CHAP 9,10,11 Fin 335

Net present value (NPV) Evaluating cash flows with the NPV method The net present value (NPV) rule is considered one of the most common and preferred criteria that generally lead to good investment decisions. Consider this case: Suppose Lumbering Ox Truckmakers is evaluating a proposed capital budgeting project (project Alpha) that will require an initial investment of $500,000. The project is expected to generate the following net cash flows: Year Cash Flow Year 1$325,000 Year 2$475,000 Year 3$450,000 Year 4$425,000 Lumbering Ox Truck makers's weighted average cost of capital is 7%, and project Alpha has the same risk as the firm's average project. Based on the cash flows, what is project Alpha's net present value (NPV)?

$910,186 EXPLANATION: The net present value (NPV) measures a project's expected contribution to shareholder wealth. To calculate the NPV, find the present value of each cash flow and the sum of all present value cash flows. You will discount the cash flows at the weighted average cost of capital, because this project has the same risk as the firm's average project. You can mathematically solve the NPV using the following formula: NPV = CF0+CF1 / (1 + r)1 +CF2 / (1 + r)2+...+CFn/ (1 + r)n NPV = −$500,000+ $325,000 / 1.071+ $475,000 / 1.072+ $450,000 / 1.073+ $425,000 / 1.074 = $910,186$910,186 Remember, the NPV is the sum of the present value of all of the project's cash flows. Project Alpha's NPV is $910,186. This is the value of the project in today's dollars.

When a firm maximizes its intrinsic stock value, in general, it is good for society

**most investors prefer companies that maximize stock prices by conducting efficient, low-cost businesses that produce high-quality goods and services at the lowest possible cost. All of this benefits consumers. Companies that maximize their stock price must generate growth in sales by creating value for customers in the form of efficient and courteous service, adequate stocks of merchandise, and well-located business establishments. Also, in general, society is better off when companies that successfully increase stock prices grow and add more employees. Governments across the world, including U.S. federal and state governments, are privatizing some of their state-owned activities by selling these operations to investors. The sales and cash flows of recently privatized companies generally improve because newly privatized companies tend to grow and thus require more employees when they are managed with the goal of stock price maximization. However, a growing firm often needs to raise external funds in the financial markets and the actual price of a firm's stock is determined in those markets. And neither investors nor consumers benefit when companies, in their efforts to raise profits and stock prices, increase product prices and gouge the public, as such companies will soon lose their market share.

Walter Utilities is a dividend-paying company and is expected to pay an annual dividend of $2.85 at the end of the year. Its dividend is expected to grow at a constant rate of 7.00% per year. If Walter's stock currently trades for $25.00 per share, what is the expected rate of return?

18.40%

Investment Value

= (Existing Price × Existing Shares) + (New Price × New Shares)(Existing Price × Existing Shares) + (New Price × New Shares) = ($50.00 × 2,000 shares) + ($40.00 × 500 shares)$50.00 × 2,000 shares + ⁡$40.00 × 500 shares = $100,000+$20,000$100,000+$20,000 = $120,000

New Market Value

=(Existing Price x Existing Shares) + (New Price x New Shares) =($50.00 x 20,000 shares) + ($40.00 x 5,000 shares) =$1,200,000

New Share Value

=New Market Value/Total Outstanding Shares =$1,200,000/25,000 shares =$48.00 per share

You can estimate the value of a company's stock using models such as the corporate valuation model and the dividend discount model. Which of the following companies would you choose to evaluate if you were using the corporate valuation model to estimate the value of the company's stock?

A company that is not expected to distribute any earnings to its stockholders for the next few years.

Which of the following statements about the relationship between the IRR and the MIRR is correct?

A typical firm's IRR will be greater than its MIRR. EXPLANATION: The IRR method uses the assumption that a project's cash flows can be reinvested at the IRR. This assumption is generally incorrect, which causes the IRR to overstate the project's true return. The MIRR is the discount rate at which the present value of a project's cost is equal to the present value of its terminal value—where the terminal value is found as the sum of the future values of the cash inflows—compounded at the firm's cost of capital. Therefore, a typical firm's IRR will be greater than its MIRR.

Corporate Valuation Model

A valuation model used as an alternative to the discounted dividend model to determine a firm's value, especially one with no history of dividends, or the value of a division of a larger firm. The corporate model first calculates the firm's free cash flows, then finds their present values to determine the firm's value. **use the corporate valuation model to determine the intrinsic value of a company that is not expected to pay dividends in the next few years.

If a stock is in equilibrium, its intrinsic value equals its current stock price. A stock's expected dividend yield (DY) equals its expected dividend one year from now divided by the current stock price, which can be calculated as follows:

DYsci= $3.3228/$34.08 = 0.097500.09750 = 9.75% per share

For which capital component must you make a tax adjustment when calculating a firm's weighted average cost of capital (WACC)?

Debt

FCF is the cash flow available to the firm's bond and stock investors after all required investments have been made. It is calculated as follows:

FCF=EBIT(1 - T) - Net Capital Expenditures - ∆NOWC *FCF1 = EBIT(1 - T) - Net Capital Expenditures - ΔNOWC = $2,400 million−$360 million−$45 million = $1,995 million

If Celestial Crane Cosmetics's managers select projects based on the MIRR criterion, they should _____ this independent project.

REJECT EXPLANATION: If Celestial Crane Cosmetics's managers use the MIRR to evaluate projects, they will reject a project if its modified rate of return is less than the cost of the capital invested in the project. The project's MIRR, or expected rate of return (assuming that cash flows are reinvested at the company's WACC), is -18.49%. The MIRR is less than the company's WACC of 10.00%, so Celestial Crane Cosmetics should reject the project.

Which of the following statements indicate a disadvantage of using the discounted payback period for capital budgeting decisions? Check all that apply.

The discounted payback period does not take the time value of money into account. The discounted payback period is calculated using net income instead of cash flows. The discounted payback period takes into account only cash flows that occur up to the point where the project recovers the amount of the initial investment. You could have two mutually exclusive payback-period projects: project A's is 5 years, and project B's is 6 years. Using just the discounted payback period, you would likely make the capital budgeting decision to accept project A and reject project B. However, project A might have no cash flows in the periods after it recovers its initial investment, and project B could have cash flows of $1 million every year for the 20 years after the project's initial investment is recovered. You can see, if this were the case, project B would be the better project to accept. The regular payback period does not take the time value of money into account when calculating a project's payback period. The discounted payback period corrects this disadvantage by taking the effects of the time value of money into account when calculating the payback period.

classes of common shares are

To meet specific requirements for a certain group of shareholders, companies issue different classes of common shares. These classes of common shares are given a special designation, such as Class A and Class B, and are called classified stock.

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 EXPLANATION: If a firm cannot invest its retained earnings in such a manner that it will generate a return equal to or greater than the shareholders' required return, then the firm will provide greater value to the shareholders by distributing the retained earnings to the shareholders via the payment of dividends.

