Chapters 11-16Chapter 11• Rate of return = (capital gain + dividend)/(initial share price)• Dividend Yield = dividend/(initial share price)• Capital Gains Yield = (capital gain)/(initial share price)• Real Rate of Return = [(1+nominal rate of return)/(1+inflation rate)] – 1• #6- Nominal interest rate cannot be negative because if it were investors would choose to hold cash (which pays a rate of return = to 0) rather than buy a Treasury bill providing a negative return. • #6- Real expected rate of return is negative, though, if the inflation rate exceeds the nominal return• Variance = average squared deviation from the mean• Standard deviation = square root of variance• #12- If investors become less willing to bear investment risk they will require higher risk premium (to compensate them for holding risky assets)• #12- Security prices of risky investments will fall until expected rates of return on those securities rise to the now-higher required rates of return• #20- Risk reduction is most pronounced when stock returns vary against each other (when one firm does bad the other will tend to do well  stable return of the overall portfolio)Chapter 12• Investors require higher expected rates of return on investments with high market risk (not high total risk).• Variability of returns is a measure of total risk• If beta = 0 then the asset’s expected return should = the risk-free rate (NOT 0)• #1c- The portfolio is invested 1/3 in Treasury bills and 2/3 in the market so its beta will be: (1/3 x 0) + (2/3 x 1) = 2/3• Risk of death of individual policyholders are largely independent and therefore are diversifiable  insurance companies satisfied to charge a premium that reflects actuarial probabilities of death w/o additional risk premium• Flood damage is not independent across policyholders and not diversifiable (if 1 coastal home floods its neighbor probably will too)  insurance company not satisfied with charging premium that reflects only expected value of payouts• Considerable variation around the regression line indicates that the fund is subject to diversifiable risk: it is not well diversified (the variation in the fund’s returns is influenced by more than just marketwide events)• Required Return = rf + B(rm – rf)• If required return is greater than the project IRR you should reject it• #5c- This project is attractive when its risk and therefore required return are low. At a higher risk level the IRR is no longer higher than the expected return on comparable-risk assets available elsewhere in the market• A diversified investor will find the lowest-beta stock safestChapter 13• r = DIV/P0• WACC = [(D/V) x rdebt x (1-TC)] + [(P/V) x rpreferred] + [(E/V x requity]o Sometimes that middle section, [(P/V) x rpreferred], is not used• r = (DIV1/P0) + g which also means [DIV0(1+g)/P0] + g Indefinite Growth• #6- Executive Fruit should use WACC of Geothermal, not its own, when evaluating an investment in Geothermal because (since risk of project determines the discount rate) Geothermal’s WACC is more reflective of the risk of the project• Number of shares can be calculated by dividing book value by the book value per share• Market value of equity = price per share x # of shares• #16- Bonds selling below par value because the yield to maturity is greater than the coupon rate• WACC can be a reasonable estimate of the discount rate if the risk of the proposed project is similar to the risk of the existing projectsChapter 14• # of shares = (par value of issued stock)/(par value per share)• Outstanding shares = (issued shares) – (Treasury stock)• If a company buys back shares, Treasury stock would increase by the amount spent on the stock• Preferred stock commits the firm to paying the security holder a fixed sum (either a specified interest payment in case of bonds or a specified dividend in the case of a preferred stock)• Failure to pay the dividend on preferred stock doesn’t set off bankruptcy• #11o Call provision requires firm to compensate investor by promising a higher yield to maturity because it gives them a valuable optiono Restriction on further borrowing protects bondholders who therefore will require a lower yield to maturityo Collateral protects the bondholder and results in lower yield to maturityo Option to convert gives bondholders a valuable option and therefore offers them a lower promised yield to maturity• Income bonds- firm promises to make specified payments to the security holder (if firm cannot make those payments the firm is not forced into bankruptcy)o For firm- advantage of income bonds over preferred stock is that the bond interest payments are tax-deductible expenses• The fact that preferred stock has lower priority in the event of bankruptcy reduces the price of the preferred stock and increases its yield compared to bondso But when high percent of preferred stock dividend payments are free of taxes to corporate holders the price can increase and the yield of the preferred stock can decreaseo For strong firms, the default premium is small and tax effect dominates, so the preferred stock has a lower yield to maturity than the bondso For weaker firms, default premium dominatesChapter 15• Rights issue requires that there are already existing shareholders• Seasoned offerings are security issues by firms that are already publicly tradedo Publicly traded firms usually find it advantageous to sell new shares in a public offering because it is less costly than a private placemento Private placement of bonds, though, can be issued with unusual terms and can allow the firm to negotiate directly with the bondholders should the firm want to change terms of the debt later• Shelf registration is more likely to be used for bonds issued by a large industrial company• #3a Large issue involves proportionately lower costs due to economies of scale• Issue costs for debt are less than for equityChapter 16• Interest tax shield is the reduction in corporate income taxes due to the fact that interest is treated as an expense that reduces taxable income• Tradeoff theory of capital structure holds that the optimal debt ratio is determined by striking a balance between the advantages and disadvantages of debt financingo Advantage of debt financing- interest tax shieldo Disadvantage- various costs of financial distresso At the optimal debt ratio, the increase in the present value of