Corp Finance Exam 2

Discounted CF and Options

We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. M = NPV + Opt A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time, the more versatile machine is more valuable because it comes with options.

What are sensitivity analysis, scenario analysis, break-even analysis, and simulation? Why are these analyses important, and how should they be used? How do real options affect the value of capital projects? What information does a decision tree provide?

What are sensitivity analysis, scenario analysis, break-even analysis, and simulation? there are tools for evaluating uncertainty in these decision capital budget decision making scenarios. Why are these analyses important, and how should they be used? The analysis are important or typically break even analysis and trying to figure out what sort of pricing you need to have in order to justify doing a project. How do real options affect the value of capital projects? You can increase the value of project by recognizing there are real options. There's chances for you to pivot, chance to make adjustment in the way you do your project. What information does a decision tree provide? tool to be able to evaluate future projects and as a way as a way to kind of figure out all those scenarios going forward and that work back to what your decision should be today.

Stability of Beta

Most analysts argue that betas are generally stable for firms remaining in the same industry. That is not to say that a firm's beta cannot change. •Changes in product line. •Changes in technology. •Deregulation. •Changes in financial leverage.

Estimating Cash Flows

Cash Flow from Operations •Recall that: OCF = EBIT − Taxes + Depreciation. Net Capital Spending •Do not forget salvage value (after tax, of course). Changes in Net Working Capital •Recall that when the project winds down, we enjoy a return of net working capital.

6.1 Incremental Cash Flows

Cash flows matter—not accounting earnings. Sunk costs do not matter. Incremental cash flows matter. Opportunity costs matter. Side effects like synergy and erosion matter. Taxes matter: We want incremental after-tax cash flows. Inflation matters.

Break-Even Analysis

Common tool for analyzing the relationship between sales volume and profitability. There are three common break-even measures: •Accounting break-even: sales volume at which net income = 0. •Cash break-even: sales volume at which operating cash flow = 0. •Financial break-even: sales volume at which net present value = 0.

Example 2

Consider Grand Sport, Inc., which is currently all-equity financed and has a beta of .90. The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity. Since the firm will remain in the same industry, its asset beta should remain .90. However, assuming a zero beta for its debt, its equity beta would become twice as large: Basset = .9 = 1/ 1+1 x Bequity Bequity = 2 x .9 = 1.8

Cost-Cutting Proposals

Cost savings will increase pretax income •But, we have to pay taxes on this amount. Depreciation will reduce our tax liability Does the present value of the cash flow associated with the cost savings exceed the cost? •If yes, then proceed.

6.4 Some Special Cases of Discounted Cash Flow Analysis

Cost-Cutting Proposals Setting the Bid Price Investments of Unequal Lives

6.2 The Baldwin Company

Costs of test marketing (already spent): $250,000 Current market value of proposed factory site (which we own): $150,000 Cost of bowling ball machine: $100,000 (depreciated according to 5-year MACRS) Increase in net working capital: $10,000 Production (in units) by year during 5-year life of the machine: 5,000, 8,000, 12,000, 10,000, 6,000 Price during first year is $20; price increases 2 percent per year thereafter. Production costs during first year are $10 per unit and increase 10 percent per year thereafter. Annual inflation rate: 5 percent Working Capital: initial $10,000 changes with sales

12.2 Portfolios and Factor Models

Now let us consider what happens to portfolios of stocks when each of the stocks follows a one-factor model. We will create portfolios from a list of N stocks and will capture the systematic risk with a 1-factor model. The ith stock in the list has return:

7.1 Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis

Each allows us to look behind the N P V number to see how stable our estimates are. When working with spreadsheets, try to build your model so that you can adjust variables in a single cell and have the N P V calculations update accordingly.

13.3 Estimation of Beta - I

Market Portfolio - Portfolio of all assets in the economy. In practice, a broad stock market index, such as the S&P 500, is used to represent the market. Beta - Sensitivity of a stock's return to the return on the market portfolio.

Firm ABC is going to pay an annual dividend of $2.00 per share. Management just announced that future dividends will increase by 5 percent annually in the first two years and 2 percent annually afterwards. What is the amount of the expected dividend in year 5? Increase by 2% annually what is the amount of dividend in year 5?

$2.00 per share is D0 or D1? D1 = Expected Dividend = D1 Growth rate during year 2 is 5 percent; growth rate during year 4 is 2 percent What is the amount of the expected dividend in year 5? 2.541 D1 = Expected Dividend = $2.00 g1 = Growth rate = 5% g2 = Growth rate = 2% n = 2 years Expected dividend in year 5 =D1 ∗ (1+g1)^n ∗ (1+g2)^n =2×(1+5%)^2×(1+2%)^2 =2.294082 D1 = Expected Dividend = $2.00 g = Growth rate = 2% n = 5-1 = 4 years Expected dividend in year 5 =D1 ∗ (1+g)^n =2×(1+2%)^4=2.164864

Chapter 13 Summary

1. A firm with excess cash can either pay a dividend or make a capital expenditure. Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital budgeting project should be at least as great as the expected return on a financial asset of comparable risk. 2. The expected return on any asset is dependent on its beta. We showed how to estimate the beta of a stock. The appropriate procedure employs regression analysis on historical returns. 3. We considered the case of a project with beta risk equal to that of the firm. If the project and firm are financed with only equity, the discount rate on the project is equal to: RF + β × (RM − RF) where RM is the expected return on the market portfolio and RF is the risk-free rate. In words, the discount rate on the project is equal to the CAPM's estimate of the expected return on the security. Conceptually, a dividend growth model could also be used to estimate the cost of equity, though it is less popular in practice 4. An asset beta measures the sensitivity of the firm's assets to changes in the value of the market portfolio. Holding the firm's assets constant, the firm's equity beta will increase with its financial leverage 5. If the project's beta differs from that of the firm, the discount rate should be based on the project's beta. We can estimate the project's beta by using the comparables method. 6. If a project is partially financed with debt, the discount rate to use is the WACC. To calculate the WACC, we must estimate the cost of equity and the cost of debt applicable to a project 7. New projects are often funded by issues of new bonds and stock. The costs of issuance, generally called flotation costs, should be included in any NPV analysis.