Common shareholders

have the right to receive distribution of corporate earnings in the form of dividends equally on a per-share basis.

Suppose that there is high unemployment, which causes interest rates to fall, which in turn pulls the preferred stock's yield to 8.20%. The value of the preferred stock will

increase

Preferred stock

is a hybrid of bond features and common stock features Preferred stockholders are entitled to receive a fixed dividend before the dividends can be paid to common stockholders. If the company should liquidate, creditors receive payments before preferred shareholders and common shareholders.

The value of a constant growth stock

is its expected dividend next year (D1) divided by the difference between the stock's required return (rs) and its expected dividend growth rate (g). The value of a constant growth stock can be calculated as follows: P0= D1 / (rs-g) Ex: =3.3228 / (0.16250-0.650) = 34.08 per share

horizon date

or the date at which the nonconstant growth period ends and the constant growth period begins—occurs at the end of year 1 (or beginning of year 2).

It is important to be comfortable with the notation of the WACC equation.

the lowercase r denotes a cost of capital component. The subscript next to the lowercase r designates which capital component the notation is referring to. rd=Before-Tax Cost of Debt rp=Cost of Preferred Stock rs= Cost of Common Equity Raised by Retaining Earnings re= Cost of Common Equity Raised by Issuing New Stock

Solving for the WACC The WACC is used as the discount rate to evaluate various capital budgeting projects. However, it is important to realize that the WACC is an appropriate discount rate only for a project of average risk. Analyze the cost of capital situations of the following company cases, and answer the specific questions that finance professionals need to address. Consider the case of Turnbull Co. Turnbull Co. has a target capital structure of 45% debt, 4% preferred stock, and 51% common equity. It has a before-tax cost of debt of 8.2%, and its cost of preferred stock is 9.3%. If Turnbull can raise all of its equity capital from retained earnings, its cost of common equity will be 12.4%. However, if it is necessary to raise new common equity, it will carry a cost of 14.2%. If its current tax rate is 25%, how much higher will Turnbull's weighted average cost of capital (WACC) be if it has to raise additional common equity capital by issuing new common stock instead of raising the funds through retained earnings?

0.92% EXPLANATION: Turnbull's target capital structure tells you that every new dollar of capital raised will consist of 45¢ from debt, 4¢ from preferred stock, and 51¢ from common equity. This problem wants you to examine the effect on Turnbull's WACC when it raises common equity from retained earnings versus issuing new common equity. Before doing any calculations, recall that the WACC resulting from issuing new common equity will be greater than the WACC resulting from raising the capital from retained earnings. This is because the cost of raising capital from issuing new common equity (NCE) is greater than the cost of raising capital from retained earnings (RE). However, you need to calculate the WACC for both scenarios to find the exact difference: WACC (RE)= wdrd(1−T)+wprp+wcrs = 0.45(8.2%(1−0.25)+0.04(9.3%)+0.51(12.4%) = 9.46% WACC (NCE)= wdrd(1−T)+wprp+wcre = 0.45(8.2%)(1−0.25)+0.04(9.3%)+0.51(14.2%) = 10.38% Difference = WACC (NCE) - WACC (RE) = 10.38%−9.46% = 0.92%

The cost of equity using the discounted cash flow (or dividend growth) approach Kirby Enterprises's stock is currently selling for $45.56 per share, and the firm expects its per-share dividend to be $2.35 in one year. Analysts project the firm's growth rate to be constant at 5.72%. Estimating the cost of equity using the discounted cash flow (or dividend growth) approach, what is Kirby's cost of internal equity?

10.88% EXPLANATION: The DCF (or DG) 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 (D1) are expected to grow at a constant rate (g), 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). You'll want to rearrange the equation to put it in terms of rsrs and then plug in the values given in the problem to solve for the company's cost of equity. That is: rs= D1 / P0+g Therefore, rs= $2.35 / $45.56+0.0572 = 0.1088, or 10.88% This computation indicates that 10.88% is the minimum rate of return that should be earned on a company's retained earnings to justify reinvesting them back into the business. If this rate of return cannot be earned, then the firm's retained earnings should be distributed to the company's shareholders through additional dividends. Therefore, you can think of this 10.88% value as the opportunity cost of the firm's retained earnings equity.

Turnbull Co. is considering a project that requires an initial investment of $270,000. The firm will raise the $270,000 in capital by issuing $100,000 of debt at a before-tax cost of 11.1%, $30,000 of preferred stock at a cost of 12.2%, and $140,000 of equity at a cost of 14.7%. The firm faces a tax rate of 25%. What will be the WACC for this project?

12.06 EXPLANATION: 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, $270,000, and you are told that you will raise $100,000 of debt, $30,000 of preferred stock, and $140,000 of common equity. You will need to perform the calculations that follow to find the weight (w) on each of these capital components: wd= $100,000/$270,000 = 0.370 wp = $30,000/$270,000 = 0.111 wc = $140,000/$270,000 = 0.519 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 = wdrd(1−T)+wprp+wcrs = 0.370(11.1%)(1−0.25)+0.111(12.2%)+0.519(14.7%) = 12.06%

True or False: Sophisticated firms use only the NPV method in capital budgeting decisions.

False This is false. NPV is considered to be the single best method for capital budgeting decisions, because it provides a direct measure of the project's added value to shareholder wealth. However, sophisticated firms generally calculate all five measures (NPV, IRR, payback period, discounted payback period, and MIRR) when evaluating capital budgeting decisions, because each provides different information. Calculating all the measures is easy, so all should be considered when making capital budgeting decisions.

Factors that affect the cost of capital equation Each of the following factors affects the weighted average cost of capital (WACC) equation. Which of the following factors are outside a firm's control?

Interest rates in the economy The performance of index funds, such as the S&P 500 EXPLANATION: Firms cannot control the interest rates in the economy. If interest rates in the economy rise, the cost of debt will increase. A firm can control its capital budgeting decision rules. Changing its capital budgeting decisions will affect a firm's risk level. Changing the firm's risk level will affect the firm's cost of capital, which will change the firm's weighted average cost of capital. Firms cannot control the general level of stock prices. If the general level of stock prices declines, the firm's stock price will decline, which will cause its cost of equity to increase.

If the project's cost of capital were to increase, how would that affect the IRR?

The IRR would not change. EXPLANATION: The IRR is the internal rate of return, or the project's expected return if cash flows earn the same return as the IRR. The IRR is the cost of capital that forces the NPV to equal zero; hence, the calculated IRR is independent of a project's cost of capital.

Which of the following statements will always hold true?

The constant growth valuation formula is not appropriate to use unless the company's growth rate is expected to remain constant in the future

True or False: The NPV and IRR methods can lead to conflicting decisions for mutually exclusive projects. True

True EXPLANATION: This is true. The NPV and IRR methods can lead to conflicting decisions for mutually exclusive projects because of cash flow timing and size differences between projects.

