5 C –0.5 B +1.0 D None of the above B&M 17 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% Calculate the correlation coefficient between the return of FC and MC A 0.0 C –0.615 B +0.615 D None of the above B&M Page of 65 MANAGEMENT ADVISORY SERVICES Coefficient of Variation - Given the Expected NPV, Standard Deviation and Correlation 12 Project has an expected NPV of $120,000 and a standard deviation of $200,000 Project has an expected NPV of $100,000 and a standard deviation of $150,000 The correlation between these two projects is 0.80 What is the coefficient of variation for the portfolio of projects? A 1.67 C 1.51 B 1.59 D 0.63 Gleim Single Stock Average Rate of Return 16 Spill Oil Company's stocks had -8%, 12% and 26% rates of return during the last three years respectively; calculate the average rate of return for the stock A 10% per year C 12% per year B 8% per year D None of the above B&M Mean of Return 13 Florida Company (FC) and Minnesota Company (MC) are both service companies Their historical return for the past three years are: FC: -10%,15%, 25%; MC: 10%, 6%, 32% Calculate the means of returns for each company A FC: 10%, MC: 16% C FC: 20%, MC:32% B FC: 12%, MC: 6% D None of the above B&M RISKS COST OF DEBT CAPITAL Yield-to-Maturity 13 What is the yield to maturity on Fox Inc.'s bonds if its after-tax cost of debt is 9% and its tax rate is 34%? (E) A 5.94% C 13.64% B 9% D 26.47% Gleim Issued at Par 14 A coupon bond that pays interest annually is selling at par value of $1,000, matures in years, and has a coupon rate of 9% The yield to maturity on this bond is (E) a 6.00% c 9.00% b 8.33% d 45.00% Bodie Yield to Maturity – Issued at a Discount * The Medium Company’s bonds have 10 years remaining to maturity Interest is paid annually; the bonds have a P1,000 face value; and the coupon interest rate is percent What is the estimated yield to maturity of the bonds at their current market price of P900? (M) a 10.64 percent c 8.53 percent b 10.00 percent d 7.50 percent Pol Bobadilla * The Spade Company’s bonds have years remaining to maturity Interest is paid annually; the bonds have a P1,000, face value; and the coupon interest rate is 9% What is the estimated yield to maturity of the bonds at their current market price of P829? (M) A 8.20% C 13.10% B 10.86% D 14.80% Pol Bobadilla 15 A coupon bond that pays interest of $100 annually has a par value of $1,000, matures in years, and is selling today at a $72 discount from par value The yield to maturity on this bond is (M) a 6.00% c 12.00% b 8.33% d 60.00% Bodie 16 A bond with a 12% coupon, 10 years to maturity and selling at 88 has a yield to maturity of (M) a over 14% d between 10% and 12% b between 13% and 14% e less than 12% c between 12% and 13% Bodie Standard Deviation 21 Macro Corporation has had the following returns for the past three years, -20%, 10%, 40% Calculate the standard deviation of the return A 10% C 60% B 30% D None of the above B&M 22 Micro Corporation has had returns of –5%, 15% and 20% for the past three years Calculate the standard deviation of the returns A 10% C 30% B 22.9% D None of the above B&M Variance & Standard Deviation 20 Mega Corporation has the following returns for the past three years: 8%, 16% and 24% Calculate the variance of the return and the standard deviation of the return A 64 and 8% C 43 and 6.5% B 128 and 11.3% D None of the above B&M RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS Page of 65 MANAGEMENT ADVISORY SERVICES A 5-year bond with 5% coupon rate and $1000 face value is selling for $852.10 Calculate the yield to maturity of the bond (Assume annual interest payments.) A 9.23% C 8.78% B 5% D None of the above B&M 17 A 10% coupon, annual payments, bond maturing in 10 years, is expected to make all coupon payments, but to pay only 50% of par value at maturity What is the expected yield on this bond if the bond is purchased for $975? (M) a 10.00% c 11.00% b 6.68% d 8.68% Bodie 102.What is the yield to maturity, to the nearest percent, for the following bond: current price is $908, coupon rate is 11 percent, $1,000 par value, interest paid annually, eight years to maturity? (M) A 11 percent C 13 percent B 12 percent D 14 percent Gitman Yield to Maturity – Issued at a Premium A 5-year bond with 10% coupon rate and $1000 face value is selling for $1054.30 Calculate the yield to maturity on the bond assuming annual interest payments A 10.53% C 10% B 8.62% D None of the above B&M 100.What is the approximate yield to maturity for a $1000 par value bond selling for $1120 that matures in years and pays 12 percent interest annually? (M) A 8.5 percent C 12.0 percent B 9.4 percent D 13.2 percent Gitman 101.Mugwump Industries has issued a bond which has a $1,000 par value and a 15 percent annual coupon interest rate The bond will mature in ten years and currently sells for $1,250 Using the approximation formula to calculate the yield to maturity (YTM) of this bond results in a YTM of (M) A 11.11 percent C 27.78 percent B 15.00 percent D 42.22 percent Gitman Before-tax Cost of Debt 23 The approximate before-tax cost of debt for a 15-year, 10 percent, $1,000 par value bond selling at $950 is (M) RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS RISKS A 10 percent B 10.6 percent C 12 percent D 15.4 percent Gitman 26 The approximate before-tax cost of debt for a 10-year, percent, $1,000 par value bond selling at $1,150 is (M) A percent C 8.8 percent B 8.3 percent D percent Gitman After-tax Cost of Debt Percentage 18 Maylar Corporation has sold $50 million of $1,000 par value, 12% coupon bonds The bonds were sold at a discount and the corporation received $985 per bond If the corporate tax rate is 40%, the after-tax cost of these bonds for the first year (rounded to the nearest hundredth percent) is (M) A 7.31% C 12.00% B 4.87% D 7.09% CMA 0690 1-11 The MNO Company believes that it can sell long-term bonds with a 6% coupon but at a price that gives a yield-to-maturity of 9% If such bonds are part of next year’s financing plans, which of the following should be used for bonds in their after-tax (40%) cost-of-capital calculation? (E) A 3.6% C 4.2% B 5.4% D 6% RPCPA 1001, 1003 36 A very large firm has a debt beta of zero If the cost of equity is 11% and the risk-free rate is 5%, the cost of debt is: (E) A 5% C 11% B 6% D 15% B&M 18 The before-tax cost of debt for a firm which has a 40 percent marginal tax rate is 12 percent The after-tax cost of debt is (E) A 4.8 percent C 7.2 percent B 6.0 percent D 12 percent Gitman 24 If a corporation has an average tax rate of 40 percent, the approximate, annual, after-tax cost of debt for a 15-year, 12 percent, $1,000 par value bond, selling at $950 is (M) A 10 percent C 7.6 percent B 10.6 percent D 6.0 percent Gitman Page of 65 MANAGEMENT ADVISORY SERVICES 27 The approximate after-tax cost of debt for a 20-year, percent, $1,000 par value bond selling at $960 (assume a marginal tax rate of 40 percent) is (M) A 4.41 percent C percent B 5.15 percent D 7.35 percent Gitman 25 If a corporation has an average tax rate of 40 percent, the approximate annual, after-tax cost of debt for a 10-year, percent, $1,000 par value bond selling at $1,150 is (M) A 3.6 percent C percent B 4.8 percent D percent Gitman Amount 67 A corporation borrows $1,000,000 at 10 percent annual rate of interest The firm has a 40 percent tax rate The yearly, after-tax cost of this debt is A $ 40,000 C $100,000 B $ 60,000 D $166,667 Gitman Rate of Return * What is the rate of return for an investor who pays $1,054.47 for a three-year bond with a 7% coupon and sells the bond year later for $1,037.19? A 5% C 6.64% B 5.08% D 7% Gleim Present Value of Face Value * In calculating the total value of a bond, how much does the $1,000 to be received upon a bond's maturity in years add to the bond's price if the discount rate is 6%? A $207.91 C $762.90 B $747.26 D $792.09 Gleim Annual interest payment 56 A 5-year treasury bond with a compound rate of 8% has a face value of $1000 What is the annual interest payment? A $80 C $100 B $40 D None of the above B&M RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS RISKS Bond Price 19 A corporation has promised to pay $10,000 20 years from today for each bond sold now No interest will be paid on the bonds during the twenty years, and the bonds are said to offer a 9% interest rate Approximately how much should an investor pay for each bond? A $10,000 C $1,784 B $9,174 D $900 Gleim 57 A 3-year bond with 10% compound rate and $1000 face value yields 8% APR Assuming annual compounding payment, calculate the price of the bond A $1051.54 C $1000.00 B $951.96 D $857.96 B&M 58 A three year bond has 8.1% compound rate and face value of $1000 If the yield to maturity on the bond is 10%, calculate the price of the bond assuming that the bond makes semiannual compound interest payments