Chapter 6 Summary

1. Capital budgeting must be evaluated on an incremental basis. This means that sunk costs must be ignored, whereas both opportunity costs and side effects must be considered. 2. In the Baldwin case, we computed NPV using the following two steps: a. Calculate the net cash flow from all sources for each period. b. Calculate the NPV using these cash flows. 3. The discounted cash flow approach can be applied to many areas of capital budgeting. In this chapter we applied the approach to cost-cutting investments, competitive bidding, and choices between equipment of different lives. 4. Operating cash flow (OCF) can be computed in a number of different ways. We presented three different methods for calculating OCF: the top-down approach, the bottom-up approach, and the tax shield approach. The three approaches are consistent with each other. 5. Inflation must be handled consistently. One approach is to express both cash flows and the discount rate in nominal terms. The other approach is to express both cash flows and the discount rate in real terms. Because both approaches yield the same NPV calculation, the simpler method should be used. The simpler method will generally depend on the type of capital budgeting problem.

Chapter 12 Summary

1. The APT assumes that stock returns are generated according to factor models. For example, we might describe a stock's return as: R = E(R) + βIFI + βGNP FGNP + βrFr + ε where I, GNP, and r stand for inflation, gross national product, and the interest rate, respectively. The three factors FI, FGNP, and Fr represent systematic risk because these factors affect many securities. The term ε is considered unsystematic risk because it is unique to each individual security 2. For convenience, we frequently describe a security's return according to a one-factor model: R = E(R) + βF + ε 3. As securities are added to a portfolio, the unsystematic risks of the individual securities offset each other. A fully diversified portfolio has no unsystematic risk but still has systematic risk. This result indicates that diversification can eliminate some, but not all, of the risk of individual securities. 4. Because of this, the expected return on a stock is positively related to its systematic risk. In a one-factor model, the systematic risk of a security is the beta of the CAPM. Thus, the implications of the CAPM and the one-factor APT are identical. However, each security has many risks in a multifactor model. The expected return on a security is positively related to its beta with each factor. 5. Empirical or parametric models that capture the relationships between returns and stock attributes such as PE or M/B ratios can be estimated directly from the data without any appeal to theory. These ratios also are used to measure the styles of portfolio managers and to construct benchmarks and samples against which they are measured.

Chapter 10 Summary

1. This chapter presented returns for a number of different asset classes. The general conclusion is that stocks have outperformed bonds over most of the 20th century, though stocks also have exhibited more risk. 2. The statistical measures in this chapter are necessary building blocks for the material of the next three chapters. In particular, standard deviation and variance measure the variability of the returns on an individual security and on portfolios of securities. In the next chapter, we will argue that standard deviation and variance are appropriate measures of the risk of an individual security if an investor's portfolio is composed of that security only

Chapter 11 Summary

1. This chapter showed us how to calculate the expected return and variance for individual securities, and the covariance and correlation for pairs of securities. Given these statistics, the expected return and variance for a portfolio of two securities A and B can be written as: Expected return on portfolio = XA E(RA) + XBE(RB) Var(portfolio) = XA 2 σA 2 + 2XA XB σAB + X^2B σ^2B 2. In our notation, X stands for the proportion of a security in a portfolio. By varying X we can trace out the efficient set of portfolios. We graphed the efficient set for the two-asset case as a curve, pointing out that the degree of curvature or bend in the graph reflects the diversification effect: The lower the correlation between the two securities, the greater the bend. The same general shape of the efficient set holds in a world of many assets. 3. As the formula for variance in the two-asset case is computed from a 2 × 2 matrix, the variance formula is computed from an N × N matrix in the N-asset case. We showed that with a large number of assets, there are many more covariance terms than variance terms in the matrix. In fact, the variance terms are effectively diversified away in a large portfolio, but the covariance terms are not. Thus, a diversified portfolio can eliminate some, but not all, of the risk of the individual securities. 4. The efficient set of risky assets can be combined with riskless borrowing and lending. In this case, a rational investor will always choose to hold the portfolio of risky securities represented by Point A in Figure 11.9. Then he can either borrow or lend at the riskless rate to achieve any desired point on Line II in the figure. 5. The contribution of a security to the risk of a large, well-diversified portfolio is proportional to the covariance of the security's return with the market's re

Chapter 7 Summary

1. Though NPV is the best capital budgeting approach conceptually, it has been criticized in practice for giving managers a false sense of security. Sensitivity analysis shows NPV under varying assumptions, giving managers a better feel for the project's risks. Unfortunately, sensitivity analysis modifies only one variable at a time, but many variables are likely to vary together in the real world. Scenario analysis examines a project's performance under different scenarios (such as war breaking out or oil prices skyrocketing). Finally, managers want to know how bad forecasts must be before a project loses money. Break-even analysis calculates the sales figure at which the project breaks even. Though break-even analysis is frequently performed on an accounting profit basis, we suggest that a net present value basis is more appropriate. 2. Monte Carlo simulation begins with a model of the firm's cash flows, based on both the interactions between different variables and the movement of each individual variable over time. Random sampling generates a distribution of these cash flows for each period, leading to a net present value calculation. 3. We analyzed the hidden options in capital budgeting, such as the option to expand, the option to abandon, and timing options. 4. Decision trees represent an approach for valuing projects with these hidden, or real, options.

