Chapter 11: Cost of Capital

The breakpoints in the MCC schedule occur at ________ of newly raised capital.

$50 and $122 Million because these are the two points in the graph shown in this question where the cost of capital line breaks and rises perpedicularly).

Water and Power Company (WPC) can borrow funds at an interest rate of 11.10% for a period of five years. Its marginal federal-plus-state tax rate is 45%. WPC's after-tax cost of debt is _____________ (rounded to two decimal places).

11.11%-(1-45%) = .111-.55 = 6.11%

If this company raises $160M, its weighted average cost of capital is ______

11.6%

target capital structure

A firm's shareholder wealth-maximizing combination of debt, and common and preferred stock.

investment opportunity schedule

A table or graph of a firm's potential investments listed in decreasing order of their internal rates of return.

investment opportunity schedule

A table or graph of a firm's potential investments ranked from the highest internal rate of return to the lowest.

Green Caterpillar Garden Supplies Inc. is closely held and, as a result, cannot generate reliable inputs for the CAPM approach. Green Caterpillar's bonds yield 11.50%, and the firm's analysts estimate that the firm's risk premium on its stock relative to its bonds is 4.50%. Using the bond-yield-plus-risk-premium approach, the firm's cost of equity is ___________.

COST OF EQUITY = BOND YEILD + RISK PREMIUM = 11.5% + 4.5% = 16%

Blue Hamster Manufacturing Inc. is considering a one-year project that requires an initial investment of $400,000; however, in raising this capital, Blue Hamster will incur an additional flotation cost of 5%. At the end of the year, the project is expected to produce a cash inflow of $520,000. The rate of return that Blue Hamster expects to earn on the project after its flotation costs are taken into account is ___________

Cost of New investment is 400,000*1.05% = 420,000 with floatation cost Cash flow after a year 520,000. Hence return is (520,000-420,000)/420,000 = .2381 = 23.81%

Blue Hamster has a current stock price of $33.35 and is expected to pay a dividend of $1.36 at the end of next year. The company's growth rate is expected to remain constant at 4%. If the issue's flotation costs are expected to equal 5% of the funds raised, the flotation-cost-adjusted cost of the firm's new common stock is ________

Cost of the firm = D1/P0 + g where D1 is the dividend next year = $1.36 P0 = the price this year = $33.35 g=growth rate = 4% =0.04 Hence Cost of Capital / equity = $33.35×(1-5%) = $1.36÷(r-4%) = $33.35×(1-.05) = $1.36÷(r-.04) = 31.6825r - 1.2673 = 1.36 = 31.6825r = 2.6273 r = 0.0429 = 4.29% Taking into consideration flotation costs of 5%: Cost of stock = 4.29% + 5% = 8.29%

True or False: The following statement accurately describes how firms make decisions related to issuing new common stock. The cost of issuing new common stock is calculated the same way as the cost of raising equity capital from retained earnings. False: Flotation costs need to be taken into account when calculating the cost of issuing new common stock, but they do not need to be taken into account when raising capital from retained earnings. True: The cost of retained earnings and the cost of new common stock are calculated in the same manner, except that the cost of retained earnings is based on the firm's existing common equity, while the cost of new common stock is based on the value of the firm's share price net of its flotation cost.

False: Flotation costs need to be taken into account when calculating the cost of issuing new common stock, but they do not need to be taken into account when raising capital from retained earnings.

Blue Hamster's addition to earnings for this year is expected to be $420,000. Its target capital structure consists of 50% debt, 5% preferred stock, and 45% common stock. Blue Hamster Manufacturing Inc.'s retained earnings breakpoint is __________ (rounded to the nearest whole dollar).

Firms prefer to raise capital from retained earnings instead of issuing new stock whenever possible, because no flotation costs are associated with raising capital from retained earnings. However, if a firm has more good investment opportunities than can be financed with retained earnings, it may need to issue new common stock. The retained earnings (RE) breakpoint is the total amount of capital that can be raised before a firm must issue new common stock. That is: RE Breakpoint = Addition to Retained Earnings for the Year / Equity Fraction of Target Capital Structure = $420,000/0.45 = $933,333

Your boss has just asked you to calculate your firm's cost of capital. Below is potentially relevant information for your calculation. What is your firm's Weighted Average Cost of Capital? Common Equity: Book Value = $100 million, Market Value = $150 million, Net Income from most recent fiscal year = $12 million, Required rate of return (from CAPM) = 11%, Dividend Yield = 2%. Debt: Book Value = $100 million, Market Value = $90 million, average coupon rate = 4%, average yield to maturity = 4.4%, average maturity = 10 years. Corporate Tax Rate = 21%.

