# Finance maths return on investment

1. Last year a company had \$355,000 of assets, \$26,275 of net income, and a debt-to-total-assets ratio of 44%.  Now suppose the newly hired CFO convinces the president to increase the debt ratio to 58%.  Sales and total assets will not be affected, but interest expenses would increase.  However, the CFO believes that better cost controls would be sufficient to offset the higher interest expense and therefore keep net income unchanged.  What was the original return on equity (ROE) for this company?  Assuming the president of the firm allows the CFO to increase the debt ratio to 58%, what will be the new ROE’?

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2.

Consider the following information for three stocks: Stock X, Stock Y, and Stock Z. The returns on each of the three stocks are positively correlated, but they are not perfectly correlated.  (That is, all of the correlation coefficients are between 0 and 1, or 0 < ρ < 1).

Expected                    Standard

Stock                       Return                     Deviation                   Beta

Stock X                       10%                           20%                         1.0

Stock Y                       10                               20                            1.0

Stock Z                       12                               20                            1.4

Portfolio A has half of its funds invested in Stock X and half invested in Stock Y.  Portfolio B has one third of its funds invested in each of the three stocks.  The risk-free rate (rrf) is 5 percent, and the market is in equilibrium.  (That is, the required return equals the expected return on all assets.) What is the expected return on the market, rMKT?

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