You own the following portfolio of stocks. What is the current portfolio weight of Stock C? Stock Your holding number of shares Current stock price A 100 30 B 200 150 C 500 20 D 200 100

100 x 30 = 3000 200 x 150 = 30000 500 x 20 = 10000 200 x 100 = 20000 3000 + 30000 + 20000 + 10000 = 63000 10,000 ⁒ 63000 = 0.1587

Market Risk Premium

Method 1: Use historical data Method 2: Use the Dividend Discount Model •Market data and analyst forecasts can be used to implement the D D M approach on a market-wide basis.

How much are you willing to pay for one share if you require a 25 percent rate of return? The Waffle House is going to pay annual dividend of $1.25 per share in year one and the constant growth rate is 5%. How much are you willing to pay for one share if you require a 25 percent rate of return? The Waffle House just paid annual dividend of $1.25 per share and the constant growth rate is 5%. How much are you willing to pay for one share if you require a 25 percent rate of return?

3A) constant annual dividend = 1.25 required rate of return = 25% calculating the current price of the stock you should willing to pay current price =annual dividend / required return=1.25/ 25%=$5.00 therefore the current price of the stock you should willing to pay = $5.00 3B) expected dividend in one year (D1) = 1.25 constant growth rate (g) = 5% required rate of return (r) = 25% calculating the current price of the stock using dividend growth model price =D1 / (r−g) =1.25/(0.25−0.05)=$6.25 the current price of the stock you should be willing to pay is = $6.25 3C) dividend just paid (D0) = 1.25 constant growth (g) = 5% required rate of return (r) = 25% expected dividend (D1) =D0∗(1+g) =1.25×(1+5%)=1.3125 calculating the current price of the stock using dividend growth model current price =D1 / (r−g) =1.3125/(0.25−0.05)=$6.56 the current price of the stock you should be willing to pay is = $6.56

12.4 The Capital Asset Pricing Model and the Arbitrage Pricing Theory

A P T applies to well diversified portfolios and not necessarily to individual stocks. With A P T it is possible for some individual stocks to be mispriced - i.e., not lie on the S M L. A P T is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio. A P T can be extended to multifactor models.

Historical Returns

A famous set of studies dealing with rates of returns on common stocks, bonds, and Treasury bills was conducted by Roger Ibbotson and Rex Sinquefield. They present year-by-year historical rates of return starting in 1926 for the following five important types of financial instruments in the United States: •Large-company common stocks. •Small-company common stocks. •Long-term corporate bonds. •Long-term U.S. government bonds. •U.S. Treasury bills.

Normal Distribution - I

A large enough sample drawn from a normal distribution looks like a bell-shaped curve. The probability that a yearly return will fall within 19.8 percent of the mean of 12.1 percent will be approximately The 19.7 percent standard deviation we found for large stock returns from 1926 through 2020 can now be interpreted in the following way: •If stock returns are approximately normally distributed, the probability that a yearly return will fall within 19.7 percent of the mean of 12.2 percent will be approximately 2/3

Risk: Systematic and Unsystematic

A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree. An unsystematic risk is a risk that specifically affects a single asset or small group of assets. Unsystematic risk can be diversified away. Examples of systematic risk include uncertainty about general economic conditions, such as GNP, interest rates or inflation. On the other hand, announcements specific to a single company are examples of unsystematic risk.

7.4 Decision Trees

Allow us to graphically represent the alternatives available to us in each period and the likely consequences of our actions This graphical representation helps to identify the best course of action.

Using the S M L

An all-equity firm should accept projects whose I R R s exceed the cost of equity capital and reject projects whose I R R s fall short of the cost of capital.

Announcements, Surprises, and Expected Returns - II

Any announcement can be broken down into two parts, the anticipated (or expected) part and the surprise (or innovation): •Announcement = Expected part + Surprise. The expected part of any announcement is the part of the information the market uses to form the expectation, R of the return on the stock. The surprise is the news that influences the unanticipated return on the stock, U.

Arbitrage Pricing Theory

Arbitrage arises if an investor can construct a zero investment portfolio with a sure profit. •Since no investment is required, an investor can create large positions to secure large levels of profit. •In efficient markets, profitable arbitrage opportunities will quickly disappear.

10.6 More on Average Returns

Arithmetic average—return earned in an average period over a particular period Geometric average—average compound return per year over a particular period The geometric average will be less than the arithmetic average unless all the returns are equal. Which is better? •The arithmetic average is overly optimistic for long horizons. •The geometric average is overly pessimistic for short horizons. The geometric average is very useful in describing the actual historical investment experience.

The Weighted Average Cost of Capital

Because interest expense is tax deductible, we multiply the last term by With preferred stock: WACC = (S/(B+P+S))RS + (P/(B+P+S))RP + (B/(B+P+S))RD(1-TC)

13.1 The Cost of Equity Capital - I

Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital budgeting project should be at least as great as the expected return on a financial asset of comparable risk.

12.5 Empirical Approaches to Asset Pricing

Both the C A P M and A P T are risk-based models. Empirical methods are based less on theory and more on looking for some regularities in the historical record. Be aware that correlation does not imply causality. Related to empirical methods is the practice of classifying portfolios by style, e.g., •Value portfolio. •Growth portfolio.