Discounted Dividend Model

Value of a stock is the present value of the future dividends expected to be generated by the stock.

Which of the following statements best explains what it means when a project has an NPV of $0?

When a project has an NPV of $0, the project is earning a rate of return equal to the project's weighted average cost of capital. It's OK to accept a project with an NPV of $0, because the project is earning the required minimum rate of return. EXPLANATION: A project will have an NPV of $0 when the project is earning a rate of return that is equal to the project's weighted average cost of capital. Although firms prefer a project's NPV to be positive—the larger the better—it is OK for a firm to accept a project with a $0 NPV, because the project is earning a rate of return equal to the minimum required rate of return. A firm will reject a project with a negative NPV, because a negative NPV indicates the project is earning a rate of return less than the required rate.

Which of the following statements is true about the constant growth model?

When using a constant growth model to analyze a stock, if an increase in the required rate of return occurs while the growth rate remains the same, this will lead to a decreased value of the stock. *Remember that the required rate of return on a stock is equal to the sum of its expected dividend yield and expected capital gains yield

Lumbering Ox Truckmakers's decision to accept or reject project Alpha is independent of its decisions on other projects. If the firm follows the NPV method, it should ____project Alpha.

accept EXPLANATION: The NPV measures a project's contribution to shareholder wealth. The NPV method states that independent projects should be accepted if their NPV is greater than zero. A positive NPV thus indicates that investors are more than compensated for the project's risk and investment, and this excess value accrues to shareholders. The NPV of $910,186 shows project Alpha adds $910,186 of shareholder value to the firm. Because the project will contribute to shareholder value, it should be accepted.

If this is an independent project, the IRR method states that the firm should

accept project Sigma EXPLANATION: The IRR identifies the cost of capital where NPV equals zero (where the project breaks even). The IRR is the project's expected rate of return, assuming that cash flows also earn the IRR. If this return exceeds the cost of the capital invested in the project, the excess value goes to the firm's shareholders. Therefore, independent projects whose IRR is greater than the WACC should be accepted. In this case, project Sigma's IRR is 27.27%, and the company's WACC is only 9.00%, so Blue Llama Mining Company should accept the project.

Founders' shares

are the stocks that the founders of the company own. They usually have special voting rights and restricted dividends for a specified number of years. Companies that have these classes of shares are said to have a dual-class share structure, which gives special voting rights to the founders of the company

A stock's dividend yield

at any given time is computed by dividing its next expected dividend divided by its current stock price. You have already calculated both D₁ and the expected P₀; The dividend yield is a financial ratio that shows how much a company pays out in dividends each year relative to its share price. If a firm hasn't earned a profit, it is highly unlikely to pay a dividend. The dividend decision determines what portion of profits should be paid out, but if no earnings are generated, then no dividend should be paid.

Today's dividend (D₀) is already expressed in present value (PV) terms, so PV(D₀) = D₀ = $1.00. To calculate the discounted value of the expected future dividends, it is first necessary to compute their expected values at the end of years 10, 20, and 50 (D₁₀, D₂₀, and D₅₀) by compounding the $1.00 current dividend at the expected dividend growth rate (g) of 3.50%. These expected future values are then discounted using the required return (rss) of 10.40% to calculate the corresponding present value of each dividend. The future value calculation is as follows: **Using these expected future cash flows, the present values are calculated by discounting the expected dividends using the expected return

future values Dt = D0 (1 + g)t D10= $1.00 × (1 + 0.035)10=$1.4106 (Dt) D20 = = $1.00 × (1 + 0.035)20=$1.9898 D50 = = $1.00 × (1 + 0.035)50=$5.5849 Present Value PVt= Dt/(1+rs)t PV10 = $1.4106 / (1 + 0.104)10=$0.5245 PV20 = = $1.9898 / (1 + 0.104)20=$0.2751 PV50 = = $5.5849 / (1 + 0.104)50=$0.0397

Do not use the constant growth valuation formula unless the company's growth rate is expected to remain constant in the future. Even rapidly growing start-ups and other firms that pay no dividends now can be expected to pay dividends at some point in the future, at which time the constant growth model will be appropriate. The constant growth valuation formula is sufficiently general to handle the case of a zero growth stock, where the dividend is expected to remain constant over time. If g = 0, the constant growth valuation formula reduces to the following:

p0= D /rs

Required Return on Stock X = Risk-Free Return + (Market Risk Premium × Stock X's Beta) rX = rRF + (rM − rRF)bX Example: The risk-free rate (rRF) is 4.00%, the market risk premium (RPM) is 4.80%, and Portman's beta is 1.30

rX = rRF + (rM − rRF)bX = 4.00%+(4.80%) × 1.30 = 10.24%

The calculation of WACC involves calculating the weighted average of the required rates of return on debt, preferred stock, and common equity, where the weights equal the percentage of each type of financing in the firm's overall capital structure. ____ is the symbol that represents the before-tax cost of debt in the weighted average cost of capital (WACC) equation.

rd

fundamental value aka intrinsic

refers to the stock's true value based on expected future cash flows and the risks involved. The value perceived by stock market investors determines the market price of a stock. When a stock's intrinsic value equals its market value, or market price of the stock, it is considered to be in a state of equilibrium. Potential investors use their available information to estimate the stock's intrinsic value and to make trading decisions (whether to buy or sell) based on their estimate. If the intrinsic value estimate of the stock is less than the market price, the investor would sell, but if the intrinsic value estimate is greater than the market price, the investor would buy. In equilibrium, investors are buying and selling stocks that are neither overvalued nor undervalued; rather, they are fairly valued.

To determine the intrinsic value of a stock, investors and managers use several models. The two basic models are

the discounted dividend model and the corporate valuation model.

A stock's intrinsic value is based on

the fundamental cash flows and the company's risk

Which of the following describe the reason(s) why maximization of intrinsic stock value benefits society?

*Successful companies higher more employees. **Stock price maximization requires efficient, low-cost businesses.

Benjamin Graham, the father of value investing, once said,

"In the short run, the market is a voting machine, but in the long run, the market is a weighing machine." In this quote, Benjamin Graham was referring to the key difference between the "price" and the "value" of a security.

White Lion Homebuilders Co.'s addition to earnings for this year is expected to be $745,000. Its target capital structure consists of 35% debt, 5% preferred, and 60% equity. Determine White Lion Homebuilders's retained earnings breakpoint:

$1,241,667 EXPLANATION: 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. RE Breakpoint = Addition to Retained Earnings for the Year / Equity Fraction of Target Capital Structure =$745,0000.60 / 0.60 = $1,241,667 Finding the retained earnings breakpoint of $1,241,667 tells you that this is the total amount of capital that White Lion Homebuilders can raise without having to issue new common stock while maintaining its target capital structure.