Market Value of Debt and Equity Market Value of Debt = $90 Million Market Value of Equity = $150 Million Total Market Value = $210 Million Weight of Capital Structure Weight of Debt = 0.3750 [$90 Million / $210 Million] Weight of Equity = 0.6250 [$150 Million / $210 Million] After Tax Cost of Debt After Tax Cost of Debt = Pre-tax Yield to maturity x (1 - Tax Rate) = 4.40% x (1 - 0.21) = 4.40% x 0.79 = 3.48% Cost of Equity = 11.00% Weighted Average Cost of Capital (WACC) Therefore, the Weighted Average Cost of Capital (WACC) = [After Tax Cost of Debt x Weight of Debt] + [Cost of equity x Weight of Equity] = 3.48% x 0.3750] + [11.00% x 0.6250] = 1.30% + 6.88% = 8.18%

Description What is your firm's Weighted Average Cost of Capital (input as a raw number, i.e. if your answer is 7.1%, enter 7.1)? Corporate taxes are 21%. The firm is financed with the following securities: Common Equity: -> 5,000,000 shares -> price per share = $50 -> β=1.25, Mkt Risk Premium = 5%, Risk-free rate = 4%. Debt: -> 200,000 bonds -> face value per bond = $1000 -> market price per bond= $1075 -> coupon rate = 6%, 5 years to maturity (assume semi-annual payment.

Market value of common equity = 5,000,000 * 50 = 250,000,000 Market value of bond = 200,000 * 1,075 = 215,000,000 Total market value = 250,000,000 + 215,000,000 = 465,000,000 Cost of equity = Risk free rate + beta (market risk premium) Cost of equity = 0.04 + 1.25 (0.05) Cost of equity = 0.1025 or 10.25% Coupon = (0.06 * 1000) / 2 = 30 Number of periods = 5 * 2 = 10 YTM = 4.3163% Keys to use in a financial calculator: 2nd I/Y 2, FV 1000, PV -1075, N 10, PMT 30, CPT I/Y WACC = Weight of debt*after tax cost of debt + weight of equity*cost of equity WACC = (215,000,000 / 465,000,000)*0.043163*(1 - 0.21) + (250,000,000 / 465,000,000)*0.1025 WACC = 0.015766 + 0.05511 WACC = 0.071 or 7.1

________ is the symbol that represents the cost of raising capital by issuing new stock in the weighted average cost of capital (WACC) equation.

Re

The current risk-free rate of return is 4.20% and the current market risk premium is 6.60%. Fuzzy Button Clothing Company has a beta of 0.87. Using the Capital Asset Pricing Model (CAPM) approach, Fuzzy Button's cost of equity is __________.

Rf + BETA * RISK PREMIUM = 4.20% + (0.87 * 6.6%) = 9.94%

The stock of Blue Hamster Manufacturing Inc. is currently selling for $45.56, and the firm expects its dividend to be $2.35 in one year. Analysts project the firm's growth rate to be constant at 5.70%. Using the discounted cash flow (DCF) approach, Blue Hamster's cost of equity is estimated to be _______

The DCF approach shows you that the price and the expected rate of return on a share of common stock ultimately depend on the stock's expected cash flows. When dividends are expected to grow at a constant rate, the DCF formula can be expressed as: P0 = D1/(rs-g) However, in this problem, you are trying to find cost of equity (rs)—not the price of the stock (P0)—so you'll want to rearrange the equation to put it in terms of rs and then plug in the values given in the problem to solve for the cost of equity. That is: rs = ($2.35/$45.56) + 0.0570 = 0.1086 = 10.86%

breakpoint

The amount of capital expenditures made, or to be made, at which the firm's marginal cost of capital increases.

Weighted Average Cost of Capital (WACC)

The average cost of a firm's financial capital when averaged across all of its outstanding debt and equity capital.

marginal cost of capital

The average cost of the next dollar of financial capital raised by a firm.