A $949.24 C $1057.54 B $857.96 D $1000.00 B&M 59 A four-year bond has an 8% compound rate and a face value of $1000 If the current price of the bond is $870.51, calculate the yield to maturity of the bond (assuming annual interest payments) A 8% C 10% B 12% D 6% B&M COST OF PREFERRED CAPITAL Market Value 48 A firm has an issue of preferred stock outstanding that has a stated annual dividend of $4 The required return on the preferred stock has been estimated to be 16 percent The value of the preferred stock is _ A $64 C $25 B $16 D $50 Gitman Dividend per Share Given 21 A firm has issued preferred stock at its $125 per share par value The stock will pay a $15 annual dividend The cost of issuing and selling the stock was $4 per share The cost of the preferred stock is (E) A 7.2 percent C 12.4 percent B 12 percent D 15 percent Gitman Page of 65 MANAGEMENT ADVISORY SERVICES 29 A firm has determined it can issue preferred stock at $115 per share par value The stock will pay a $12 annual dividend The cost of issuing and selling the stock is $3 per share The cost of the preferred stock is (E) A 6.4 percent C 10.7 percent B 10.4 percent D 12 percent Gitman 20 What is the after-tax cost of preferred stock that sells for $5 per share and offers a $0.75 dividend when the tax rate is 35%? (E) A 5.25% C 10.50% B 9.75% D 15% Gleim 20 A firm has issued 10 percent preferred stock, which sold for $100 per share par value The cost of issuing and selling the stock was $2 per share The firm's marginal tax rate is 40 percent The cost of the preferred stock is (E) A 3.9 percent C 9.8 percent B 6.1 percent D 10.2 percent Gitman 21 A preferred stock is sold for $101 per share, has a face value of $100 per share, underwriting fees of $5 per share, and annual dividends of $10 per share If the tax rate is 40%, the cost of funds (capital) for the preferred stock is (E) A 6.2% C 10.4% B 10.0% D 5.2% CMA 0692 1-14 22 Global Company Press has $150 par value preferred stock with a market price of $120 a share The organization pays a $15 per share annual dividend Global's current marginal tax rate is 40% Looking to the future, the company anticipates maintaining its current capital structure What is the component cost of preferred stock to Global? (E) a 4% c 10% b 5% d 12.5% Gleim 23 Maloney Inc.'s $1,000 par value preferred stock paid its $100 per share annual dividend on April of the current year The preferred stock's current market price is $960 a share on the date of the dividend distribution Maloney's marginal tax rate (combined federal and state) is 40%, and the firm plans to maintain its current capital structure relationship The component cost of preferred stock to Maloney would be closest to (E) A 6% C 10% B 6.25% D 10.4% Gleim RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS RISKS 24 Ambry Inc is going to use an underwriter to sell its preferred stock Four underwriters have given estimates (below) on their fees and the selling price of the stock, as well as the expected dividend for each: Fees Selling Price Dividends Underwriter $5 $101 $10 Underwriter 102 11 Underwriter 3 97 Underwriter 98 Which underwriter will produce the lowest cost of funds for the preferred stock? (E) A Underwriter C Underwriter B Underwriter D Underwriter Gleim Dividend Rate Given 25 Acme Corporation is selling $25 million of cumulative, non-participating preferred stock The issue will have a par value of $65 per share with a dividend rate of 6% The issue will be sold to investors for $68 per share, and issuance costs will be $4 per share The cost of preferred stock to Acme is (E) A 5.42% C 6.00% B 5.74% D 6.09% CMA 0690 1-12 115 Mars Company plans to issue some P100 preferred stock with an 11% dividend The stock is selling on the market for P97, and Mars must pay flotation costs of 5% of the market price The company is under the 40% corporate tax rate The cost of preferred stock for Mars Company is A 7.16% C 11.34% B 6.80% D 11.94% Pol Bobadilla Amount 68 A corporation has $5,000,000 in percent preferred stock outstanding and a 40 percent tax rate The after-tax cost of the preferred stock is A $400,000 C $666,667 B $240,000 D $160,000 Gitman EBIT Required 69 A corporation has $10,000,000 in 10 percent preferred stock outstanding and a 40 percent tax rate The amount of earnings before interest and taxes (EBIT) required to pay the preferred dividends is Page of 65 MANAGEMENT ADVISORY SERVICES A B $ 400,000 RISKS $1,000,000 D $1,666,667 C $ 600,000 Gitman Financial Breakeven 70 A corporation has $5,000,000 in 10 percent bonds and $3,000,000 in 12 percent preferred stock outstanding The firm's financial breakeven (assuming a 40 percent tax rate) is A $ 860,000 C $1,100,000 B $ 716,000 D $1,400,000 Gitman 27 Stephenson & Sons has a capital structure that consists of 20 percent equity and 80 percent debt The company expects to report $3 million in net income this year, and 60 percent of the net income will be paid out as dividends How large must the firm’s capital budget be this year without it having to issue any new common stock? (E) a $ 1.20 million d $ 0.24 million b $13.00 million e $ 6.00 million c $ 1.50 million Brigham * COST OF COMMON EQUITY Retained Earnings Breakpoint 26 A company has $1,500,000 of outstanding debt and $1,000,000 of outstanding common equity Management plans to maintain the same proportions of financing from each source if additional projects are undertaken If the company expects to have $60,000 of retained earnings available for reinvestment in new projects in the coming year, what dollar amount of new investments can be undertaken without issuing new equity? (E) A $0 C $90,000 B $24,000 D $150,000 CIA 0594 IV-47 * Gravy Company expects earnings of P30 million next year Its dividend payout ratio is 40%, and its equity/asset ratio is 40% Gravy uses no preferred stock At what amount of financing will there be a break point in Gravy’s marginal cost of capital? (E) A P45 million C P20 million B P30 million D P18 million Pol Bobadilla * Gravy Company expects earnings of P30 million next year Its dividend payout ratio is 40%, and its debt ratio is 60% Gravy uses no preferred stock At what amount of financing will there be a break point in Gravy’s marginal cost of capital? (E) A P45 million C P20 million B P30 million D P18 million Pol Bobadilla * Gravy Company expects earnings of P30 million next year Its dividend payout ratio is 40%, and its debt/equity ratio is 1.50 Gravy uses no preferred stock At what amount of financing will there be a break point in Gravy’s marginal cost of capital? (E) A P45 million C P20 million B P30 million D P18 million Pol Bobadilla RPCPA, AICPA, CMA & CIA EXAMINATION QUESTIONS During the past five years, Alen Company had consistently paid 50% of earnings available to common as dividends Next year, the Alen Company projects its net income, before the P1.2 million preferred dividends, at P6 million The capital structure for the company is maintained at: Debt 25.0% Preferred Stock 15.0% Common Equity 60.0% What is the retained earnings breakpoint next year (M) A P5,760,000 C P4,000,000 B P4,800,000 D P6,000,000 Pol Bobadilla 74 A firm expects to have available $500,000 of earnings in the coming year, which it will retain for reinvestment purposes Given the following target capital structure, at what level of total new financing will retained earnings be exhausted? (E) Source of capital Target market proportions Long-term debt 40% Preferred stock 10 Common stock equity 50 A $500,000 C $1,000,000 B $800,000 D $1,500,000 Gitman 75 A corporation expects to have earnings available to common shareholders (net profits minus preferred dividends) of $1,000,000 in the coming year The firm plans to pay 40 percent of earnings available in cash dividends If the firm has a target capital structure of 40 percent long-term debt, 10 percent preferred stock, and 50 percent common stock equity, what capital budget could the firm support without issuing new common stock? (E) A $2,000,000 C $1,200,000 B $ 600,000 D $ 800,000 Gitman Page 10 of 65 62 63 Answer (A) is correct R is the required return on equity capital, RF is the risk-free rate of return, b is the beta coefficient (a measure of the firm's risk), and RM is the market return The basic equation for the CAPM is R = RF + ß (RM - RF ) Thus, the required rates of return for A, B, and C are 13% [6% + (1.4 x 5%)], 10% [6% + (.8 x 5%)], and 13.5% [6% + (1.5 x 5%)], respectively A should be rejected (R is greater than the 12% expected return) B should be accepted (R is less than the 11% expected return) C should be rejected (R is greater than the 13% expected return) Answer (B) is incorrect because the required rates of return for A and C exceed their expected returns Answer (C) is incorrect because R for C exceeds its expected return Answer (D) is incorrect because the