Tropetech Inc. has an expected net operating profit after taxes, EBIT(1 - T), of $2,400 million in the coming year. In addition, the firm is expected to have net capital expenditures of $360 million, and net operating working capital (NOWC) is expected to increase by $45 million. How much free cash flow (FCF) is Tropetech Inc. expected to generate over the next year?

$1,995 million

Allied Biscuit Co.'s debt has a market value of $196,845 million, and Allied Biscuit Co. has no preferred stock. If Allied Biscuit Co. has 300 million shares of common stock outstanding, what is Allied Biscuit Co.'s estimated intrinsic value per share of common stock? (Note: Round all intermediate calculations to two decimal places.)

$218.72 Explanation: Allied Biscuit Co.'s total firm value is $262,460.07, but this figure includes the value of its debt. Subtract the market value (MV) of Allied Biscuit Co.'s debt as follows: MV of Common Equity= Total Firm Value - MV of Debt - MV of Preferred Stock =$262,460.07 million - $196,845 million - $0 million =$65,615.07 million **The intrinsic value per share is the value of common equity divided by the number of common shares outstanding. This figure is calculated as follows: Intrinsic Value per Share=MV of Common Equity/Number of Common Shares Solve for the intrinsic value of Allied Biscuit Co.'s share as follows: Intrinsic Value per Share =$65,615.07 million/ 300 million shares =$218.71690, or $218.72 per share

Allied Biscuit Co. is expected to generate a free cash flow (FCF) of $10,860.00 million this year (FCF₁ = $10,860.00 million), and the FCF is expected to grow at a rate of 21.40% over the following two years (FCF₂ and FCF₃). After the third year, however, the FCF is expected to grow at a constant rate of 2.82% per year, which will last forever (FCF₄). Assume the firm has no nonoperating assets. If Allied Biscuit Co.'s weighted average cost of capital (WACC) is 8.46%, what is the current total firm value of Allied Biscuit Co.? (Note: Round all intermediate calculations to two decimal places.)

$262,460.07 million

Companies that have preferred stock outstanding promise to pay a stated dividend for an infinite period. Preferred stock is treated like a perpetuity if the payments last forever. Preferred stocks are considered to be a hybrid of a common stock and a bond. For example, one of the major differences between preferred shares and bonds is that the issuing companies can suspend the payment of their preferred dividends without throwing the company into bankruptcy. However, similar to bonds, preferred stockholders receive a fixed payment—their dividend—before the company's residual earnings are paid out to its common stockholders and, as with common stock, preferred stockholders can benefit from an appreciation in the value of the firm's stock securities. Consider the following case of International Imports (I2): International Imports (I2) pays an annual dividend rate of 10.20% on its preferred stock that currently returns 13.67% and has a par value of $100.00 per share. What is the value of I2's preferred stock?

$74.62 per share Remember that finding dividends from the dividend rate is similar to finding a coupon payment by multiplying the coupon rate by the bond's par value. You can compute the value of I2's preferred stock as follows: Dp= Dividend Rate×Par Value =10.20%×$100.0 = $10.20 per share Vp = $10.20/13.67% =$10.20/0.1367 = $74.62 per share

Understanding the IRR and NPV The net present value (NPV) and internal rate of return (IRR) methods of investment analysis are interrelated and are sometimes used together to make capital budgeting decisions. Consider the case of Blue Hamster Manufacturing Inc.: Last Tuesday, Blue Hamster Manufacturing Inc. lost a portion of its planning and financial data when both its main and its backup servers crashed. The company's CFO remembers that the internal rate of return (IRR) of Project Zeta is 13.8%, but he can't recall how much Blue Hamster originally invested in the project nor the project's net present value (NPV). However, he found a note that detailed the annual net cash flows expected to be generated by Project Zeta. They are: Year Cash Flow Year 1 $1,800,000 Year 2 $3,375,000 Year 3 $3,375,000 Year 4 $3,375,000 The CFO has asked you to compute Project Zeta's initial investment using the information currently available to you. He has offered the following suggestions and observations: •A project's IRR represents the return the project would generate when its NPV is zero or the discounted value of its cash inflows equals the discounted value of its cash outflows—when the cash flows are discounted using the project's IRR. •The level of risk exhibited by Project Zeta is the same as that exhibited by the company's average project, which means that Project Zeta's net cash flows can be discounted using Blue Hamster's 10% WACC. Given the data and hints, Project Zeta's initial investment is ______ , and its NPV is________ (rounded to the nearest whole dollar).

$8490228, $776250 EXPLANATION: Project Zeta has an initial investment of $8,490,228 and a net present value of $776,250. The project's initial cost is unknown, but you can determine it using the internal rate of return (IRR) data. (Remember the CFO's hint that the IRR is the yield, or return, produced when the project exhibits an NPV of zero.) You can discount the project's cash inflows by the IRR, and the project's initial investment must equal the sum of the IRR-discounted cash inflows. Using the IRR (13.8%) as the discount rate, compute the present value of all of the project's cash flows as follows: Initial Investment = $1,800,000 / (1.138)1+ $3,375,000 / (1.138)2+ $3,375,000 / (1.138)3+ $3,375,000 / (1.138)4 = $8,490,228 The project's cost, or initial investment, must equal the present value of its cash inflows discounted at the project's IRR. Therefore, the project's initial cost is $8,490,228. Next, use the initial investment and the project's cost of capital to solve for the NPV: NPV= -$8,490,228+ $1,800,000 / (1.10)1+ $3,375,000 / (1.10)2+ $3,375,000 /(1.10)3+ $3,375,000 / (1.10)4 = $776,250 You first used the project's IRR to solve for the initial investment in the project. After finding that the project's initial investment is $8,490,228, you can then solve for the project's NPV of $776,250 by discounting the expected future cash flows at the project's cost of capital of 10%

The IRR evaluation method assumes that cash flows from the project are reinvested at the same rate equal to the IRR. However, in reality the reinvested cash flows may not necessarily generate a return equal to the IRR. Thus, the modified IRR approach makes a more reasonable assumption other than the project's IRR. Consider the following situation: Celestial Crane Cosmetics is analyzing a project that requires an initial investment of $3,225,000. The project's expected cash flows are: Year Cash Flow Year 1 375,000 Year 2 -200,000 Year 3 475,000 Year 4 475,000 Celestial Crane Cosmetics's WACC is 10%, and the project has the same risk as the firm's average project. Calculate this project's modified internal rate of return (MIRR):