Weighted Average Cost of Capital (WACC)

The average rate paid by a firm to secure the outstanding financial capital used to acquire the firm's assets.

target capital structure

The combination of debt, preferred stock, and common equity that will maximize the value of the firm's common stock.

cost of debt

The cost associated with a firm's borrowed financial capital.

flotation costs

The costs associated with issuing new financial securities.

capital components

The elements in a firm's capital structure.

Turnbull Company is considering a project that requires an initial investment of $570,000.00. The firm will raise the $570,000.00 in capital by issuing $230,000.00 of debt at a before-tax cost of 11.10%, $20,000.00 of preferred stock at a cost of 12.20%, and $320,000.00 of equity at a cost of 14.70%. The firm faces a tax rate of 40%. The WACC for this project is ___________

The first step to solving this problem is finding the weights of debt, preferred stock, and common equity. You are given the total amount of the initial investment, $570,000.00, and you are told that you will raise $230,000.00 of debt, $20,000.00 of preferred stock, and $320,000.00 of common equity. You will need to perform the calculations that follow to compute the weight (w) of each of these capital components: Wd = $230,000.00/ $570,000.00 = 0.4035=40.35% Wps = $20,000.00/$570,000.00 = 0.0351 = 3.51% Ws = $320,000.00/$570,000.00 = 0.5614=56.14% Now that you have found the weights of debt, preferred stock, and common equity, plug this information—along with the before-tax costs of debt, preferred stock, and common equity given in the problem—into the equation to solve for the WACC: WACC = (Wd×Rd(1−T))+(Wps×Rps)+(Ws×Rs) = (0.4035×(11.10%×(1−0.40)))+(0.0351×12.20%)+(0.5614×14.70%) = 11.37%

cost of capital

The minimum return that must be earned on a firm's investments to ensure that the firm's value does not decrease.

breakpoint

The point along the firm's marginal cost of capital (MCC) curve or schedule at which the MCC increases.

Cost of Debt

The return required by providers of capital loaned to the firm.

cost of capital

The return that providers of financial capital require to induce them to provide capital to a firm, and the associated cost to the firm for securing these funds.

marginal cost of capital

The weighted average cost of the last dollar raised by a firm, or the firm's incremental cost of capital.

flotation costs

These costs are generally expressed as a percentage of the total amount of securities sold, including the costs of printing the security certificates, applicable taxes, and issuance and marketing fees.

opportunity cost principle

This concept argues that a firm's retained earnings are not free to the firm.

opportunity cost principle

This concept maintains that the firm's retained earnings should generate a return for the firm's shareholders.

capital components

This term refers to the individual sources of the firm's financing, including its debt, preferred stock, retained earnings, and newly issued common equity.

Estimate your firm's Weighted Average Cost of Capital. Assume that the current risk-free rate of interest is 3.5%, the market risk premium is 5%, and the corporate tax rate is 21%. -> Debt: • Total book value: $10 million • Total market value: $12 million • Coupon rate: 6% • Yield to Maturity: 5% -> Common Stock: • Total book value: $15 million • Total market value: $20 million • Beta = 1.1 -> Preferred Stock: • Total book value: $2 million • Total market value: $2.5 million • Price per share: $20 • Dividend per share: $1.50 What is your firm's Weighted Average Cost of Capital (input as a raw number, i.e. if your answer is 7.1%, input 7.1)?

Total Value = Total Market value of Debt + Total Market value of Equity + Total market value of Preferred stock = 12 + 20 +2.5 = 34.5 Cost of debt = 5% Cost of Equity = 3.5% + 1.1*5% = 9% Cost of Preferred Stock = 1.50/20 = 7.5% WACC = Weight of Debt * Cost of Debt*(1-Tax Rate) + Weight of Equity* Cost of equity + weight of Preferred Stock * Cost of Preferred Stock = 12/34.5 * 5%*(1-21%) + 20/34.5 * 9% + 2.5/34.5*7.5% = 7.10% or 0.070986 or 0.071

If its current tax rate is 40%, Turnbull's weighted average cost of capital (WACC) will be ________ higher if it has to raise additional common equity capital by issuing new common stock instead of raising the funds through retained earnings.