13.4 Determinants of Beta

Business Risk •Cyclicality of Revenues. •Operating Leverage. Financial Risk •Financial Leverage.

You are considering to buy stocks of a new firm NNN. The firm's most recent dividend was $1 per share. The dividend payment is expected to increase by 20% in year 1, 10% in year 2 and year 3, afterwards 2% forever. Your required return is 10%. What is the maximum price you are willing to pay?

D1=(1*1.2)=1.2 D2=(1.2*1.1)=1.32 D3=(1.32*1.1)=1.452 Value after year 3=(D3*Growth rate)/(Required rate-Growth rate) =(1.452*1.02)/(0.1-0.02) =18.513 Hence current value=Future dividend and value*Present value of discounting factor(rate%,time period) =1.2/1.1+1.32/1.1^2+1.452/1.1^3+18.513/1.1^3 =$17.18(Approx).

Diversification and Portfolio Risk

Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns. This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another. However, there is a minimum level of risk that cannot be diversified away, and that is the systematic portion.

You are a financial manager of a firm and are asked to assess the cost of capital of your firm. You know that Your firm is going to pay dividend $3 per share The current stock price is $60 per share Firm beta is 10% lower than market average Constant growth rate is 3% Expected market return is 10% and risk free rate is 2% There is totally 10 million of outstanding shares of stocks, and for each dollar equity, firm issued $1.5 debt Cost of borrowing/issuing bond is 5% Corporate tax rate 30%

Dividend $3 here is [D1 or D0]? D1 What is the cost of equity (common stock) using dividend growth model? 3$ x 3% = .09 + $3 = 3.09 3.09 / 60 = .0515 + .03 (growth rate) = .08 risk_free_rate = 0.02 # Risk-free rate (2% converted to decimal) expected_market_return = 0.10 # Expected market return (10% converted to decimal) market_beta = 1 # Market beta is typically assumed to be 1 firm_beta = market_beta - (0.10 * market_beta) # Firm beta is 10% lower than market average # Calculating the cost of equity using CAPM cost_of_equity_capm = risk_free_rate + firm_beta * (expected_market_return - risk_free_rate) Market Beta = 1 - (.1 * 1) .02 + .9 * (.1 - .02) = .092

10.1 Returns

Dollar Returns the sum of the dividend income and the capital gain or loss on the investment Percentage Returns The sum of the dividend income and the change in value of the asset, divided by the initial investment. Dollar return = dividend income + capital gain (or loss) percentage return = dollar return / beginning market value

Setting the Bid Price

Find the sales price that makes N P V = 0 Step 1: Use known changes in NWC and capital to estimate "preliminary" N P V Step 2: Determine what yearly O C F is needed to make N P V = 0 Step 3: Determine what NI is required to generate the O C F •O C F = NI + Depreciation. Step 4: Identify what sales (and price) are necessary to create the required NI •NI = (Sales − Costs − Depreciation)*(1 − T)

13.11 Flotation Costs

Flotation costs represent the expenses incurred upon the issue, or float, of new bonds or stocks. These are incremental cash flows of the project, which typically reduce the N P V since they increase the initial project cost Amount raised = Necessary proceeds / (1-% floatation cost) The % flotation cost is a weighted average based on the average cost of issuance for each funding source and the firm's target capital structure:

Inflation and Capital Budgeting

For low rates of inflation, this is often approximated: Real rate = nominal rate - inflation rate While the nominal rate in the U.S. has fluctuated with inflation, the real rate has generally exhibited far less variance than the nominal rate. In capital budgeting, one must compare real cash flows discounted at real rates or nominal cash flows discounted at nominal rates.

The Cost of Equity Capital - II

From the firm's perspective, the expected return is the cost of equity capital: To estimate a firm's cost of equity capital, we need to know three things: 1.The risk-free rate, Rf 2.The market risk premium, Rm - Rf 3.The company beta,

Cyclicality of Revenues

Highly cyclical stocks have higher betas. •Empirical evidence suggests that retailers and automotive firms fluctuate with the business cycle. •Transportation firms and utilities are less dependent on the business cycle. Note that cyclicality is not the same as variability—stocks with high standard deviations need not have high betas. •Movie studios have revenues that are variable, depending upon whether they produce "hits" or "flops," but their revenues may not be especially dependent upon the business cycle.

How do we determine the cost of equity capital? How can we estimate a firm or project beta? How does leverage affect beta? How do we determine the weighted average cost of capital? How do flotation costs affect the capital budgeting process?

How do we determine the cost of equity capital? trimming the cost of capital using primarily the cap IM we talked about How can we estimate a firm or project beta? How does leverage affect beta? It always increases the equity beta How do we determine the weighted average cost of capital? we talked about the weighted average cost of capital being the number that that being the R that we're going to evaluate the firm by ultimately. How do flotation costs affect the capital budgeting process? when you think about how much money you need to raise

How do you compute the expected return and standard deviation for an individual asset? For a portfolio? What is the difference between systematic and unsystematic risk? What type of risk is relevant for determining the expected return? Consider an asset with a beta of 1.2, a risk-free rate of 5 percent, and a market return of 13 percent. •What is the expected return on the asset?