required rates of return for A and C exceed their expected returns 64 Answer (A) is correct The capital asset pricing model calculates the required return on a stock as the sum of the risk-free rate and the product of the beta coefficient and the market risk premium According to the CAPM, the expected return (R) of each of the four stocks is calculated as shown below Thus, M and N are undervalued because their expected returns exceed their required returns, and O and Q are overvalued because their expected returns are less than their required returns In equilibrium, the expected and required returns are equal Accordingly, investors will purchase shares of M and N, driving up their prices and lowering their expected returns until equilibrium is reached Investors will sell shares of O and Q, reducing their prices and increasing their expected returns until equilibrium is reached RM = 12 + (.18 - 12).9 = 174 = 17.4% RN = 12 + (.18 - 12)1.2 = 192 = 19.2% RO = 12 + (.18 - 12)1.5 = 210 = 21.0% RQ = 12 + (.18 - 12)1.7 = 222 = 22.2% Answer (B) is incorrect because N is undervalued Answer (C) is incorrect because M and N are undervalued Answer (D) is incorrect because O and Q are overvalued 65 Answer (D) is correct The correct answer is -$32,012, based on a 14% cost of capital kProject = 5% + (10% - 5%)(1.8) = 14% NPV = -$100,000 + $12,000(PVIFA14%, 10) + $20,000 (PVIF14%, 10) = -$100,000 + $12,000(5.2161) + $20,000(0.2697) = -$32,012.80 = approx -$32,012 (rounded) Answer (A) is incorrect because they are not based on a 14% cost of capital Answer (B) is incorrect because they are not based on a 14% cost of capital Answer (C) is incorrect because it results from a failure to consider salvage value ks = 10% + (4%)1.5 = 16% P0 = $3.00(1.10) = $55.00 0.16 - 0.10 66 Cost of new common equity: ke = 67 $3.30 + 0.10 = 16.32% $55.00(0.95) Answer (A) is correct Arbitrage pricing theory (APT) is based on the assumption that an asset's return is based on multiple systematic risk factors In contrast, the CAPM is a model that uses just one systematic risk factor to explain the asset's return That factor is the expected return on the market portfolio, i.e., the market-valued weighted average of all securities available in the market Accordingly, APT provides for a separate beta and a separate risk premium for each systematic risk factor identified in the model Examples of the many potential systematic risk factors are the gross domestic product (GDP), inflation, and real interest rates The APT for a three-factor model may be formulated as follows: R = RF + ß1 k1 + ß2 k2 + ß3 k3 If: R = expected rate of return RF= risk-free rate ß1, 2, = individual factor beta coefficients k1, 2, = individual factor risk premiums Thus, the expected return under the APT is 13.6% [.05 + (.5 x 03) + (.3 x 04) + (.3 x 07) + (.4 x 05) + (.6 + 03)] Answer (B) is incorrect because 10.3% is based on the three factors with the highest betas Answer (C) is incorrect because 8.3% is based on the two factors with the highest betas Answer (D) is incorrect because 5.0% is the risk- free rate 68 Answer (C) is correct The marginal cost of new equity financing is given as 16% The after-tax cost of new debt financing is 4.5% [9% x (1 - 5)] Answer (A) is incorrect because 15% is the cost of existing equity financing Answer (B) is incorrect because 15% is the cost of existing equity financing, and 5.0% is the after-tax cost of existing debt financing Answer (D) is incorrect because 5.0% is the after-tax cost of existing debt financing 69 ProjectRate of ReturnRisk-Adjusted Cost of CapitalA 16%13%B1411C129D1113E1011F109G79 Projects A, B, and C are profitable because their returns surpass their risk-adjusted costs of capital D is not profitable because its return (11%) is less than its risk-adjusted cost of capital (13%) E is not acceptable for the same reason: Its return (10%) is less than its risk-adjusted cost of capital (11%) F is accepted since it is low risk and its return (10%) surpasses the risk-adjusted cost of capital of 9% G is rejected because its return (7%) < riskadjusted cost of capital (9%) 70 Answer (A) is correct Assume the share of stock was worth $100 The 18% nominal rate of return brings your total wealth to $118 However, the 14% real return means your real wealth is only $114 The problem is to determine what rate of inflation will equate the $118 to the $114 of real wealth Assuming that the price level index was 100% initially, the solution's approach is as follows: $118 = $114, or x = 1.0351 x Thus, the inflation rate is 3.51% Answer (B) is incorrect because 4% is the difference in percentage points, not the rate of inflation Answer (C) is incorrect because it will not equate nominal wealth to real wealth Answer (D) is incorrect because it will not equate nominal wealth to real wealth 71 Answer (D) is correct The after-tax weighted-average cost of capital is 12%, resulting in a total capital charge of $360,000 on $3 million of total capital However, the WACC is an after-tax rate, so the cost of debt is 4.8% [8% x (1.0 - 40% tax rate)] Accordingly, the debt component of the capital charge is $96,000 (4.8% x $2,000,000) The cost of equity must therefore be 26.4% [($360,000 - $96,000) ÷ $1,000,000] Answer (A) is incorrect because 8% is the pre-tax cost of debt capital Answer (B) is incorrect because 12% is the after-tax weighted-average cost of both debt and equity Answer (C) is incorrect because 15% is the hurdle rate 72 73 SourceProportion of Total Funds After-tax CostWeightedAverage CostCommon Stock.60.15.090Bonds.40.08.032.122 Answer (C) is correct The 12% debt coupon rate is reduced by the 35% tax shield, resulting in a cost of debt of 7.8% [12% x (1 - 35)] The average of the 15% equity capital and 7.8% debt is 11.4% Answer (D) is incorrect because 13.50% overlooked the tax shield on the debt capital Answer (A) is incorrect because 8.775% assumed that dividends on equity capital are tax deductible Answer (B) is incorrect because 9.60% used the complement of the tax rate instead of the tax rate 74 Answer (D) is correct All three rates are quoted as after-tax rates since there is no tax shield associated with common equity capital Thus, simply weight the three rates to determine the weighted average cost Debt 8% x = 3.2 Preferred 13% x = 2.6 Common 17% x = 6.812.6%Answer (A) is incorrect because 10.22% assumed that dividends on common equity are tax deductible, which is incorrect Answer (B) is incorrect because 10.52% uses the complement of the tax rate, and assumed the debt rate was before tax rather than after tax Answer (C) is incorrect because 11.48% assumed the rate given for debt was before tax rather than after tax 75 Answer (C) is correct The cost for equity capital is given as 15%, and preferred stock is 10% The before-tax rate for debt is given as 6%, which translates to an after-tax cost of 3.9% [6% x (1 - 35)] The rates are weighted as follows: 15% x 65 = 9.750 10% x 10 = 1.000 3.9% x 25 =.975 11.725%Answer (A) is incorrect because 10.333% is an unweighted average of the three costs, and also ignores the tax shield Answer (B) is incorrect because 11.325% used the complement of the tax rate instead of the tax rate to calculate the tax shield Answer (D) is incorrect because 12.250% ignores the tax savings on debt capital 76 Answer (B) is correct The problem can be solved by using the three-step process of unlevering and relevering the WACC First, unlever the WACC to calculate the opportunity cost of capital, r: r = r D(D/V) + rE(E/V) = 0.08(0.4) + 0.13(0.6) = 0.11 = 11% Next, the cost of equity at a 20% debt ratio can be calculated: r E = r + (rA - rD)D/E = [0.11 + (0.11 - 0.078)(0.2/0.8)] = 0.118 = 11.8% Finally, the new WACC can be calculated: WACC = 0.078(1 - 0.35)(0.2) + 0.118(0.8) = 10.45% Answer (A) is incorrect because 9.11% is the WACC if the 20% is replaced by the original 40%, and the 80% is thus decreased to 60% in the final WACC calculation Answer (C) is incorrect because 11% is the opportunity cost of capital Answer (D) is incorrect because 11.8% is the cost of equity at a 20% debt ratio 77 Answer (C) is correct The important consideration is whether the overall cost of capital will be lower for a given proposal According to the Capital Asset Pricing Model, the change will result in a lower average cost of capital For the existing structure, the cost of equity capital is 15.5% [6% + 95 (16% - 6%)] Because the company has no debt, the average cost of capital is also 15.5% Under the proposal, the cost of equity capital is 16.5% [6% + 1.05 (16% 6%)], and the weighted average cost of capital is 13.8% [.3(.075) + 7(.165)] Hence, the proposal of 13.8% should be accepted Answer (A) is incorrect because the average cost of capital needs to be considered Answer (B) is incorrect because the average cost of capital needs to be considered Answer (D) is incorrect because the weighted average cost of capital will decrease 78 Solve for ks: WACC 11.5% ks Solve for g: 15.75% 15.75% g 79 = 11.5% = wdkd(1 - T) + wcks = 0.45(0.09)(0.70) + 0.55ks = 15.75% = D1/P0 + g = $5/$45 + g = 4.64% Capital structure: 40% D, 10% P, 50% E WACC = 12.30% (given) kd = 11% (given) WACC = 0.4(kd)(1 - T) + 0.1(kp) + 0.5(ke) Because the firm has insufficient retained earnings to fund the equity portion of the firm’s capital budget, use k e in the WACC calculation a Calculate ke: ke = $2(1.08) + 8% = 8.47% + 8% = 16.47% $30(0.85) b Calculate kp: kp = Dp PN = $2 = 11.11% $20(0.9) c Find T by substituting values for kd, kp, and ke in the WACC equation: 0.1230 = 0.4(0.11)(1 - T) + 0.1(0.1111) + 0.5(0.1647) 0.1230 = 0.044(1 - T) + 0.0111 + 0.0824 0.0295 = 0.044(1 - T) 0.6713 = - T 0.3287 = T 2.10 80 81 Find the dividend, D0 = [(0.5)$40,000]/# of Shares = $20,000/10,000 = $2.00 Since the firm will not have enough retained earnings to fund the equity portion of its capital budget, the firm will have to issue new common stock Find the cost of new common stock: k e = D1/[P0(1 - F)] + g = $2.00/ [$25(1 - 0.15)] + 0% = 0.0941 = 9.41% Finally, calculate WACC, using ke = 0.0941, and kd = 0.08, so WACC = (D/A)(1 - Tax rate)kd + (E/A)ke = 0.4(0.08)(1 - 0.4) + 0.6(0.0941) = 0.0757 ≈ 7.6% R= + 8% = 13% 42 Retention ratio = (P4.80 – P2.10) ÷ P4.80 = 56.25% Growth rate = ROE x Retention ratio = 8% x 56.25% =4.5% P2.10 = P24.71 Market Price Po = 13% - 4.5% 82 WACC = [0.3 × 0.084 × (1 - 0.4)] + [0.7 × ($2.5/($45 × (1 - 0.1)) + 0.07)] = 10.73% 83 AT cost of debt = 0.08(1 - 0.40) = 0.048 = 4.80% Cost of retained earnings = $2.12/$32 + 0.06 = 0.1263 = 12.63% WACC = 0.75(0.1263) + 0.25(0.048) = 10.67% 84 WACC = wdkd(1 - T) + wcke kd is given = 9% Find ke: ke = D1/[P0(1 - F)] + g = $0.8/[$25(1 - 0.1)] + 0.09 = 0.125556 Now you can calculate WACC: WACC = (0.3)(0.09)(0.6) + (0.7)(0.125556) = 10.41% 85 Questions thru are based on the following information Brigham J Ross and Sons Inc has a target capital structure that calls for 40 percent debt, 10 percent preferred stock, and 50 percent common equity The firm’s current after-tax cost of debt is percent, and it can sell as much debt as it wishes at this rate The firm’s preferred stock currently sells for $90 a share and pays a dividend of $10 per share; however, the firm will net only $80 per share from the sale of new preferred stock Ross’s common stock currently sells for $40 per share, but the firm will net only $34 per share from the sale of new common stock The firm recently paid a dividend of $2 per share on its common stock, and investors expect the dividend to grow indefinitely at a constant rate of 10 percent per year Assume the firm has sufficient retained earnings to fund the equity portion of its capital budget What is the firm’s cost of retained earnings? (E) a 10.0% d 16.5% b 12.5% e 18.0% c 15.5% What is the firm’s cost of newly issued common stock? (E) a 10.0% d 16.5% b 12.5% e 18.0% c 15.5% What is the firm’s cost of newly issued preferred stock? (E) a 10.0% d 16.5% b 12.5% e 18.0% c 15.5% What is the firm’s weighted average cost of capital? (E) a 9.5% d 11.4% b 10.3% c 10.8% 86 ke = $2.00(1.05) + 0.05 = 17% $21.88(1 - 0.2) WACC = 0.4(0.14)(1 - 0.4) + 0.6(0.17) = 0.1356 = 13.56% ≈ 13.6% 87 e 11.9% Answer (D) is correct Use the following calculations: R= D1 $3.18 +G= + 06 = 17.16% P0 (1 - Flotation) $30.00(.95) Answer (A) is incorrect because 16% ignores the increase in dividends and flotation costs Answer (B) is incorrect because 16.53% ignores the next dividend increasing to $3.18 Answer (C) is incorrect because 16.6% ignores the flotation costs 88 Answer (C) is correct In the calculation below, the cost of preferred stock equals the preferred dividend divided by the net issuance price The preferred stock will yield $4,800,000 after subtracting the 4% flotation cost, so it must sell for $5,000,000 ($4,800,000 ÷ 96) The annual dividend on the preferred stock is $300,000 (6% x $5,000,000) Consequently, the cost of capital raised by issuing preferred stock is 6.25% ($300,000 dividend ÷ $4,800,000 net issuance price) WeightBonds 40%x 9% x (1-.4) = 2.16 %Preferred stock 10%x 6.25% = 625Common stock 50%x 15%= 7.50 10.285%Flotation costs are ignored for the bonds because $20 million must be repaid at maturity date, which is not the case for preferred stock Answer (A) is incorrect because they not appear to be the result of a common error Answer (B) is incorrect because they not appear to be the result of a common error Answer (D) is incorrect because they not appear to be the result of a common error 89 Answer (D) is correct Multiply (1 - effective tax rate) times the effective interest rate of 11%, which is 6.60% [11% x (1 - 4)] Answer (A) is incorrect because 5.13% is 5.40% reduced by the 5% stock flotation costs Answer (B) is incorrect because 5.40% is 60% of 9% Answer (C) is incorrect because 6.25% is 6.60% reduced by the 5% stock flotation costs 90 Answer (C) is correct As a larger proportion of an entity's capital is provided by debt, the debt becomes riskier and more expensive Hence, it requires a higher interest rate Answer (A) is incorrect because the diversity decreases, not increases, risk Answer (B) is incorrect because $50,000,000 is minuscule in the debt markets Answer (D) is incorrect because the combination alternative maintains the same debt-equity mixture, which would not warrant a rate increase in the cost of debt or equity 91 First, calculate the after-tax component cost of debt as 7%(1 - 0.3) = 4.9% Next, calculate the retained earnings breakpoint as $500,000/0.5 = $1,000,000 Thus, to finance its optimal capital budget, Longstreet must issue some new equity and flotation costs of 10% will be incurred The cost of new equity is then [$5(1.10%)/$75(1 0.1)] + 10% = 8.15% + 10% = 18.15% Finally, the WACC = 4.9%(0.3) + 9%(0.2) + 18.15%(0.5) = 12.34% 92 REQUIRED: The weighted-average cost of capital DISCUSSION: (C)The first step is to determine the after-tax cost of the long-term debt Multiplying the current yield of 9% times one minus the tax rate (1 – 0.4 – 0.6) results in an after-tax cost of debt of 5.4% (9% x 0.6) The cost of the preferred stock is 6% (the annual dividend rate) The Gordon growth model for measuring the cost of equity capital combines the dividend yield with the growth rate Dividing the $1.20 dividend by the $40 market price produces a dividend yield of 3% Adding the 3% dividend yield and the 10% growth rate gives a 13% dividend yield and the 10% growth rate gives a 13% cost of common equity capital Once the costs of the of the three types of capital have been computed, the next step is to weight them according to the market values of the elements of the current capital structure The $1,000,000 of preferred stock is selling at par The market value of the long-term debt is 80% of book value, or $5,600,000 (80% x $7,000,000) The common stock has a current market price of $8,000,000 ($40 x 200,000 shares) Thus, the weighted-average cost of capital is 9.6% ($1,402,000 ÷ $14,600,000) as shown below Debt0.54 x $5,600,000=$ 302,400Preferred0.06 x $1,000,000=60,000Common 0.13 x $8,000,000=1,040,000Total$14,600,000=$1,402,400Answer (A) is incorrect because 13% is the cost of equity Answer (B) is incorrect because 8.3% is the simple average Answer (D) is incorrect because 9% is based on book values 93 94 WACC Answer: b Diff: M R AT cost of debt = 0.07(1 - 0.40) = 0.042 = 4.2% Cost of preferred stock = $4/$42 = 0.0952 = 9.52% Cost of retained earnings = $2/$28 + 0.07 = 0.1414 = 14.14% WACC = 0.40(0.042) + 0.10(0.0952) + 0.50(0.1414) = 0.0970 = 9.70% Answer (B) is correct According to the dividend growth model, the three elements required to calculate the cost of equity capital are (1) the dividends per share, (2) the expected growth rate, and (3) the market price of the stock If flotation costs are incurred when issuing new stock, they are deducted from the market price to arrive at the amount of capital the corporation will actually receive Accordingly, the $100 selling price is reduced by the $3 discount and the $5 flotation costs to arrive at the $92 to be received for the stock Because the dividend is not expected to increase in future years, no growth factor is included in the calculation Thus, the cost of the common stock is 7.6% ($7 dividend ÷ $92) Answer (A) is incorrect because the 7.0% figure would only be correct if $100 were received from the sale of the stock Answer (C) is incorrect because 7.4% would be correct only if the stock could be sold without giving a $3 discount Answer (D) is incorrect because 8.1% would be correct only if the amount received were about $86 or if some growth factor were assumed 95 Answer (A) is correct The three elements required to calculate the cost of equity capital are (1) the