-18.49% EXPLANATION: The project has a modified internal rate of return (MIRR) of -18.49%. The first step in solving for the MIRR is to discount each cash outflow to the present using the WACC. There is a cash outflow at t = 0 of -$3,225,000 from the initial investment in the project. Because this cash flow occurs at t = 0, you don't need to discount it. There is another cash outflow at t = 2 of -$200,000, which you must discount for two years at the WACC: PV of CF2 in Year 0 =- $200,000 / 1.102- = - $165,289 You will also need to compound each cash inflow (at t = 1 and t = 3) to the project's terminal year using the WACC. Additionally, there is a cash inflow of $475,000 in year 4; however, you do not need to compound this value, because it is already valued at t = 4: FV of CF1 in Year 4 = $375,000 × (1.10)3 = $499,125 FV of CF3 in Year 4 = $475,000 × (1.10)1 =$522,500 The terminal value (FV) of all cash inflows is $1496625 ($499,125 + $522,500 + $475,000 = $1496625), and the present value (PV) of all the cash outflows is -$3390289 (-$3,225,000 + -$165,289 = -$765289). You have found that Celestial Crane Cosmetics's MIRR for this project is -18.49%. This means that the project's expected rate of return, assuming that cash flows are reinvested at the company's WACC, is -18.49%. The MIRR is generally considered to be a better estimate of a project's rate of return than the IRR, because it assumes that the cash flows are reinvested at the company's WACC, whereas the IRR assumes that cash flows are reinvested at the project's IRR.

Mitchell Co. has $3.9 million of debt, $2.5 million of preferred stock, and $3.3 million of common equity. What would be its weight on preferred stock?

0.26 Explanation: To find the weight (w) on Mitchell's preferred stock, you need to find the percentage of its total capital that is represented by preferred stock. wp= Preferred Stock / (Debt +Preferred Stock + Common Equity) = $2.5 million / ($3.9 million + $2.5 million + $3.3 million) = 0.26, or 26% It is important to note that, even though you can express the weight of a capital component as either a decimal or a percentage, you will always want to use weight in decimal form when calculating the WACC.

At the present time, Tamin Enterprises does not have any preferred stock outstanding but is looking to include preferred stock in its capital structure in the future. Tamin has found some institutional investors that are willing to purchase its preferred stock issue provided that it pays a perpetual dividend of $12 per share. If the investors pay $98.90 per share for their investment, then Tamin's cost of preferred stock (rounded to four decimal places) will be ____.

12.1335% EXPLANATION: Recall that preferred stock is a hybrid, because it is similar to bonds in some respects and to common stock in others. Like bonds, preferred stock has a par value and a fixed dividend that must be paid before dividends can be paid to common stockholders. Owners of preferred stock are entitled to regular, fixed dividend payments. However, a company can choose not to pay preferred dividends without putting the company into bankruptcy. Calculating the cost of preferred stock is fairly straightforward when dealing with traditional preferred stock that pays a fixed dividend in perpetuity. When dealing with preferred stock that pays perpetual dividends, you can use the following equation to calculate the cost of the company's preferred stock: rp = Dp / Pp = = $12 per share / $98.90 per share = 0.121335, or 12.1335% Therefore, the after-tax cost of this preferred stock issue is 0.121335, or 12.1335%.

Consider the case of Kuhn Co. Kuhn Co. is considering a new project that will require an initial investment of $45 million. It has a target capital structure of 58% debt, 6% preferred stock, and 36% 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 at a price of $95.70 per share. Kuhn 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 $22.35 per share, and it is expected to pay a dividend of $2.78 at the end of next year. Flotation costs will represent 8% of the funds raised by issuing new common stock. The company is projected to grow at a constant rate of 8.7%, and they face a tax rate of 25%. What will be the WACC for this project?

12.35 EXPLANATION: 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 $45 million 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. Finding the yield to maturity (YTM) on the five-year noncallable bonds issued by Kuhn tells you what the before-tax cost of debt will be on any new bonds that the company wants to issue. There is not a simple equation that can be used to easily solve for YTM, but you can use your financial calculator to quickly find this value. However, you will first need to solve the bonds' annual coupon payment, using the annual coupon rate given in the problem: Annual Coupon=Bond's Face Value x Annual Coupon Rate =$1,000 x 0.10=$100 This tells you that the YTM on the outstanding five-year noncallable bonds is 8.70%. This means that the before-tax cost of debt, rd, you will use when solving Kuhn's WACC will also be 8.70%. To solve for the company's cost of preferred stock, use the equation that follows: rp= DP/ PP = $9/$95.70 = 0.0940, or 9.40% 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 =$2.78/[$22.35(1−0.08)]+0.087 = 0.2222, or 22.22% Now that you have found the cost of each of the capital components, use this information to solve for the WACC: WACC =wdrd(1−T)+Wprp+Wcre = 0.58(8.70%)(1−0.25)+ 0.06(9.40%)+0.36(22.22%) = 12.35%

The cost of equity using the bond yield plus risk premium approach The Lincoln Company is closely held and, therefore, cannot generate reliable inputs with which to use the CAPM method for estimating a company's cost of internal equity. Lincoln's bonds yield 11.52%, and the firm's analysts estimate that the firm's risk premium on its stock over its bonds is 3.55%. Based on the bond-yield-plus-risk-premium approach, Lincoln's cost of internal equity is:

15.07% EXPLANATION: There will be times when reliable inputs for the CAPM method are not available. This would be the case when dealing with a closely-held company. In these situations, analysts often have to use more subjective procedures to estimate a firm's cost of equity. For a typical firm, the risk premium on the firm's stock over its bonds generally ranges from 3% to 5%. In this problem, Lincoln's analysts have estimated the appropriate risk premium on the firm's stock over its bonds to be 3.55%. To compute Lincoln's cost of retained earnings using the bond-yield-plus-risk-premium approach, add this risk premium to the firm's bond yield. That is: rs= Bond Yield + Risk Premium =11.52%+3.55% = 15.07% Therefore, the estimated cost of Lincoln's internal equity is 15.07%.

Alpha Moose Transporters has a current stock price of $22.35 per share, and is expected to pay a per-share dividend of $1.36 at the end of the year. The company's earnings' and dividends' growth rate are expected to grow at the constant rate of 8.70% into the foreseeable future. If Alpha Moose expects to incur flotation costs of 5.00% of the value of its newly-raised equity funds, then the flotation-adjusted (net) cost of its new common stock (rounded to two decimal places) should be

15.11% Explanation: Another approach that incorporates the effect of flotation costs on the cost of a company's external equity is to adjust its cost of capital instead of increasing the cost of a project's initial investment. When there are flotation costs, a firm will receive only a portion of the capital provided by investors; the remainder will go to the investment bank that helped raise the capital. To provide investors with their required rate of return on their investment, each dollar must earn a higher rate of return than the investors' required rate of return. In this example, Alpha Moose Transporters is paying flotation costs of 5.00%. This means that the firm will be able to keep and invest only 95.00% of the amount that investors supplied. Use the following equation to calculate the cost of equity associated with issuing new stock (re) net of any flotation costs: re=D1 / P0×(1 - F)+g= D1 / Pnet+g That is: re = $1.36 / $22.35×(1 - 0.0500)+0.087 =0.1511, or 15.11%

Internal rate of return (IRR) The internal rate of return (IRR) refers to the compound annual rate of return that a project generates based on its up-front cost and subsequent cash flows. Consider the case of Blue Llama Mining Company: Blue Llama Mining Company is evaluating a proposed capital budgeting project (project Sigma) that will require an initial investment of $900,000. Blue Llama Mining Company has been basing capital budgeting decisions on a project's NPV; however, its new CFO wants to start using the IRR method for capital budgeting decisions. The CFO says that the IRR is a better method because returns in percentage form are easier to understand and compare to required returns. Blue Llama Mining Company's WACC is 9%, and project Sigma has the same risk as the firm's average project. The project is expected to generate the following net cash flows: Year Cash Flow Year 1 $300,000 Year 2 $425,000 Year 3 $475,000 Year 4 $450,000 Which of the following is the correct calculation of project Sigma's IRR?