How do you compute the expected return and standard deviation for an individual asset? For a portfolio? we're going to compute the expected return, the standard deviation for individual assets and for a portfolio What is the difference between systematic and unsystematic risk? systematic risk There's a price for it that's represented by the buy beta unsystematic risk There's no price for it because it should be free for us to our to diversify our portfolio and get rid of it. What type of risk is relevant for determining the expected return? Only the systematic risk Consider an asset with a beta of 1.2, a risk-free rate of 5 percent, and a market return of 13 percent. Calculate now if we know the beta and the risk free rate and the market rate, we can now calculate the expected return on any particular asset or project that we might want to undertake in our in our corporate and our corporate corporation or in our own individual portfolio. •What is the expected return on the asset?f

Relationship Between b and Expected Return - I

If shareholders are ignoring unsystematic risk, only the systematic risk of a stock can be related to its expected return.

Portfolio Risk and Number of Stocks

In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not.

6.5 Inflation and Capital Budgeting

Inflation is an important fact of economic life and must be considered in capital budgeting. Consider the relationship between interest rates and inflation, often referred to as the Fisher equation: (1 + Nominal interest rate) = (1 + Real interest rate) × (1 + Inflation rate)

Cost of Debt

Interest rate required on new debt issuance (i.e., yield to maturity on outstanding debt) Adjust for the tax deductibility of interest expense Lecture Tip: The Tax Cuts and Jobs Act of 2017 reduced corporate tax rates to a flat 21 percent, which will reduce the attractiveness of debt and increase the aftertax cost.

Using an Industry Beta

It is frequently argued that one can better estimate a firm's beta by involving the whole industry. If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta. If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm's beta. Do not forget about adjustments for financial leverage.

Chapter 6 and 7 Summary

Looking at the incremental cash flows is they key to answering the three financial decision questions Sunk cost are sunk and not part of decision making Opportunity cost do

Break-Even Revenue: PBE

Now that we have break-even revenue of $5,332.60 million, we can calculate break-even price. The original plan was to generate revenues of $7 billion by selling the cold cure at $10 per dose and selling 700 million doses per year, We can reach break-even revenue with a price of only: 5332.6 million = 700 million x Pbe Pbe = 5332.6 million / 700 million = 7.62

7.3 Real Options

One of the fundamental insights of modern finance theory is that options have value. The phrase "We are out of options" is surely a sign of trouble. Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation. The Option to Expand. •Has value if demand turns out to be higher than expected. The Option to Abandon. •Has value if demand turns out to be lower than expected. The Option to Delay. •Has value if the underlying variables are changing with a favorable trend.

Financial Leverage and Beta

Operating leverage refers to the sensitivity to the firm's fixed costs of production. Financial leverage is the sensitivity to a firm's fixed costs of financing. The relationship between the betas of the firm's debt, equity, and assets is given by: Financial leverage always increases the equity beta relative to the asset beta.

10.7 The U.S. Equity Risk Premium: Historical and International Perspectives

Over 1926 to 2020, the U.S. equity risk premium has been quite large: •Earlier years (beginning in 1802) provide a smaller estimate at 5.4 percent. •Comparable data for 1900 to 2010 put the international equity risk premium at an average of 6.9 percent, versus 7.2 percent in the U.S. Going forward, an estimate of 7 percent seems reasonable, although somewhat higher or lower numbers could also be considered rational

Cost of Preferred Stock

Preferred stock is a perpetuity, so its price is equal to the coupon paid divided by the current required return. Rearranging, the cost of preferred stock is:

Estimation of Beta - II

Problems 1.Betas may vary over time. 2.The sample size may be inadequate. 3.Betas are influenced by changing financial leverage and business risk. Solutions 1.Problems 1 and 2 can be moderated by more sophisticated statistical techniques. 2.Problem 3 can be lessened by adjusting for changes in business and financial risk. 3.Look at average beta estimates of comparable firms in the industry.

Valuing the Option to Abandon

Recall that we can calculate the market value of a project as the sum of the N P V of the project without options and the value of the managerial options implicit in the project. M = NPV + Opt

Risk When Holding the Market Portfolio

Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta security. Beta measures the responsiveness of a security to movements in the market portfolio (i.e., systematic risk).

Arbitrage Pricing Theory (APT)

Risk-return relationships from no-arbitrage considerations in large capital markets Rs = Rrp + Bm(MRP) + Boil(change in oil)+Binterest(change in interest)

Assume a project has these estimated values: Sales quantity of 4,000 units, plus or minus 5 percent; variable cost per unit of $20, plus or minus 3 percent; fixed costs of $50,000, plus or minus 2 percent; depreciation of $20,000; and a sales price of $50 a unit, plus or minus 10 percent. The tax rate is 30 percent. The company bases its sensitivity analysis on the expected case scenario.

SaleUnits SalePricerperunit Revenue Cost Optimistic 4,000*(1+.05) = 4,200 50*(1+.1)= 55.00 231,000 (4,200×20× (1-.03)+50,000× (1-.02) =130,480) Expected 4,000 50.00 200,000 (4,000×20+50,000= 130,000) Pessimistic 3,800 45.00 (3800x45) = 171,000 (3,800×20× (1+.03)+50,000× (1+.02) =129,280 )

One portfolio has three securities. Stock A accounts for 50% with beta =1, stock B accounts for 10% with beta 50% lower than market beta and stock C accounts for the rest with beta 20% higher than market average.

Stock B = 50% lower than market average beta = 1×0.5=0.5 Stock C= 20% higher than market average beta= 1.2×1= 1.2 Stock A weight= 50%, beta =1, stock B weight =10% Beta=0.5 and stock c = 40% and beta = 1.2 Systematic risk of the portfolio = weighted average beta of the portfolio = 0.5×1+0.1×0.5+0.4×1.2 = 1.03

Incremental Cash Flows

Sunk costs are not relevant •Just because "we have come this far" does not mean that we should continue to throw good money after bad. Opportunity costs do matter. Just because a project has a positive N P V, that does not mean that it should also have automatic acceptance. Specifically, if another project with a higher N P V would have to be passed up, then we should not proceed. Side effects matter. •Erosion is a "bad" thing. If our new product causes existing customers to demand less of our current products, we need to recognize that. •If, however, synergies result that create increased demand of existing products, we also need to recognize this gain.