dividends per share, (2) the expected growth rate, and (3) the market price of the stock Because growth is not expected, the calculation is simply to divide the dividend of $7 by the $100 market price of the stock to arrive at a cost of equity capital of 7% Answer (B) is incorrect because 7.6% would be the cost of new equity capital from selling stock if the stock resulted in proceeds of $92 per share Answer (C) is incorrect because 7.4% would be correct only if new stock were sold and resulted in proceeds of $95 per share Answer (D) is incorrect because dividing the $7 dividend by the $100 market price of the stock produces a ratio of 7%, not 8.1% 96 Answer (C) is correct Williams' preferred capital structure is 50% common stock However, $100,000 of retained earnings (50% of the required $200,000 of capital) will be used before any common stock is issued Thus, the weighted-average cost of capital will be determined based on the respective costs of the bonds, preferred stock, and retained earnings The cost of the bonds is given as 4.8%, the cost of the preferred stock is 8%, and the cost of the retained earnings is 7% ($7 dividend ÷ $100 market price of the common stock) These three costs are then weighted by the preferred capital structure ratios: 30% x 4.8% = 1.44%20% x 8.0% = 1.60%50% x 7.0% = 3.50%Total 6.54%Rounding to the nearest tenth produces the correct answer of 6.5% Answer (A) is incorrect because 19.8% represents the unweighted sum of each of the three elements of cost Answer (B) is incorrect because 4.8% is the cost of the long-term debt All funding will not be obtained from debt because the firm wants to maintain a capital structure in which debt represents only 30% of the total capital Answer (D) is incorrect because the 6.8% figure can only be obtained if new stock is sold New stock will not be sold because the retained earnings can be used at a lower cost, and there is no need to sell stock when the total capital required is only $200,000 97 Answer (A) is correct The cost of the bonds is given as 4.8% The cost of the preferred stock is 8% ($8 dividend ÷ $100), the cost of new common stock is 7.6% ($7 dividend ÷ $92 proceeds), and the cost of the retained earnings is 7% ($7 dividend ÷ $100 market price) These four costs are then weighted by the preferred capital structure ratios, a process that requires subdividing the common stock portion into retained earnings of $100,000 (10% of capital) and new common stock of $400,000 (40% of capital): 30% x 4.8% = 1.44%20% x 8.0% = 1.60%40% x 7.6% = 3.04%10% x 7.0% = 70%Total6.78%Rounding to the nearest tenth results in the correct answer of 6.8% Answer (B) is incorrect because 4.8% is the cost of the long-term debt Answer (C) is incorrect because 6.5% would be correct only if the equity capital were obtained totally from retained earnings Because only $100,000 of retained earnings is available, the remainder of equity capital must come from sales of new stock Answer (D) is incorrect because 27.4% represents the unweighted total of each of the four elements of cost 98 The firm will not be issuing new equity because there are adequate retained earnings available to fund available projects Therefore, WACC should be calculated using ks rather than ke ks = D1/P0 + g = $3.00/$60.00 + 0.07 = 0.12 = 12% WACC = wdkd(1 - T) + wcks = (0.6)(0.08)(1 - 0.4) + (0.4)(0.12) = 0.0768 = 7.68% 99 EBIT $1,000,000 Interest 400,000 EBT $ 600,000 Taxes (40%) 240,000 Net income $ 360,000 EPS1 = $360,000/100,000 = $3.60 D1 = $3.60(0.5) = $1.80 ks = ($1.80/$40.00) + 0.125 = 17.0% 100 Cost of new common equity: $1.80 + 0.125 = 17.5% ($40)(0.90) $0.90(1.05) ks = + 0.05 = 0.1600 = 16.00% $8.59 ke = 101 102 103 104 ke = $0.90(1.05) + 0.05 = 0.1722 = 17.22% $8.59(1 - 0.10) Since the firm can fund the equity portion of its capital budget with retained earnings, use ks in WACC WACC = wdkd(1 - T) + wcks = 0.3(0.12)(1 - 0.4) + 0.7(0.16) = 0.0216 + 0.112 = 0.1336 = 13.36% Answer (B) is correct Because the bonds are issued at their face value, the pretax effective rate is 10% However, interest is deductible for tax purposes, so the government absorbs 40% of the cost, leaving a 6% after-tax cost Answer (A) is incorrect because 4% assumes a 60% tax rate Answer (C) is incorrect because 10% is the beforetax rate Answer (D) is incorrect because the after-tax cost will be less than the effective before-tax rate 105 Answer (D) is correct The cost of internal equity capital equals the dividend yield (dividends per share ÷ market price) plus the dividend growth rate Dividing the $3 dividend by the $60 market price results in a yield of 5% Adding the 10% dividend growth rate produces a cost of 15% for retained earnings No adjustment is made for taxes because dividends are not tax deductible Answer (A) is incorrect because 5% is the dividend yield; the growth rate is ignored Answer (B) is incorrect because 9% would be the after-tax cost if dividends were deductible Answer (C) is incorrect because 10% is the dividend growth rate; it ignores the dividend yield 106 Answer (C) is correct The company will receive only 80% of the $60 market price, or $48 Consequently, the dividend yield is 6.25% ($3 ÷ $48) Adding the 10% growth rate produces a cost of new equity capital of 16.25% Answer (A) is incorrect because 6.25% ignores the dividend growth rate Answer (B) is incorrect because 15% ignores the flotation costs Answer (D) is incorrect because 10% is the dividend growth rate 107 Answer (C) is correct The current optimal capital structure is 40% debt and 60% equity The $3 million to be retained from earnings in the coming year represents the equity portion of the maximum new capital outlay To retain the optimal capital structure, $2 million of debt must be added to the $3 million of retained earnings Hence, the maximum capital expansion is $5 million Answer (A) is incorrect because $2 million is the amount of debt that must be added to maintain the optimal structure Answer (B) is incorrect because $3 million is the amount of earnings retained Answer (D) is incorrect because the amount of $5 million can be calculated 108 REQUIRED: The after-tax weighted average cost of capital given the amount of the budget DISCUSSION: (B) To maintain a capital structure of 40% debt and 60% equity, the $7 million total must consist of $2.8 million of debt and $4.2 million of equity The equity will consist of $3 million of retained earnings and $1.2 million of new stock The weighted-average cost of the three sources of new capital is determined as follows: $3,000,000 ÷ $7,000,000 x 14% = 6.00% $1,200,000 ÷ $7,000,000 x 16% = 2.74% $2,800,000 ÷ $7,000,000 x 10% = 4.00% 12.74% Answer (A) is incorrect because 11/14% assumes a tax adjustment for the cost of debt, but the 10% rate is an aftertax amount Answer (C) is incorrect because 13.6% assumes the equity consists solely of new common stock Answer (D) is incorrect because 16% is the cost of new common stock 109 REQUIRED: The marginal cost of capital after projects exceed the capital budget DISCUSSION: (C) For this calculation, the weighted-average cost of capital is based on the 16% cost of new common stock and the 10% cost of debt Retained earnings will not be considered because the amount available has been exhausted Thus, the weighted-average of any additional capital required will be 13.6% [(60% x 16% cost of new equity) + (40% x 10% cost of new debt)] Answer (A) is incorrect because 10% is the cost of debt capital Answer (B) is incorrect because 12.74% is the weighted-average cost of capital calculated for a $7 million budget Answer (D) is incorrect because 16% is the cost of new common stock 110 Cost of retained earnings Answer: c Diff: E ks = 111 $2.00(1.10) + 0.10 = 15.5% $40.00 Cost of external equity Answer: d Diff: E Cost of new common equity: ke = $2.20 + 0.10 = 0.1647 16.5% $34.00 112 Cost of preferred stock Answer: b Diff: E $10 kp = = 12.5% $80 113 Since the firm has sufficient retained earnings to fund the equity portion of its capital budget, use k s in WACC equation WACC = wdkd(1 - T) + wpkp + wcks = 0.4(6%) + 0.1(12.5%) + 0.5(15.5%) = 11.4% 114 We need to find kp at the point where all projects are accepted In other words, the capital budget = $2,000 + $3,000 + $5,000 + $3,000 = $13,000 The WACC at that point is equal to IRRD = 9.5% Step 1: Find the retained earnings break point to determine whether ks or ke is used in the WACC calculation: BPRE = $1,000 = $2,500 0.4 Since the capital budget > the retained earnings break point, ke is used in the WACC calculation Step 2: Calculate ke: ke = $3.00 + 5% = 12.80% $42.75(0.9) Step 3: Find kp: 9.5% = 0.4(10%)(0.65) + 0.2(kps) + 0.4(12.80%) 9.5% = 2.60% + 0.2(kps) + 5.12% 1.78% = 0.2kp 8.90% = kp 115 116 Data given: wd = 0.3; wc = 0.7; kd = 8%; T = 0.4; kRF = 5.5%, kM - kRF = 5% Step 1: Determine the firm’s cost of equity