WACC = (36%12.40%) + (6%x9.30%) + (58%x[8.20%x(1-40%)]) = 4.45 + .56% + 2.85% =7.86% WACC = (36%x14.20%) + (6%x9.30%) + (58%x[8.20%x(1-40%)]) = 5.11% + .56% + 2.85% =8.52% Difference in WACC = 8.52% - 7.86% = .66% or .64% with no rounding of previous numbers

Kuhn Corporation is considering a new project that will require an initial investment of $4,000,000. It has a target capital structure consisting of 45% debt, 4% preferred stock, and 51% common equity. Kuhn has noncallable bonds outstanding that mature in five years with a face value of $1,000, an annual coupon rate of 10%, and a market price of $1,050.76. The yield on the company's current bonds is a good approximation of the yield on any new bonds that it issues. The company can sell shares of preferred stock that pay an annual dividend of $9.00 at a price of $92.25 per share. Kuhn Corporation does not have any retained earnings available to finance this project, so the firm will have to issue new common stock to help fund it. Its common stock is currently selling for $33.35 per share, and it is expected to pay a dividend of $1.36 at the end of next year. Flotation costs will represent 8.00% of the funds raised by issuing new common stock. The company is projected to grow at a constant rate of 8.70%, and they face a tax rate of 40%. Kuhn Company's WACC for this project will be _________

You are given the weights of debt, preferred stock, and common equity in this problem. You must solve for the before-tax cost of debt, the cost of preferred stock, and the cost of common equity before you can solve for Kuhn's WACC. You don't need to know that the project's initial investment is $4,000,000 to solve the WACC, because you already know the company's target capital structure. The first step to solving this problem is finding the company's before-tax cost of debt. Computing the yield-to-maturity (YTM) on the five-year noncallable bonds issued by Kuhn tells you the before-tax cost of debt will be on any new bonds that the company wants to issue. There isn't a simple equation that can be used to easily solve for YTM, but you can use your financial calculator to quickly determine this value. However, you will first need to solve the bonds' annual coupon payment, using the annual coupon rate given in the problem: Annual couponAnnual coupon = = Bond's Face value×Annual Coupon rateBond's Face value×Annual Coupon rate = = $1,000×0.10 = $100 Remember, this annual coupon represents the PMT in the computation of the bonds' yield-to-maturity. Next, use your financial calculator to compute the bonds' YTM, as follows: Input 5 -1050.76. 100 1,000 Keystroke. N PV PMT. FV I Output 8.70 This tells you that the YTM on the outstanding five-year noncallable bonds is 8.70%. This represents the before-tax cost of debt, Rd, that will be used when you solve for Kuhn's WACC. To solve for the company's cost of preferred stock, use the equation that follows: Rps = = Dps/NP0 = $9.00/$92.25 = 0.0976 = 9.76% Finally, you need to solve for the cost of issuing new common stock. Because the company is issuing new common stock, make sure to include the flotation costs associated with issuing new common stock in your calculations: Re = D1/P0×(1−F) + g = $1.36/$33.35×(1−0.08) + 0.09 = 0.1343 = 13.43% Now that you have found the cost of each of the capital components, use this information to solve for the WACC: = (Wd × Rd(1−T))+(Wps × Rps)+(ws×rs)wd×rd1−T+wps×rps+ws×rs = = (0.45×(8.70% × (1−0.40)) + (0.04 × 9.76%)+(0.51×13.43%)= 9.59% Therefore, Kuhn will incur an expected cost of 9.59% for its financial capital of if it elects to undertake this new project.

After it pays its underwriter, how much will Blue Panda receive from each share of preferred stock that it issues? $88.65 $1.50 $1.65 $98.50 $1.27

amount left after payment to underwriter, x = p - a = 100-1.5 = $98.50

The _________ is the interest rate that a firm pays on any new debt financing.

before-tax cost of debt

Based on this information, Blue Panda's cost of preferred stock is ______

cost of preferred stock = d/x = 5/98.50 = 0.05076 or 5.076% = 5.08% (after rounding off)