27.27 EXPLANATION: The internal rate of return (IRR) is the cost of capital at which the project's NPV is zero. The IRR is solved by setting the NPV equation equal to zero and solving for the interest rate as follows: $0=-$900,000 + [$300,000/(1 + IRR)¹] + [$425,000/(1 + IRR)²] + [$475,000/(1 + IRR)³] + [$450,000/(1 + IRR)⁴] You have found that the IRR for project Sigma is 27.27%. This means that if the cost of capital for this project were 27.27%, the project would have an NPV of $0. Because project Sigma's IRR is greater than Blue Llama Mining Company's WACC of 9.00% and the cash flows are normal (only one sign change), the project will have a positive NPV.

White Lion Homebuilders is considering investing in a one-year project that requires an initial investment of $450,000. To do so, it will have to issue new common stock and will incur a flotation cost of 2.00%. At the end of the year, the project is expected to produce a cash inflow of $595,000. The rate of return that White Lion expects to earn on its project (net of its flotation costs) is ____

29.63% EXPLANATION: One approach to dealing with flotation costs is to simply add them to the cost of the initial investment. Because this will increase the cost of the initial investment, it will reduce the project's expected rate of return. In this problem, look for the return on a one-year project. You are given the amount of the initial investment, but this amount does not include the flotation cost. The first step to solving this problem is to find the flotation cost associated with raising the capital for the initial investment: Flotation Cost =$450,000×0.02=$9,000 Next, you can now use the following equation to solve for the expected rate of return on this project. (Note that you can use this equation because you are dealing with only a one-year project. If you were dealing with a project that was expected to generate cash flows for more than one year into the future, you would generally want to use a financial calculator to solve the problem.) Expected Rate of Return = Cash Inflow / Initial Investment + Flotation Cost−1 = $595,000 / $450,000 + $9,000−1 = 0.2963, or 29.63%

Andalusian Limited (AL) can borrow funds at an interest rate of 7.30% for a period of eight years. Its marginal federal-plus-state tax rate is 25%. AL's after-tax cost of debt is ___(rounded to two decimal places).

5.48% Explanation: Given AL's before-tax cost of debt of 7.30% and a marginal tax rate of 25%, Andalusian Limited's after-tax cost of debt is 5.48%. This is calculated as: After-tax cost of debt = Interest rate on new debt−Tax saving = rd−(rd × T) = rd × (1−T) = 7.30% × (1−0.25) = 5.48%

At the present time, Andalusian Limited (AL) has 20-year noncallable bonds with a face value of $1,000 that are outstanding. These bonds have a current market price of $1,382.73 per bond, carry a coupon rate of 13%, and distribute annual coupon payments. The company incurs a federal-plus-state tax rate of 25%. If AL wants to issue new debt, what would be a reasonable estimate for its after-tax cost of debt (rounded to two decimal places)? (Note: Round your YTM rate to two decimal place.)

6.64% Explanation: The after-tax cost of Andalusian Limited's (AL) bonds is 6.64%. Remember, the before-tax cost of debt (rdrd) of Andalusian Limited's 20-year 13% 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 × Annual coupon rate = $1,000 × 0.13 = $130 per year Now that you have found that the bonds' before-tax cost of debt (rd) is 8.85%, then multiply the before-tax cost of debt by 1 minus the tax rate to determine the bonds' after-tax cost of debt: After-tax cost of debt = rd × (1−T) = 8.85% × (1−0.25 = 6.64%

Estimating growth rates It is often difficult to estimate the expected future dividend growth rate for use in estimating the cost of existing equity using the DCF or DG approach. In general, there are three available methods to generate such an estimate: •Carry forward a historical realized growth rate, and apply it to the future.•Locate and apply an expected future growth rate prepared and published by security analysts.•Use the retention growth model. Suppose Kirby is currently distributing 45% of its earnings in the form of cash dividends. It has also historically generated an average return on equity (ROE) of 16%. Kirby's estimated growth rate is __

8.8 %. Explanation: Using the retention growth model, it is possible to formulate an estimate of a company's future growth rate. The formula by which to compute the growth rate estimate (g) is: Growth Rate (g) = Return on Equity (ROE) × Earnings Retention Ratio The first step in the calculation is the computation of the earnings retention rate given knowledge of the dividend payout ratio. In Kirby's situation, the company's retention rate (55.00%) is calculated by the difference between 100% of the company's earnings available to common shareholders and the percentage of these earnings distributed as cash dividends, or the dividend payout ratio (45%). Then, given knowledge of the earnings retention rate, the estimated future growth rate (8.8%) is calculated by expressing the retention rate in its decimal format and multiplying it by Kirby's ROE (16%). That is: g= ROE × Retention Ratio = 16% × 0.5500 = 8.8% This value can then be compared to the company's historical growth rate and estimates generated by security analysts, such as those published in Value Line. Remember, many studies suggest that analysts' forecasts are more accurate predictors of actual future growth, but in the absence of this data, the retention growth model can be used when it is not realistic to believe that the past results will be repeated in the future.

The cost of equity using the CAPM approach The current risk-free rate of return (rRF) is 3.86% while the market risk premium is 6.63%. The Allen Company has a beta of 0.78. Using the capital asset pricing model (CAPM) approach, Allen's cost of equity is ___.

9.03% EXPLANATION: The capital asset pricing model (CAPM) approach tends to be the most widely used method to solve for a company's cost of common equity. The CAPM estimate of the required return on equity, rsrs, is equal to the risk-free rate, rRF, plus the market risk premium (RPM), which is the difference between the return on the market and the risk-free rate (rRF), scaled up or down to incorporate the particular stock's risk as measured by its beta coefficient (bi). That is: rs= rRF+(RPM) bi = 3.86%+ (6.63% × 0.78) = 9.03% Therefore, using the CAPM method, the cost of Allen Company's internal equity (retained earnings) is 9.03%.