Risk Premiums

Suppose that The Wall Street Journal announced that the current rate for one-year Treasury bills is 2 percent. What is the expected return on the market of small-company stocks? Recall that the average excess return on small-company common stocks for the period 1926 through 2020 was 12.9 percent. Given a risk-free rate of 2 percent, we have an expected return on the market of small-company stocks of 14.9% = 12.9% + 2%

Example - I

Suppose the stock of Stansfield Enterprises, a publisher of online presentations, has a beta of 1.5. The firm is 100 percent equity financed. Assume a risk-free rate of 3 percent and a market risk premium of 7 percent. What is the appropriate discount rate for an expansion of this firm? Rs = Rf + b(Rm - Rf) Rs = 3% + 1.5% x 7% Rs = 13.5%

The Option to Abandon: Example - I

Suppose we are drilling an oil well. The drilling rig costs $300 today, and in one year the well is either a success or a failure. The outcomes are equally likely. The discount rate is 10 percent. The P V of the successful payoff at time one is $575. The P V of the unsuccessful payoff at time one is $0. Traditional N P V analysis would indicate rejection of the project. Expected pay off = prob success x successful pay off + prob failure x failure payoff Expected pay off = .50 x 575 + .5 x 0 = 287.5 NPV = -$300 + 287.5/1.1 = 38.64

Differentiate systematic risk from unsystematic risk. Which type is essentially eliminated with well diversified portfolios? Define arbitrage. Explain how the C A P M can be considered a special case of Arbitrage Pricing Theory?

Systematic risk, also known as market risk, is the risk inherent to the entire market or market segment. This type of risk affects a large number of assets and is linked to factors like economic, political, or natural events that impact the financial markets as a whole. Unsystematic risk, or specific risk, pertains to a particular company or industry. It is associated with factors that affect the operation and performance of individual companies or specific sectors. Well-diversified portfolios essentially eliminate unsystematic risk. Arbitrage refers to the practice of profiting from price differences of the same or similar financial instruments, in different markets or in different forms. Arbitrageurs take advantage of these price differences by simultaneously buying and selling assets to lock in a risk-free profit. CAPM: CAPM calculates expected return based on the systematic risk of an asset, represented by beta, and the expected market return. It focuses solely on market risk (systematic risk) and assumes a linear relationship between expected return and beta. APT: APT, on the other hand, is more general and flexible. It considers multiple factors

13.5 Dividend Discount Model

The D D M is an alternative to the C A P M for calculating a firm's cost of equity. The D D M and C A P M are internally consistent, but academics generally favor the C A P M and companies seem to use the C A P M more consistently. •The C A P M explicitly adjusts for risk and it can be used on companies that do not pay dividends. Note that even if a firm pays no dividend, there is still a cost to equity, as investors expect to receive future payouts (i.e., the growth). Further, investors also face opportunity costs for investing in one firm versus another, implying that dividend yield is only a piece of the whole issue.

Equivalent Annual Cost (E A C)

The E A C is the value of the level payment annuity that has the same PV as our original set of cash flows. •For example, the E A C for the Cadillac air cleaner is $750.98. •The E A C for the Cheapskate air cleaner is $763.80, thus we should reject it. C F0, negative 4,000 C F1, negative 100 F1, 10 I, 10 N P V, negative 4,614.46 N, 10 I/Y 10 P V, negative 4,614.46 P M T, 750.98 F V

12.1 Systematic Risk and Betas - I

The beta coefficient, tells us the response of the stock's return to a systematic risk. In the C A P M, measures the responsiveness of a security's return to a specific risk factor, the return on the market portfolio.

11.1 Individual Securities

The characteristics of individual securities that are of interest are the: •Expected Return. •Variance and Standard Deviation. •Covariance and Correlation (to another security or index).

Operating Leverage - I

The degree of operating leverage measures how sensitive a firm (or project) is to its fixed costs. Operating leverage increases as fixed costs rise and variable costs fall. Operating leverage magnifies the effect of cyclicality on beta. The degree of operating leverage is given by: the percentage change in EBIT for a given percentage change in sales.

10.2 Holding Period Returns

The holding period return is the return that an investor would get when holding an investment over a period of T years, when the return during year i is given as Ri:

Announcements, Surprises, and Expected Returns - I

The return on any security consists of two parts. •Expected returns. •Unexpected or risky returns. A way to write the return on a stock in the coming month is: R = R + U R is the expected part of the return U is the unexpected part of the return

10.4 Average Stock Returns and Risk-Free Returns

The risk premium is the added return (over and above the risk-free rate) resulting from bearing risk. One of the most significant observations of stock market data is the long-run excess of stock return over the risk-free return. •The average excess return from large-company common stocks for the period 1926 through 2020 was: 8.9% = 12.2% − 3.3% •The average excess return from small-company common stocks for the period 1926 through 2020 was: 12.9% = 16.2% − 3.3% •The average excess return from long-term corporate bonds for the period 1926 through 2020 was: 3.2% = 6.5% − 3.3%

Firm Valuation

The value of the firm is the present value of expected future (distributable) cash flow discounted at the W A C C. To find equity value, subtract the value of the debt from the firm value.