At the present time, Water and Power Company (WPC) has 5-year noncallable bonds with a face value of $1,000 that are outstanding. These bonds have a current market price of $1,229.24 per bond, carry a coupon rate of 10%, and distribute annual coupon payments. The company incurs a federal-plus-state tax rate of 45%. If WPC wants to issue new debt, what would be a reasonable estimate for its after-tax cost of debt (rounded to two decimal places)? 3.00% 3.13% 2.09% 2.61%

coupon rate = 10% NPER = years to maturity = 5 PMT = face value x coupon rate = 1000 x .10 = $100 Face Value = $1,000 Price = PV = 1229.24 after-tax cost of debt = 2.61% Remember, the before-tax cost (generic) of Water and Power Company's 5-year 10% outstanding bonds can be estimated by computing the bonds' yield-to-maturity (YTM). Unfortunately, there isn't a simple equation that can be used to easily solve for YTM, however, you can use your financial calculator to quickly determine this value. To do this, you will first need to compute the bonds' annual coupon payment (using the annual coupon rate given in the problem). That is: Annual Coupon = Bond's face value x Annual coupon rate = $1,000×0.10 = $100 per year Then, the following inputs can be used in your financial calculator to calculate the bonds' YTM (I): N PV PMT FV I 5 -1,229.24 100 1,000 4.74 Now that you have found that the bonds' before-tax cost of debt (generic) is 4.74%, then multiply the before-tax cost of debt by 1 minus the tax rate to determine the bonds' after-tax cost of debt (generic): After-tax cost of debt (generic)= generic x (1 - T) = 4.74%×(1−0.45) = = 2.61%

A firm will increase in value if it invests in projects based on a WACC that is lower than the investors' required rate of return.

false

The amount that an investor is willing to pay for a firm's bonds is inversely related to the firm's cost of preferred stock.

false

The firm's cost of debt is what an investor is willing to pay for the firm's stock before considering flotation costs.

false

Estimation Methods Formula Discounted Cash Flow Approach ? Capital Asset Pricing Model Approach ?

formula for Discounted Cash Flow Approach : rs = D1/P0 + g formula for Capital Asset Pricing Model Approach : rs = rRF +Bs x (rm-rRF)

If a firm cannot invest retained earnings to earn a rate of return _________________ the required rate of return on retained earnings, it should return those funds to its stockholders.

greater than or equal to

Blue Panda has preferred stock that pays a dividend of $5.00 per share and sells for $100 per share. It is considering issuing new shares of preferred stock. These new shares incur an underwriting (or flotation) cost of 1.50%. How much will Blue Panda pay to the underwriter on a per-share basis? $1.27 $1.50 $1.65 $98.50

preferred dividend = d = $5 price of preferred share = p = 100 floatation cost , f = 1.5% = 0.015 amount paid to underwriter, a = f*p = 0.015*100 = $1.50

A firm will never have to take flotation costs into account when calculating the cost of raising capital from ________

retained earnings

Nick Co. has $3.99 million of debt, $1.36 million of preferred stock, and $1 million of common equity. The appropriate weight of the firm's preferred stock in the calculation of the company's weighted average cost of capital is ________

total value = 3.99 + 1.36+1 = 6.35 million weight of preferred stock = 1.36/6.35 = 21.42%

A firm will lose wealth if it invests in projects based on a WACC that is lower than the investors' required rate of return.

true

A firm's cost of capital is determined by the investors who purchase the firm's stocks and bonds.

true

Flotation costs increase the cost of newly issued stock compared to the cost of the firm's existing, or already outstanding, common stock or retained earnings.

true

The amount that an investor is willing to pay for a firm's bonds is inversely related to the firm's cost of debt without considering the cost of issuing the bonds.

true

The amount that an investor is willing to pay for a firm's preferred stock is inversely related to the firm's cost of preferred stock before flotation costs.

true

The cost of retained earnings is the same as the cost of internal (common) equity.

true

The difference between the cost of retained earnings and the cost of new common equity is the cost to issue the new common stock. also known as the flotation costs

true

The firm's cost of debt is what an investor is willing to pay for the firm's bonds before considering the cost of issuing the debt.

true

true or false: The amount that an investor is willing to pay for a firm's stock is inversely related to the firm's cost of common equity before flotation costs.

true

Does the cost of capital schedule below match the MCC schedule depicted on the graph? Yes No

yes