The impact of a firm's cost of capital on managerial decisions Consider the following case: National Petroleum Refiners Corporation (NPR) has two divisions, L and H. Division L is the company's low-risk division and would have a weighted average cost of capital of 8% if it was operated as an independent company. Division H is the company's high-risk division and would have a weighted average cost of capital of 14% if it was operated as an independent company. Because the two divisions are the same size, the company has a composite weighted average cost of capital of 11%. Division L is considering a project with an expected return of 9.5%. Should National Petroleum Refiners Corporation (NPR) accept or reject the project?

Accept the project On what grounds do you base your accept-reject decision? Division L's project should be accepted, since its return is greater than the risk-based cost of capital for the division. EXPLANATION: Division L's project should be accepted as its return is greater than the risk-based cost of capital for the division. It would be inappropriate to compare the project's return to the company's composite weighted average cost of capital, because division L has a lower risk level than the company as a whole.

Which of the following statements accurately describes the relationship between earnings and dividends when all other factors are held constant?

All else being equal, growth in dividends requires growth in earnings. **Dividends are paid out of earnings, so growth in dividends requires growth in earnings. Long-run earnings growth occurs primarily because firms retain earnings and reinvest them in the business. Therefore, the higher the percentage of earnings retained, the higher the growth rate.

Using the short-run FCF growth rate, calculate FCF₂ and FCF₃. Then use the long-run FCF growth rate to calculate the horizon value (V₃) of Allied Biscuit Co.'s FCFs in years 4 through infinity. The calculations are performed as follows:

FCF1= $10,860.00 million $10,860.00 million FCF2 = = $10,860.00 million × (1 + 21.40%)=$13,184.04 million FCF3 = = $10,860.00 million × (1 + 21.40%)2=$16,005.42 million FCF4 = = $16,005.42 million × (1 + 2.82%)=$16,456.77 million You should discount the FCFs with the WACC because the FCFs are cash flows available to all the firm's investors (bondholders and stockholders). Therefore, discount the FCFs with the discount rate that reflects the cost of all the firm's investor-supplied capital (the WACC). Calculate the horizon value, using the following formula: Horizon Value(VCo. at t = n) = FCFN + 1/(WACC−gFCF) Solve for the horizon value as follows: V3=FCF4/(WACC−gFCF) = $16,456.77 million/(8.46%−2.82%) = $291,786.70 million The total current firm value of Allied Biscuit Co. equals the present value (PV) of all the FCF that the firm is expected to generate. Calculate the PV of FCF₁, FCF₂, FCF₃, and V₃ as follows: Total Firm Value= [FCF1/(1 + WACC)1]+[FCF2/(1 + WACC)2]+[ FCF3/(1 + WACC)3]+[V3/(1 + WACC)3] = [$10,860.00/(1+8.46%)1]+[$13,184.04/(1+8.46%)2]+[$16,005.42/(1+8.46%)3]+[$291,786.70/(1+8.46%)3] = $262,460.07 million

Larry Nelson holds 1,000 shares of General Electric (GE) common stock. As a stockholder, he has the right to be involved in the election of its directors, who are responsible for managing the company and achieving the company's objectives. True or False: Larry will receive dividends together with preferred stockholders.

False

The cost of new common stock True or False: The following statement accurately describes how firms make decisions related to issuing new common stock. Taking flotation costs into account will reduce the cost of new common stock.

False: Flotation costs are additional costs associated with raising new common stock. EXPLANATION: As flotation costs increase, the cost of issuing new common stock will also increase, because higher flotation costs make issuing new common stock more expensive.

It's true that dividends are in the numerator of the equation, and all else being equal, an increase in dividends would cause Pˆ0P̂0 to increase. However, a firm can't simply increase its dividends without affecting other factors.

Firms face the fundamental decision of paying out earnings as dividends or retaining them for future investment. *If a firm increases its dividends, it is retaining less earnings for future investment. *An increase in current dividends might jeopardize future dividends—that is, the dividend growth rate might decrease. *There are two competing forces here: Higher dividends increase stock prices, but lower growth rates decrease stock prices. *A firm's specific situation will determine whether a dividend increase will raise the stock price. Thus, the correct statement in the options given is "Increasing dividends may not always increase the stock price, because less earnings may be invested back into the firm and that impedes growth."

Preferred stock is a hybrid security, because it has some characteristics typical of debt and others typical of equity. The following table lists various characteristics of preferred stock. Determine which of these characteristics is consistent with debt and which is consistent with equity.

Has a par, or face, value- DEBT Failure to pay a preferred dividend does not send the firm into bankruptcy- Equity EXPLANATION: Like debt, preferred stock has a par value, whereas the value of equity is market determined. Failure to pay a preferred dividend does not send the firm into bankruptcy, so preferred dividends are like equity in that sense. A firm may miss preferred dividends, but preferred dividends are usually cumulative. This means that the firm must pay all preferred dividends it missed before it is allowed to pay any common stock dividends.

A project's IRR will____if the project's cash inflows increase, and everything else is unaffected.

Increase EXPLANATION: Calculate a project's IRR by finding the cost of capital that would give the project an NPV of zero ($0). If the amount of a project's cash inflows increase, and everything else stays the same, the IRR of the project will increase, because the project has become more profitable.

Which of the following statements is true?

Increasing dividends may not always increase the stock price, because less earnings may be invested back into the firm and that impedes growth.

Which of the following statements is true?

Increasing dividends may not always increase the stock price, because less earnings may be invested back into the firm and that impedes growth. ***dividends are in the numerator of the equation, and all else being equal, an increase in dividends would cause Pˆ0P̂0 to increase. However, a firm can't simply increase its dividends without affecting other factors. Firms face the fundamental decision of paying out earnings as dividends or retaining them for future investment. If a firm increases its dividends, it is retaining less earnings for future investment. Therefore, an increase in current dividends might jeopardize future dividends—that is, the dividend growth rate might decrease. There are two competing forces here: Higher dividends increase stock prices, but lower growth rates decrease stock prices. A firm's specific situation will determine whether a dividend increase will raise the stock price. Thus, the correct statement in the options given is "Increasing dividends may not always increase the stock price, because less earnings may be invested back into the firm and that impedes growth."

The decision process Before making capital budgeting decisions, finance professionals often generate, review, analyze, select, and implement long-term investment proposals that meet firm-specific criteria and are consistent with the firm's strategic goals. Companies often use several methods to evaluate the project's cash flows and each of them has its benefits and disadvantages. Based on your understanding of the capital budgeting evaluation methods, which of the following conclusions about capital budgeting are valid?