using the WACC equation: WACC = wd × kd × (1 - T) + wc × ks 10% = 0.3 × 8% × (1 - 0.4) + 0.7 × ks 8.56% = 0.7 × ks ks = 12.2286% Step 2: Calculate the firm’s beta using the CAPM equation: ks = kRF + (kM - kRF)b 12.2286% = 5.5% + (5%)b 6.7286% = 5%b b = 1.3457 ≈ 1.35 WACC = wdkd(1 - T) + wcks ks = kRF + RPM(b) ks = 5.5% + 5%(1.4) ks = 5.5% + 7% = 12.5% WACC = wdkd(1 - T) + wcks WACC = 0.4(9%)(1 - 0.4) + (0.6)12.5% WACC = 9.66% 117 Cost of debt = 0.09(1 - 0.35) = 0.0585 = 5.85% Cost of retained earnings = kRF + (RPM)b = 6% + 6%(1.5) = 15% WACC = 0.60(0.0585) + 0.40(0.1500) = 0.0951 = 9.51% 118 Answer (C) is correct The current rate for Treasury bonds is 7% If the company can issue debt at 150 basis points (1.5%) over U.S Treasury bonds, the market rate of interest for Martin is 8.5% Given a 40% tax rate, the net cost of debt is 60% of the rate actually paid, or 5.1% (60% x 8.5%) Answer (A) is incorrect because 5.5% is the Treasury rate minus 150 bonus points Answer (B) is incorrect because 7.0% is the Treasury rate Answer (D) is incorrect because 8.5% ignores the income tax effect 119 Answer (D) is correct The CAPM adds the risk-free rate (determined by government securities) to the product of the beta coefficient (a measure of the firm's risk) and the difference between the market return and the risk-free rate Thus, the current cost of equity using the CAPM is 17% [7% + 1.25 (15% - 7%)] Answer (A) is incorrect because 8.75% equals the product of beta and the risk-free rate Answer (B) is incorrect because 10.00% fails to add the risk-free rate to the risk premium Answer (C) is incorrect because 15.00% is the expected market return 120 Answer (A) is correct Proceeds are $14,850,000 [(1.01 x $15,000,000) - (.02 x $15,000,000)] The annual interest is $1,200,000 (.08 coupon rate x $15,000,000) Thus, the company is paying $1,200,000 annually for the use of $14,850,000, a rate of 8.08% ($1,200,000 ÷ $14,850,000) Answer (B) is incorrect because 10.00% is the sum of the coupon rate and the flotation rate Answer (C) is incorrect because 7.92% ignores the 2% flotation costs Answer (D) is incorrect because 8.00% is the coupon rate 121 Answer (A) is correct The 7% debt cost and the 12% equity cost should be weighted by the proportions of the total investment represented by each source of capital The total project costs $50 million, of which debt is $15 million, or 30% of the total Equity capital is the other 70% Consequently, the weighted-average cost of capital is 10.5% [(7%)(30%) + (12%)(70%)] Answer (B) is incorrect because 8.50% reverses the weights Answer (C) is incorrect because 9.50% assumes debt and equity are equally weighted Answer (D) is incorrect because the weighted-average cost cannot be less than any of its components 122 Answer (A) is correct The market return (RM), given as 12%, minus the risk-free rate (RF), given as 5%, is the market risk premium It is the rate at which investors must be compensated to induce them to invest in the market The beta coefficient (ß) of an individual stock, given as 60%, is the correlation between volatility (price variation) of the stock market and the volatility of the price of the individual stock Consequently, the expected rate of return is 9.20% [RF + ß(RM - RF) = 05 + 6(.12 - 05)] Answer (B) is incorrect because 12.20% equals the risk-free rate plus 60% of the market rate Answer (C) is incorrect because 7.20% results from multiplying both the market rate premium and the risk-free rate by 60% Answer (D) is incorrect because 12.00% is the market rate 123 Cost of debt = 0.084(1 - 0.30) = 0.0588 = 5.88% Cost of preferred stock = 0.09 = 9% Cost of retained earnings = kRF + (RPM)b = 6.57% + (5%)1.3 = 13.07% WACC = 0.4(0.0588) + 0.10(0.09) + 0.50(0.1307) = 9.79% 124 Answer (D) is correct According to SMA 4A, the cost of capital is defined as the composite cost of various sources of funds included in a firm's capital structure It is the minimum rate of return that must be earned on new investments that will not dilute the interests of the shareholder In this problem, Company X has three sources of funds: debt, common stock, and preferred stock The cost of debt capital is the after-tax cost of debt to the firm Given that the firm is taxed at 40% and interest is a tax deduction, the cost to the firm is only 0.066 [(1.0 - 0.4) x (.11)] The cost of preferred stock is the annual dividend requirement divided by the current price per share or the proceeds from issuance per share Thus, the component cost of preferred stock for Company X is 0.075 ($2.25 ÷ 30) The cost of common stock is difficult to determine accurately, but one of the most common estimations involves using the capital asset pricing model to determine the cost Thus, the cost of common stock equals the risk-free rate plus the product of beta for Company X and the market risk premium The component cost of common stock for Company X is 0.082 [.04 + (.7 x 06)] To determine the weighted-average cost of capital, each component cost is multiplied by its respective weight in the company capital structure, and these values are summed to arrive at 0.0733 [(.066 x 5) + (.082 x 4) + (.075 x 1)] Answer (A) is incorrect because 0.0743 is the simple average Answer (B) is incorrect because 0.0820 is the cost of common stock Answer (C) is incorrect because 0.0660 is the cost of debt 125 Time line: 60 60 60 kd/2 = ? VB = 1,000 PMT = 60 40 6-month • • • 60 FV = 1,000 Periods Since the bond sells at par of $1,000, its YTM and coupon rate (12 percent) are equal Thus, the before-tax cost of debt to Rollins is 12.0 percent The after-tax cost of debt equals: kd,After-tax = 12.0%(1 - 0.40) = 7.2% Financial calculator solution: Inputs: N = 40; PV = -1,000; PMT = 60; FV = 1,000; Output: I = 6.0% = kd/2 kd = 6.0% = 12% kd(1 - T) = 12.0%(0.6) = 7.2% 126 Cost of preferred stock Answer: d Diff: E Cost of preferred stock: kp = $12/$100(0.95) = 12.6% 127 128 Cost of equity: CAPM Answer: c Diff: E Cost of retained earnings (CAPM approach): ks = 10% + (5%)1.2 = 16.0% Cost of equity: DCF Answer: c Diff: E Cost of retained earnings (DCF approach): ks = $2.00(1.08) + 8% = 16.0% $27 129 Cost of equity: risk premium Answer: c Diff: E Cost of retained earnings (bond yield-plus-risk-premium approach): ks = 12.0% + 4.0% = 16.0% 130 WACC Answer: b Diff: E R Calculate ke: ke = 131 $2.00(1.08) + 8% = 16.89% $27(1 − 0.1) WACC = wdkd(1 - T) + wpkp + wcke = 0.2(12.0%)(0.6) + 0.2(12.6%) + 0.6(16.89%) = 14.09 14.1% Answer (C) is correct If earnings before interest and taxes increased by 17%, and net income was up 42%, the firm is using leverage effectively The degree of financial leverage is the percentage change in net income divided by the percentage change in EBIT Accordingly, Nelson's degree of financial leverage is 2.47 Answer (A) is incorrect because the degree of financial leverage is calculated by dividing the percentage change in net income by the percentage change in EBIT Answer (B) is incorrect because the degree of financial leverage is calculated by dividing the percentage change in net income by the percentage change in EBIT Answer (D) is incorrect because the degree of financial leverage is calculated by dividing the percentage change in net income by the percentage change in EBIT 132 Answer (B) is correct Financial leverage is the amount of the fixed cost of capital, principally debt, in a firm's capital structure relative to its operating income Leverage creates financial risk and is directly related to the cost of capital Because the company is retiring bonds, the total debt is decreased Given that the amount of debt and leverage are directly related, a decrease in the amount of debt results in a decrease in financial leverage Answer (A) is incorrect because the bond retirement decreases the debt equity ratio Answer (C) is incorrect because the total assets will decrease (assets will be used to retire the debt, resulting in an increased asset turnover ratio (net sales ÷ average total assets) Answer (D) is incorrect because the interest expense avoided will increase net income and the return on shareholders' equity 133 Answer (B) is correct The degree of financial leverage for Company B may be calculated as earnings before interest and taxes, divided by EBIT minus interest EBIT is $200 ($95 NI + $10 interest + $95 tax expense) Thus, the DFL is 1.05 [$200 ÷ ($200 - $10)] Answer (A) is incorrect because 1.03 results if depreciation expense is omitted from the calculation of EBIT Answer (C) is incorrect because 1.12 results if net income is used instead of EBIT Answer (D) is incorrect because 1.25 is the degree of financial leverage for Company A 134 Answer (C) is correct The book value per share for Company A equals the sum of common stock and retained earnings, divided by the number of shares, or 4.17 [($100 + $150) ÷ 60] Answer (A) is incorrect because $1.67 results if retained earnings is omitted from the numerator Answer (B) is incorrect because $2.50 results if common stock is omitted from the numerator Answer (D) is incorrect because $5.00 is the book value per share for Company B 135 Answer (A) is correct The degree of total leverage equals the degree of financial leverage (DFL) times the degree of operating leverage (DOL) The DFL may be stated as earnings before interest and taxes (EBIT) divided by EBIT minus interest and preferred dividends (before the tax effect) If EBIT is $100,000 [($2 x 300,000 units) sales - ($1.50 x 300,000 units) VC - $50,000 FC], the DFL is 1.25 [$100,000 ÷ ($100,000 - $20,000 - $0)] The DOL may be stated as contribution margin divided by the contribution margin minus fixed costs Hence, if the contribution margin is $150,000 [($2 unit price - $1.50 unit VC) x 300,000 units], the DOL is 1.5 [$150,000 ÷ ($150,000 $50,000)], and the degree of total leverage is 1.875 (1.25 x 1.50) Answer (B) is incorrect because 1.50 is the DOL Answer (C) is incorrect because 1.25 is the DFL Answer (D) is incorrect because 1.20 equals the DOL divided by the DFL 136 Answer (B) is correct Operating leverage is the percentage change in operating income resulting from a percentage change in sales It measures how a change in volume affects profits Companies with larger investments and greater fixed costs ordinarily have higher contribution margins and more operating leverage The degree of operating leverage measures the extent to which fixed assets are used in the production process A company with a high percentage of fixed costs is more risky than a firm in the same industry that relies more on variable costs to produce Based on a contribution margin of $.16 per unit ($1 - $.84 variable cost), the degree of operating leverage is (400,000 x $.16) ÷ [(400,000 x $.16) - 28,000] = 1.78 Answer (A) is incorrect because 2.4 is obtained by overstating the contribution margin or the fixed costs Answer (C) is incorrect because 2.13 includes a nonoperating expense (interest) as a fixed cost Answer (D) is incorrect because 1.2 is obtained by understating the $64,000 contribution margin or understating the $28,000 of fixed costs 137 Answer (C) is correct The degree of financial leverage is the percentage change in earnings available to common shareholders that is associated with a given percentage change in net operating income Operating income equals earnings before interest and taxes The more financial leverage employed, the greater the degree of financial leverage and the riskier the firm Earnings before interest and taxes equal $36,000 [$400,000 sales - ($.84 x 400,000 units) VC - $28,000 FC] Using the formula, the calculation is as follows: $36,000 =$36,000 = 1.35$36,000 - $6,000 - ($2,000 ÷ 6)$26,667Answer (A) is incorrect because 2.4 is obtained by overstating the contribution margin or the fixed costs Answer (B) is incorrect because 1.78 is the degree of operating leverage, not financial leverage Answer (D) is incorrect because 1.2 is obtained by understating the $64,000 of contribution margin or understating the $28,000 of fixed costs 138 Answer (A) is correct The degree of total leverage is equal to the degree of operating leverage times the degree of financial leverage Thus, a decrease in either of these ratios results in a decrease in total leverage If the company had no preferred stock, the DFL and the DTL would be lower because the pretax income necessary to pay the preferred dividends [P ÷ (1 - t)] is subtracted from the denominator of the DFL Answer (B) is incorrect because the DTL would decrease, not increase Answer (C) is incorrect because the elimination of preferred stock would change the equation Answer (D) is incorrect because the decrease would be proportional 139 140 Answer (D) is correct The company will have higher expected tax expense under arrangement #1 because, with lower interest expense, taxable income will be higher #1 #2Sales revenue $500,000 $500,000Cost of sales (200,000) (200,000)G&A expense(100,000) (100,000)Interest expense (24,000) (70,000)Taxable income$176,000 $130,000Tax payable (30%) (52,800) (39,000)Net income $123,200 $ 91,000Answer (A) is incorrect because expected gross margin is unaffected by the choice of financing arrangement Answer (B) is incorrect because the degree of operating leverage measures the effect of a change in sales on operating income (earnings before interest and taxes) Hence, the two arrangements have the same degree of operating leverage because the financing arrangement does not affect sales and cost of sales Answer (C) is incorrect because interest expense will be higher under arrangement #2 Answer (B) is correct The weighted-average cost of capital is calculated as follows: (Weight of equity)(Cost of equity) + (Weight of debt)(Before-tax cost of debt)(1 - Tax rate) = (.7)(.12) + (.3)(.08)(1 - 3) = 10% Answer (A) is incorrect because 8% is the before-tax cost of debt Answer (C) is incorrect because 11% is calculated using the before-tax cost of debt instead of the after-tax cost of debt Answer (D) is incorrect because 12% is the cost of equity 141 Answer (D) is correct The degree of financial leverage may be expressed as earnings before interest and taxes, divided by earnings before interest and taxes minus interest For financial arrangement #2, the DFL is 1.54 {($500,000 sales - $200,000 CGS - $100,000 G&A) ÷ [($500,000 sales - $200,000 CGS - $100,000 G&A) - (10% x $700,000 debt)]} Answer (A) is incorrect because 1.09 uses the after-tax interest cost for arrangement #1 in the denominator Answer (B) is incorrect because 1.14 is the degree of financial leverage for arrangement #1 Answer (C) is incorrect because 1.32 uses the after-tax interest cost in the denominator 142 Answer (A) is correct As calculated below, net profit amounts for #1 and #2 are $123,200 and $91,000, respectively Thus, #2 has a 30.3% return on equity [$91,000 ÷ ($1,000,000 total assets - $700,000 debt)] compared with a 17.6% return on equity for #1 [$123,200 ÷ ($1,000,000 total assets - $300,000 debt)] Moreover, the debt ratio (debt financing ÷ total assets) is 70% ($700,000 ÷ $1,000,000) for #2, and 30% ($300,000 ÷ $1,000,000) for #1 #1 #2Sales revenue $500,000 $500,000Cost of sales (200,000)(200,000)General & admin expense (100,000) (100,000)Interest expense (24,000) (70,000)Taxable profit$176,000 $130,000Tax payable (30%) (52,800) (39,000)Net profit $123,200 $ 91,000Answer (B) is incorrect because the return on equity and the debt ratio are higher for #2 than for #1 Answer (C) is incorrect because the return on equity and the debt ratio are higher for #2 than for #1 Answer (D) is incorrect because the return on equity and the debt ratio are higher for #2 than for #1 143 Answer (A) is correct The coefficient of variation is useful when the rates of return and standard deviations of two investments differ It measures the risk per unit of return because it divides the standard deviation ( σ ) by the expected return ( kˆ ) Coefficient of variation = σ kˆ The investment in the U.S and Britain has a coefficient of variation of 143 (3% ÷ 21%), whereas the investment in the U.S and Canada has a coefficient of variation of 625 (15% ÷ 24%) Accordingly, the company should undertake the British investment because it has substantially less risk per unit of return Answer (B) is incorrect because the Canadian investment is significantly riskier per unit of return Answer (C) is incorrect because the company should undertake the British investment As a result, its return will increase and its risk will decrease Answer (D) is incorrect because the company should undertake the British investment As a result, its return will increase and its risk will decrease 144 Answer (A) is correct The expected rate of return on an investment is determined using an expected value calculation It is an average of the outcomes weighted according to their probabilities For Techspace, the average is accomplished by multiplying each probability by the corresponding return for each state of the economy and then calculating the sum of the products Numerically, the calculation is performed as follows: 05(-.45) + 15(-.10) + 2(.05) + 4(.10) + 15(.30) + 05(.35) = 075 = 7.5% Answer (B) is incorrect because 15% adds positive products instead of negative products for the first two states Answer (C) is incorrect because 35% is the sum of the returns (assuming all are positive) minus Answer (D) is incorrect because 25% is the sum of the returns 145 Answer (B) is correct The variance σ is calculated using the equation σ2= ∑ (k n i =1 i ) − kˆ pi If: k i is the return from the ith outcome, kˆ is the expected return, and p i is the probability of the ith outcome n kˆ = ∑ k i p i or i =1 05(-.45) + 15(-.10) + 2(.05) + 4(.10) + 15(.30) + 05(.35) = 075 σ = 05(-.45-.075)2 + 