P8-32 Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following situations. a. Find the required return for an asset with a beta of 2.20 when the risk-free rate and market return are 5% and 32%, respectively. b. Find the risk-free rate for a firm with a required return of 23.75% and a beta of t 1.25 when the market return is 20%. c. Find the market return for an asset with a required return of 18% and a beta of 1.20 when the risk-free rate is 8%. d. Find the beta for an asset with a required return of 15% when the risk-free rate and market return are 3% and 15%, respectively. Scanned with CamScanner PART FOUR Risk and the Required Rate of Return Personal Finance Problem the following PB-33 Portfolio return and beta Jamie Peters invested $100,000 to set up portfolio one year ago. Yearly income Value today Asset Cost Beta at purchase $1,600 $20,000 $20,000 0.80 1,400 36,000 0.95 35,000 34,500 30,000 1.50 375 16,500 15,000 1.25 a. Calculate the portfolio beta on the basis of the original cost figures. b. Calculate the percentage return of each asset in the portfolio for the year. c. Calculate the percentage return of the portfolio on the basis of original cost, us- ing income and gains during the year. d. At the time Jamie made his investments, investors were estimating that the market return for the coming year would be 10%. The estimate of the risk-free rate of re- turn averaged 4% for the coming year. Calculate an expected rate of return for each stock on the basis of its beta and the expectations of market and risk-free returns. e. On the basis of the actual results, explain how each stock in the portfolio per- formed relative to those CAPM-generated expectations of performance. What factors could explain these differences? LG3 LG6 BUD P8-32 Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following situations. a. Find the required return for an asset with a beta of 2.20 when the risk-free rate and market return are 5% and 32%, respectively. b. Find the risk-free rate for a firm with a required return of 23.75% and a beta of t 1.25 when the market return is 20%. c. Find the market return for an asset with a required return of 18% and a beta of 1.20 when the risk-free rate is 8%. d. Find the beta for an asset with a required return of 15% when the risk-free rate and market return are 3% and 15%, respectively. Scanned with CamScanner PART FOUR Risk and the Required Rate of Return Personal Finance Problem the following PB-33 Portfolio return and beta Jamie Peters invested $100,000 to set up portfolio one year ago. Yearly income Value today Asset Cost Beta at purchase $1,600 $20,000 $20,000 0.80 1,400 36,000 0.95 35,000 34,500 30,000 1.50 375 16,500 15,000 1.25 a. Calculate the portfolio beta on the basis of the original cost figures. b. Calculate the percentage return of each asset in the portfolio for the year. c. Calculate the percentage return of the portfolio on the basis of original cost, us- ing income and gains during the year. d. At the time Jamie made his investments, investors were estimating that the market return for the coming year would be 10%. The estimate of the risk-free rate of re- turn averaged 4% for the coming year. Calculate an expected rate of return for each stock on the basis of its beta and the expectations of market and risk-free returns. e. On the basis of the actual results, explain how each stock in the portfolio per- formed relative to those CAPM-generated expectations of performance. What factors could explain these differences? LG3 LG6 BUD