Managers have been slow to adopt the IRR, because percentage returns are a harder concept for them to grasp. ***The MIRR reinvestment rate assumption is more realistic than the IRR assumption, because most firms are more likely to earn their WACC when they reinvest a project's cash flows. The MIRR assumes that cash flows are reinvested at the WACC, whereas the IRR assumes that they earn the IRR. The regular payback period fails to account for the time value of money and any cash flows received after the payback period. The discounted payback period can correct the cash flow timing issue, but it still does not consider cash flows after the payback period. The IRR is actually a popular measure among managers, because percentage returns are an easy concept to understand and can be compared to the firm's cost of capital very easily. Even though the NPV offers a better indication of value added, many managers continue using the IRR for these reasons.

constant growth formula Super Carpeting Inc. (SCI) just paid a dividend (D₀) of $3.12 per share, and its annual dividend is expected to grow at a constant rate (g) of 6.50% per year. If the required return (rss) on SCI's stock is 16.25%, then the intrinsic value of SCI's shares is $34.08 per share.

Po= D0 x (1+g) / (rx -g) = D1 / (rs-g ex: 3.12 x (1 + 0.0650) = 3.3228 per share

A firm's cost of debt (rd) represents the return that the firm must pay to induce an investor to purchase one or more of a firm's debt securities. Since the interest earned from holding the company's debt security is paid from the issuer's pre-tax income, then the unadjusted return (to the investor) or cost (to the issuing company) represents the firm's before-tax cost of debt (rd). However, since the U.S. Internal Revenue Service allows businesses to deduct the interest paid on their debt securities from their pre-tax income—and thereby reduce their taxable income—the tax savings associated with the use of debt financing must be recognized. Therefore, to compute a loan or debt issue's after-tax cost, the before-tax cost of debt must be multiplied by one minus its marginal tax rate (1 - T).

That is: After-tax cost of debt = Interest rate on new debt−Tax savings = rd−(rd × T) = rd × (1−T) Remember, the costs of a firm's preferred and common equity are already expressed in after-tax terms. This is because dividends (1) do not constitute a tax-deductible expense, and (2) are paid from net income (or after-tax) dollars. As a result, the costs of the firm's preferred stock and common equity do not require a tax savings adjustment, and their costs (rp and rs, respectively) can be used directly in the firm's weighted cost of capital calculation. Knowledge of the firm's weighted cost of capital increases the likelihood that decisions will be made that will increase the wealth of the firm's shareholders.

One key assumption of the constant growth model is that dividends will grow at a constant rate until infinity. There is no terminal year when using this model. The dividend growth rate must be less than the required return. If it were equal to the required return, the denominator of the constant growth formula would be zero, and you can't divide by zero. If it were greater than the required return, the denominator would be negative, and the stock value that you would calculate would be negative. For these reasons, the expected dividend growth rate must be less than the stock's required return. Expected return is the sum of dividend yield and growth rate, so the required rate of return will be higher than the growth rate. Also, the model makes the assumption that dividends will grow at a constant rate until infinity, but if the company were to grow more quickly than the expected rate of return in perpetuity, then the company would grow more quickly than the market and at some point become larger than the entire market. This is impossible. Thus, the growth rate is lower than the required rate of return.

The constant growth formula can even be used to value negative and zero growth stocks, because in both cases the growth rate is constant and less than the required return. When using the constant growth model, if the growth rate (g) remains constant and the required rate of return (rss) increases, the value of (rss - g) will increase. Because the value of the denominator increases, the value of Pˆ0P̂0 will decrease. If the required rate of return (rss) remains constant and the growth rate (g) increases, the value of (rss - g) will decrease. Because the value of the denominator decreases, the value of Pˆ0P̂0 will increase.

The discount rate used in valuation models depends on the cash flows used in the analysis. The dividend discount model uses dividend cash flows in the analysis, so the cost of the equity is used as the discount rate. In the FCF approach to common stock valuation, FCFs to the firm are used for analysis; thus, you would use the cost of capital (the WACC) as the discount rate. Tropetech Inc.'s FCFs are expected to grow at a constant rate, so you can use the constant growth formula that you already used for stocks. Use FCFs and the firm's WACC instead of dividends and the required return on equity, respectively. You use the WACC because you want to discount all the firm's cash flows, not just the dividends being paid to shareholders. If you use the constant growth formula, solve for the total firm value as follows:

Total Firm Value=MV of Company's Operations + MV of non-Operating Assets Since the firm has zero non-operating assets, the firm's value is simply calculated as: Total Firm ValueTotal Firm Value = FCF1 / WACC−gFCF **Using the preceding equation, solve for Tropetech Inc.'s total value as follows: Total Firm Value= $1,995 million/(11.70% - 3.90%) =$1,995 million/(0.1170 - 0.0390) =$25,576.92 million Tropetech Inc.'s total firm value is $25,576.92 million, but this figure includes the value of debt and preferred stock. Next, find the value of equity by subtracting the market value (MV) of Tropetech Inc.'s debt and preferred stock as follows: Total Firm Value=MV of Debt + MV of Preferred Stock + Intrinsic value of Common Equity Thus, the intrinsic value of common equity can be solved as follows: Intrinsic Value of Common Equity =Total Firm Value - MV of Debt - MV of Preferred Stock =$25,576.92 million - $11,510 million - $6,394 million =$7,672.92 million Remember, equity claims on the firm's assets are residual claims. That is why you subtract the market values of debt and preferred stock; equity holders are entitled to the value of the firm's assets after debt and preferred stock claims are satisfied. To find the intrinsic value per share, divide the intrinsic value of equity by the number of common shares outstanding as follows: Intrinsic Value per Share=Intrinsic Value of Common Equity/Number of Common Shares Solve for the intrinsic value of Tropetech Inc.'s share as follows: Intrinsic Value per Share=$7,672.92 million/675 shares=$11.36729, or $11.37 per share

If interest rates fall and the return on I2's preferred stock decreases to 8.20%, the new value of the preferred stock will be calculated as follows:

VpV= $10.20/8.20% =$10.20/0.0820 = $124.39 per share Thus, a decrease in preferred stock yield will lead to an increase in the value of the preferred stock.

Classified shares

havesuper voting rights, which give more control to a certain class of investors. are often designed to provide specific shareholder control to a certain class of shareholders, usually the owners, founders, executives, and key insiders of the firm. Classified shares give a certain class special voting rights—also called super voting rights—in which each share in the class has more votes per share than shares in other classes.

A company's valuation and stock prices depend on a certain growth rate, and it is critical to use appropriate growth rates in the fundamental analysis process. With the information available, calculate the growth rate by using the following formula:

r̂s = = Expected Dividend Yield(D1/P0) + Expected Growth Rate (g)

r̂s = = Expected Rate of Return

r̂s = Expected Rate of Return = Expected Dividend Yield + Expected Capital Gains Yield

Robert knows that expected year-end dividend (D1) is $0.66 and expected rate of return (r̂s) is 6.60%. PAMC's stock price (P0P0) is $13.75. Use the preceding equation to solve for PAMC's growth rate (g) as follows:

r̂s − ⁡D1/P0 = 0.0660−(0.66/13.75) 0.0660− 0.04800 = 0.0180, or 1.80%