15(-.1-.075) + 2(.05-.075) + 4(.1-.075) + 15(.30-.075) + 05(.35-.075) = 0301 Answer (A) is incorrect because 1735 is the square root of 0301, which is the standard deviation of Techspace returns Answer (C) is incorrect because 075 is the expected return Answer (D) is incorrect because 2738 is the square root of the expected return 146 Answer (B) is correct The standard deviation (å) gives an exact value for the tightness of the distribution and the riskiness of the investment It is calculated by taking the square root of the variance Given that the variance is 0301, the standard deviation is 1735, or 17.35% Answer (A) is incorrect because 7.5% is the expected return Answer (C) is incorrect because 3.01% is the variance Answer (D) is incorrect because the standard deviation is 17.35% 147 Answer (C) is correct A coinsurance clause requires the insured to maintain insurance equal to or greater than a specified percentage (usually 80%) of the value of the insured property If the insured has not carried the specified percentage and a partial loss occurs, the insurance company is liable for only a proportionate part of the loss This is to deter people from paying for insurance on only a small part of the property's value However, the coinsurance clause has no application when an insured building is totally destroyed Thus, Hart can recover the $300,000 face value of the policy Answer (A) is incorrect because partial recovery is available when a coinsurance requirement is not complied with Answer (B) is incorrect because a coinsurance clause does not limit recovery when the insured property is a total loss Answer (D) is incorrect because an insured cannot collect more from an insurance company than the face value of the policy 148 Answer (B) is correct Under a standard coinsurance clause, the insured agrees to maintain insurance equal to a specified percentage of the value of the property If the insured has not carried the specified percentage and a loss occurs, the insurance company pays only part of the loss The coinsurance requirement is $750,000 (75% x $1,000,000 FMV at the time of the loss) Under the formula below, Ritz might recover $600,000 of the $900,000 loss Amount of insurance x Loss = Recovery Coinsurance requirement $500,000 x $900,000 = $600,000 $750,000 But Ritz may recover no more than the face amount of the policy Answer (A) is incorrect because the coinsurance percentage is applied to compute the coinsurance requirement, which in turn is the denominator of the fraction multiplied by the loss Answer (C) is incorrect because under no circumstances would the insurance company pay more than the face value of the policy Answer (D) is incorrect because under no circumstances would the insurance company pay more than the face value of the policy 149 Answer (C) is correct A coinsurance clause requires the insured to maintain insurance equal to or greater than a specified percentage (usually 80%) of the value of the insured property If the insured has not carried the specified percentage and a partial loss occurs, the insurance company is liable for only a proportionate part of the loss A pro rata clause generally provides that a person who is insured with multiple policies can collect from each insurance company only a proportionate amount of the loss based on the amount of insurance carried with each insurer Pod was in compliance with the coinsurance clause (80% x $250,000 = $200,000) Pod would recover in full The pro rata portion Pod would recover from Owners is $135,000 [($150,000 ÷ $200,000) x $180,000] Answer (A) is incorrect because, since Pod was in compliance with the coinsurance requirement, Owners will pay a proportionate amount of the loss based on the amount of insurance carried with each insurer Answer (B) is incorrect because, since Pod was in compliance with the coinsurance requirement, Owners will pay a proportionate amount of the loss based on the amount of insurance carried with each insurer Answer (D) is incorrect because, since Pod was in compliance with the coinsurance requirement, Owners will pay a proportionate amount of the loss based on the amount of insurance carried with each insurer 150 Answer (B) is correct A coinsurance clause does not apply when the property insured is totally destroyed Pod would recover the face amount of the policies Answer (A) is incorrect because a coinsurance clause does not apply when the property insured is totally destroyed Answer (C) is incorrect because recovery is limited to the face amount of the policies Answer (D) is incorrect because recovery is limited to the face amount of the policies 151 Answer (C) is correct Under a coinsurance clause, the insured agrees to maintain the insurance equal to a specified percentage of the value of his/her property If a loss occurs, the insurer pays only a proportionate share if the insured has not carried the specified percentage In this case, the insured agreed to carry 80%, but in fact carried only 40%; thus, it became a 50% insurer, and the insurance companies' liability was reduced to 50% of any loss The total combined liability of the fire insurance companies in the problem is $20,000 Under the standard pro rata clause, a person who is insured with multiple policies can collect from each insurance company only a proportionate amount of the loss Even though Ace issued a policy for $24,000, it is liable for only three-fifths (24,000/40,000) of the recoverable loss after applying the coinsurance formula (3/5 x $20,000 = $12,000) Likewise, Thrifty is liable for 2/5 of $20,000 Answer (A) is incorrect because part of the loss is recovered when a coinsurance clause is not complied with Answer (B) is incorrect because each pays the amount recoverable times the percentage of the total insurance it agreed to provide Answer (D) is incorrect because the insurer pays only a proportionate share if the insured has not carried the specified percentage 152 Answer (A) is correct Following a loss, the owner will be able to collect the lesser of (1) the face amount of the policy, (2) the amount of the loss, or (3) the amount of the co-insurance limitation The co-insurance limitation is calculated by multiplying the loss times the following co-insurance formula: [Face amount of policy ($120,000) over Co-insurance requirement (80% x $200,000 fair value)] = 75% Thus, 75% of any loss will be covered, up to the face amount of the policy The recovery is $112,500 (75% x $150,000 loss) Answer (B) is incorrect because the recovery is limited to the amount calculated in the co-insurance formula Answer (C) is incorrect because the recovery is limited to the amount calculated in the co-insurance formula Answer (D) is incorrect because the recovery is limited to the amount calculated in the co-insurance formula 153 Answer (B) is correct Under a standard coinsurance clause, the insured agrees to maintain insurance equal to a specified percentage of the value of the property If the insured has not carried the specified percentage and a loss occurs, the insurance company pays only part of the loss The coinsurance requirement is $750,000 (75% x $1,000,000 FMV at the time of the loss) Under the formula below, Ritz might recover $600,000 of the $900,000 loss Amount of insurance x Loss = RecoveryCoinsurance requirement$500,000 x $900,000 = $600,000$750,000But Ritz may recover no more than the face amount of the policy Answer (A) is incorrect because the coinsurance percentage is applied to compute the coinsurance requirement, which in turn is the denominator of the fraction multiplied by the loss Answer (C) is incorrect because under no circumstances would the insurance company pay more than the face value of the policy Answer (D) is incorrect because under no circumstances would the insurance company pay more than the face value of the policy ... Return Standard Deviation R and X Pharmaceuticals 10% 12% Walden Automotive 16% 15% YMOC Industrials 17% 16% Trustshield Banks 13% 13% Waterstone Tires 22% 18% Page of 65 MANAGEMENT ADVISORY SERVICES. .. B&M Page of 65 MANAGEMENT ADVISORY SERVICES Coefficient of Variation - Given the Expected NPV, Standard Deviation and Correlation 12 Project has an expected NPV of $120,000 and a standard deviation... outstanding and a 40 percent tax rate The amount of earnings before interest and taxes (EBIT) required to pay the preferred dividends is Page of 65 MANAGEMENT ADVISORY SERVICES A B $ 400,000 RISKS
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Xem thêm: Test bank management advisory services by tan p04 risks , Test bank management advisory services by tan p04 risks , . WACC = wdkd(1 - T) + wcke. kd is given = 9%. Find ke:, . The firm will not be issuing new equity because there are adequate retained earnings available to fund available projects. Therefore, WACC should be calculated using ks rather than ke.