Investments of Unequal Lives

There are times when application of the NPV rule can lead to the wrong decision. Consider a factory that must have an air cleaner that is mandated by law. There are two choices: •The "Cadillac cleaner" costs $4,000 today, has annual operating costs of $100, and lasts 10 years. •The "Cheapskate cleaner" costs $1,000 today, has annual operating costs of $500, and lasts 5 years. Assuming a 10 percent discount rate, which one should we choose? Cadillac Air Cleaner: CF0, negative 4,000 CF1, negative 100 F1, 10 I, 10 NPV, negative 4,614.46 Cheapskate Air Cleaner: CF0, negative 1,000 CF1, negative 500 F1, 5 I, 10 NPV, negative 2,895.39 This overlooks the fact that the Cadillac cleaner lasts twice as long. When we incorporate the difference in lives, the Cadillac cleaner is actually cheaper (that is, has a higher NPV).

10.5 Risk Statistics

There is no universally agreed-upon definition of risk. The measures of risk that we discuss are variance and standard deviation. •The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time. •Its interpretation is facilitated by a discussion of the normal distribution. The Sharpe ratio, or reward-to-risk ratio, can be calculated as the risk premium (or excess return) divided by the standard deviation.

Expected Return on a Security

This formula is called the capital asset pricing model (C A P M): Expected return on a security = Risk-free rate + Beta of the security × Market risk premium

A project has the following cash flows. Year 0: -$50,000 Year 1: $20,000 Year 3: $10,000 Year 5: $50,000 Suppose that your required return is 5%.

To compute the PV of cash flow at Year 5, how many times it is discounted (power of discounting)? 5 NPV (20,000) / (1+5%)^1 + (10,000) / (1+5%)^3 + (50,000) / (1+5%)^5 - 50,000 = 16862.31 Profitability Index 16862.31 / 50,000 = .337 = 1.34

6.3 Alternative Definitions of Operating Cash Flow

Top-Down Approach •OCF = Sales − Cash costs − Taxes. •Do not subtract noncash deductions. Bottom-Up Approach •Works only when there is no interest expense. •OCF = Net income + Depreciation. Tax Shield Approach •OCF = (Sales − Cash costs)(1 − TC) + Depreciation × TC.

Total Risk

Total risk = Systematic risk + Unsystematic risk The standard deviation of returns is a measure of total risk. For well-diversified portfolios, unsystematic risk is very small. Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk.

Total Risk 2

Total risk = Systematic risk + Unsystematic risk The standard deviation of returns is a measure of total risk. For well-diversified portfolios, unsystematic risk is very small. Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk.

The Risk-Free Rate

Treasury securities are close proxies for the risk-free rate. The C A P M is a period model. However, projects are long-lived, so average period (short-term) rates need to be used. The historic premium of long-term (20-year) rates over short-term rates for government securities is in the range of 1-2 percent. So, the risk-free rate to be used in the C A P M could be estimated as 2 percent below the prevailing rate on 20-year Treasury securities.

There are three economy situations and two stocks. Information is as follows. Assume you have %10,000 and allocate $4,000 on stock A. Economy Probability Stock A Stock B Booming 0.2 10% 20% Neutral ? 5% 0% Recession 0.5 0% -10% b. What is the standard deviation/ risk for stock A? c. What is the expected portfolio? d. What is the portfolio return when economy is booming?

What are the expected returns for both stock A (.2 x 10%) + (.3 x 5%) + (.5 x 0) 2% + 1.5% + 0% = 3.5% Stock B (.2 x 20%) + (.3 x 0%) + (.5 x -10%) 4% + -5% = -1% https://i.gyazo.com/b160f2f42218f650b863201707e77c4c.png

How do we determine if cash flows are relevant to the capital budgeting decision? What are the different methods for computing operating cash flow, and when are they important? What is equivalent annual cost, and when should it be used? How should cash flows and discount rates be matched when inflation is present?

What is equivalent annual cost, and when should it be used? When you're looking at expenses, you have to think about the equivalent annual cost and so on. You want to be kind of turning the expenses into an annuity in order to be able to compare them an apples to apples basis, You want to be kind of turning the expenses into an annuity in order to be able to compare them an apples to apples basis especially for capital equipment that it's different lifetimes How should cash flows and discount rates be matched when inflation is present? we're going to use the match, the cash flows, discount rate when inflation's present. So inflation's present, that discount rate is going to go up and down. It's going to offset.

You are considering to buy stocks of a new firm NNN. The firm just paid dividends $1 per share. The dividend payment is expected to increase by 25% in the first two year, 10% in the following two years, afterwards 3% forever. Your required return is 10%. What is the maximum price you are willing to pay?

What is the value of D1? D1 = 1 * 125% = 1.25 D2 = 1.25 * 125% = 1.56 What is the value of D4? 10% increase in following 2 years, D3 = 1.56 * 110%= 1.72 D4 = 1.72* 110%=1.89 In which year, growth rate becomes constant? (fill with integer, for example, in year 3, fill "3") In 5th year , growth rate becomes constant. In the first step, you can compute price from constant growth rate at which period? What is the maximum price you are willing to pay? 1.89 * 103% = 1.95 1.95 * 1/(0.10-0.03) = 27.86 (1.25/1.1)+(1.56/1.1^2)+(1.72/1.1^3)+(1.89/1.1^4)+(27.86/1.1^4)

Which of the investments discussed has had the highest average return and risk premium? Which of the investments discussed has had the highest standard deviation? Why is the normal distribution informative? What is the difference between arithmetic and geometric averages?

