Chp 13 return risk and sml CHp14

expected return

the return on a risky asset expected in the future

Systematic Risk

A risk that influences a large number of assets. Also, market risk.

Risk premium

expected return - risk free rate

To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, then add all of these up. The result is the variance. So, the variance and standard deviation of each stock are:

10.9 expected return σA2 = .10(.04 - .1090)^2 + .60(.09 - .1090)^2 + .30(.17 - .1090)^2 σA2 = .00181 σA = .00181^1/2 σA =.0425, or 4.25%

Using the debt-equity ratio to calculate the WACC, we find: WACC = (.60/1.60)(.046) + (1/1.60)(.10) WACC = .0798, or 7.98%

Sommer, Inc., is considering a project that will result in initial aftertax cash savings of $2.3 million at the end of the first year, and these savings will grow at a rate of 2 percent per year indefinitely. The firm has a target debt-equity ratio of .60, a cost of equity of 10 percent, and an aftertax cost of debt of 4.6 percent. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and applies an adjustment factor of +3 percent to the cost of capital for such risky projects. What is the maximum inital cost the company would be willing to pay for the project?

WACC formula

Starset, Inc., has a target debt-equity ratio of .85. Its WACC is 9.1 percent, and the tax rate is 23 percent. a. If the company's cost of equity is 14 percent, what is its pretax cost of debt?WACC = .091 = (1/1.85)(.14) + (.85/1.85)(1 - .23)RD RD = .0433, or 4.33%

Cully Company needs to raise $80 million to start a new project and will raise the money by selling new bonds. The company will generate no internal equity for the foreseeable future. The company has a target capital structure of 70 percent common stock, 5 percent preferred stock, and 25 percent debt. Flotation costs for issuing new common stock are 7 percent, for new preferred stock, 4 percent, and for new debt, 2 percent. What is the true initial cost figure the company should use when evaluating its project?

We first need to find the weighted average flotation cost. Doing so, we find: fT = .70(.07) + .05(.04) + .25(.02) fT = .056, or 5.6% And the total cost of the equipment including flotation costs is: (Amount raised)(1 - .056) = $80,000,000 Amount raised = $80,000,000/(1 - .056) Amount raised = $84,745,763

unsystematic risk

a risk that affects at most a small number of assets. Also, unique or asset-specific risk

Dinklage Corp. has 7 million shares of common stock outstanding. The current share price is $68, and the book value per share is $8. The company also has two bond issues outstanding. The first bond issue has a face value of $70 million, a coupon rate of 6 percent, and sells for 97 percent of par. The second issue has a face value of $40 million, a coupon rate of 6.5 percent, and sells for 108 percent of par. The first issue matures in 21 years, the second in 6 years. Both bonds make semiannual payments. a. What are the company's capital structure weights on a book value basis? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .3216.) b. What are the company's capital structure weights on a market value basis? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .3216.)

The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company's debt, so: BVE = 7,000,000($8) BVE = $56,000,000 BVD = $70,000,000 + 40,000,000 BVD = $110,000,000 So, the total value of the company is: V = $56,000,000 + 110,000,000 V = $166,000,000 And the book value weights of equity and debt are: E/V = $56,000,000/$166,000,000 E/V = .3373 D/V = 1 - E/V D/V = .6627 b. The market value of equity is the share price times the number of shares, so: MVE = 7,000,000($68) MVE = $476,000,000 Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: MVD = .97($70,000,000) + 1.08($40,000,000) MVD = $111,100,000 This makes the total market value of the company: V = $476,000,000 + 111,100,000 V = $587,100,000 And the market value weights of equity and debt are: E/V = $476,000,000/$587,100,000 E/V = .8108 D/V = 1 - E/V D/V = .1892

Suppose your company needs $24 million to build a new assembly line. Your target debt-equity ratio is .75. The flotation cost for new equity is 7 percent, but the flotation cost for debt is only 3 percent. Your boss has decided to fund the project by borrowing money because the flotation costs are lower and the needed funds are relatively small. a. What is your company's weighted average flotation cost, assuming all equity is raised externally? (Do not round intermediate calculations and enter your answer as a percent round to 2 decimal places, e.g., 32.16.) b. What is the true cost of building the new assembly line after taking flotation costs into account? (Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to the nearest whole number, e.g., 1,234,567.)

The weighted average flotation cost is the weighted average of the flotation costs for debt and equity, so: fT = .03(.75/1.75) + .07(1/1.75) fT = .0529, or 5.29% b. The total cost of the equipment including flotation costs is: (Amount raised)(1 - .0529) = $24,000,000 Amount raised = $24,000,000/(1 - .0529) Amount raised = $25,339,367 Even if the specific funds are actually being raised completely from debt, the flotation costs, and hence true investment cost, should be valued as if the firm's target capital structure is used.

Titan Mining Corporation has 7.5 million shares of common stock outstanding, 250,000 shares of 4.2 percent preferred stock outstanding, and 140,000 bonds with a semiannual coupon of 5.1 percent outstanding, par value $1,000 each. The common stock currently sells for $51 per share and has a beta of 1.15, the preferred stock has a par value of $100 and currently sells for $103 per share, and the bonds have 15 years to maturity and sell for 107 percent of par. The market risk premium is 7.5 percent, T-bills are yielding 2.4 percent, and the company's tax rate is 22 percent. a. What is the firm's market value capital structure? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .1616.) b. If the company is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

a. We will begin by finding the market value of each type of financing. We find: MVD = 140,000($1,000)(1.07) = $149,800,000 MVP = 250,000($103) = $25,750,000 MVE = 7,500,000($51) = $382,500,000 And the total market value of the firm is: V = $149,800,000 + 382,500,000 + 25,750,000 V = $558,050,000 So, the market value weights of the company's financing are: D/V = $149,800,000/$558,050,000 = .2684 P/V = $25,750,000/$558,050,000 = .0461 E/V = $382,500,000/$558,050,000 = .6854 b. For projects equally as risky as the firm itself, the WACC should be used as the discount rate. First we can find the cost of equity using the CAPM. The cost of equity is: RE = .024 + 1.15(.075) RE = .1103, or 11.03% The cost of debt is the YTM of the bonds, so: P0 = $1,070 = $25.50(PVIFAR%,30) + $1,000(PVIFR%,30) R = 2.228% YTM = 2.228% × 2 YTM = 4.46% And the aftertax cost of debt is: RD = (1 - .22)(.0446) RD = .0348, or 3.48% The cost of preferred stock is: RP = $4.20/$103 RP = .0408, or 4.08% Now we can calculate the WACC as: WACC = .2684(.0348) + .0461(.0408) + .6854(.1103) WACC = .0868, or 8.68%