Which of the investments discussed has had the highest average return and risk premium? The highest average return tend to be the ones that have the high have had the highest risk premium, but also had the highest risk. So which which which investment had the highest risk? It was the small stock portfolio which had the highest return Which of the investments discussed has had the highest standard deviation? Why is the normal distribution informative? it's because in the in the real world, with the law of large numbers, as we draw randomly from the real world, we tend to generate a normal distribution What is the difference between arithmetic and geometric averages? whereas the arithmetic average is going to be the one you calculate is the average return over a And in periods where the geometric is the compounded return, which is always going to tend to be lower over those same time periods.

What are weights of equity and debt to compute WACC, respectively? What is the WACC for your firm using cost of equity from CAPM ? (keep 4-digit after decimal point, e.g., 0.1234)

cost_of_equity_capm = 0.092 # Cost of equity from CAPM (9.20% converted to decimal) cost_of_debt = 0.05 # Cost of debt (5% converted to decimal) corporate_tax_rate = 0.30 # Corporate tax rate (30% converted to decimal) total_value = market_value_of_equity + market_value_of_debt # Total value of the firm weight_of_equity = market_value_of_equity / total_value weight_of_debt = market_value_of_debt / total_value wacc = (weight_of_equity * cost_of_equity_capm) + (weight_of_debt * cost_of_debt * (1 - corporate_tax_rate)) weight_of_equity, weight_of_debt, wacc * 100 # Converting WACC to percentage

What is total value of the firm

current_stock_price = 60 # Current stock price in dollars total_outstanding_shares = 10000000 # Total number of outstanding shares debt_to_equity_ratio = 1.5 # For each dollar equity, $1.5 in debt market_value_of_equity = current_stock_price * total_outstanding_shares market_value_of_debt = market_value_of_equity * debt_to_equity_ratio total_value_of_firm = market_value_of_equity + market_value_of_debt market_value_of_equity, market_value_of_debt, total_value_of_firm The market value of equity is $600,000,000 (calculated as $60 per share times 10 million shares). The market value of debt is $900,000,000, calculated based on the debt-to-equity ratio of 1.5. Therefore, the total value of the firm (equity plus debt) is $1,500,000,000

A 5-year coupon bond with coupon rate 9% and semi-annual payment. The required return is 7%. What is semi-annual coupon payment? What is the current value of such bond?

face value = 1000 coupon rate = 9% semi annual coupon payment =face value∗coupon rate / 2=1,000×9%2=45 periods to maturity = 5*2 = 10 (n) yield per period (r) = 7%/2 = 3.5% bond′s price =semi annual coupon∗(1−(1+r)^(−n))/r + face value/(1+r)^n =45× ((1−(1+3.5%)^−10)÷3.5%) + (1,000÷(1+3.5%)^10)=$1,083.17 semi annual coupon payment = $45 current value of this bond = $1,083.17

Suppose that beta for a given stock is same as market beta. Risk-free rate is 2%. a. What is the expected return for this stock if expected market return is 10%? b. What is the expected return for this stock if market risk premium is 10%?

now that market beta is equal to 1. Therefore, the beta of the stock = βS = 1 Risk-free rate = RF = 2% Part a Expected market return = RM = 10% The expected return of the stock can be calculated using CAPM E[RS] = RF + βS*(RM-RF) = 2% + 1*(10%-2%) = 10% Answer a -> 10% Part b Market risk premium = RM-RF = 10% The expected return of the stock can be calculated using CAPM E[RS] = RF + βS*(RM-RF) = 2% + 1*10% = 12% Answer b -> 12%

What will be the operating cash flow under best-case scenario

sales_quantity_best = 4000 * 1.05 # 4,000 units plus 5% sales_price_best = 50 * 1.10 # $50 plus 10% variable_cost_per_unit_best = 20 * 0.97 # $20 minus 3% fixed_costs_best = 50000 * 0.98 # $50,000 minus 2% depreciation = 20000 # Constant tax_rate = 0.30 # 30% total_sales_best = sales_quantity_best * sales_price_best total_variable_costs_best = sales_quantity_best * variable_cost_per_unit_best profit_before_tax_best = total_sales_best - total_variable_costs_best - fixed_costs_best - depreciation operating_cash_flow_best = (profit_before_tax_best * (1 - tax_rate)) + depreciation Operating Cash Flow=(231000−81480 −49,000−20,000)×(1−.3)+20000

Worst Case Scene

sales_quantity_worst = 4000 * 0.95 # 4,000 units minus 5% sales_price_worst = 50 * 0.90 # $50 minus 10% variable_cost_per_unit_worst = 20 * 1.03 # $20 plus 3% fixed_costs_worst = 50000 * 1.02 # $50,000 plus 2% total_sales_worst = sales_quantity_worst * sales_price_worst total_variable_costs_worst = sales_quantity_worst * variable_cost_per_unit_worst profit_before_tax_worst = total_sales_worst - total_variable_costs_worst - fixed_costs_worst - depreciation operating_cash_flow_worst = (profit_before_tax_worst * (1 - tax_rate)) + depreciation

Capital Asset Pricing Model

the equation of the SML showing the relationship between expected return and beta Rs = Rrf + B(Rsq =- Rrf) Rs = Rrf + B(MRP)

Financial Leverage

the use of borrowed funds to increase the return on owners' equity

There are two economy situations and three stocks. Information is as follows https://i.gyazo.com/2e76b99d0eef352b693ddc9a45c381bf.png

to compute expected return of 2a formula 1 to compute expected return of 2b formula 2 to compute risk of 2a formula 3 to compute risk of 2b formula 4