FIN305W-Exam-3-formula-sheet

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Jan 9, 2024

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“Official” Formula Sheet for Exam 3, FIN305W, Fall 2022, Peter Iliev Feel free to add anything to this sheet. R ELEVANT C ASH F LOWS : + Revenues (Sales) - Costs (both fixed and variable costs) - Taxes [=(Sales-Costs-Depreciation) x Tax rate] - Investment in net working capital (- change in NWC) - Investment in fixed assets + After-tax salvage value [=Re-Sale Value- Tax rate x (Re-Sale Value-End Book Value)] - After-tax cleanup costs + Positive/Negative side effects (after tax) - Opportunity costs (after tax) = Net Cash Flow (NCF) Accounting break-even : sales volume (quantity) at which NI = 0 Cash break-even: sales volume (quantity) at which OCF = 0 Financial break-even: sales volume (quantity) at which NPV = 0 Bid Price: Lowest price at which NPV = 0 Return over a year = Price This Year - Price Last Year + Distributions (coupons/dividends) Price Last Year Weak Form Market Efficiency : Market prices reflect all historical information such as price, volume, returns, short interest. Semi-Strong Form Market Efficiency : Market prices reflect all publicly available information such as earnings announcements, balance sheet, patents, analyst forecasts. Strong Form Market Efficiency : Market prices reflect all information, both public and private, including inside information from the firm. Portfolio Expected Return : E(r P ) = w 1 ∙ µ 1 + w 2 ∙ µ 2 = w 1 ∙ E(r 1 ) + w 2 ∙ E(r 2 ) Weights : w 1= (Investment in Asset 1)/Overall Investment, w 1+ w 2=1, weights can be neg Portfolio Variance : σ P 2 = w 1 2 ∙ σ 1 2 + w 2 2 ∙ σ 2 2 + 2 ∙ w 1 ∙ w 2 ∙ σ 1 ∙ σ 2 ∙ ρ 1,2 Portfolio Standard Deviation : σ P = √ σ P 2 Portfolio standard deviation if combining a risky asset (1) and risk-free asset (RF): σ P = w 1 ∙ σ 1 CAPM β : β = σ i, m σ m 2 , β P = w 1 ∙ β 1 + w 2 ∙ β 2 CAPM : E ( r E ) = r f + β E ∙ ( E ( r E ) − r f ) Dividend Growth Model: r E = D 1 P 0 + g = ( 1 + g ) ∙ D 0 P 0 + g WACC: WACC = r A = D D + E r D + E D + E r E After-tax WACC: WACC =( 1 − T C ) D D + E r D + E D + E r E Modigliani & Miller Proposition 2: r E = r A + D E ( r A − r D ) Value of a levered firm: V L = V U + PV ( Interest Tax Shield ) , Interest Tax Shield = D ∙r D ∙T C If debt is maintained forever: PV ( Interest Tax Shield ) = T C ∙D Exam 1 formulas (maybe still useful): A company has ten existing projects financed exclusively by equity with a cost of equity of 9 percent. It can borrow all the money it needs for a new project at 5 percent. The new project is similar in risks to the existing projects. Should it use 5 percent as its cost of capital for the project? No. The company cost of capital is 9% so it should not start projects with IRR smaller than 9% Suppose that a project requires a $50 million investment in equipment at date zero. Initially, the company planned to depreciate the plant and equipment straight-line to $0 million. How will the project NPV and IRR change if the company instead depreciates the equipment straight-line to $4 million? The company will use the end book value to reduce its tax obligation when reselling the equipment and the re-sale value does not change. NPV decreases, IRR decreases; Slower depreciation reduces the tax savings early on and leads to lower NPV and IRR Stacey is analyzing a project that currently has a projected positive NPV. What will be the effect of the following change that she is considering? Increasing in the level of accounts receivable will: decrease the NPV of the project; Higher account receivables leads to higher NWC and decreases firm value . A company announces that its CEO decided to devote himself to a higher meaning in life and is resining immediately. The stock price of the company goes 12% down upon this announcement. This is an example of: diversifiable risk; invest in more companies The pure-play approach to assessing project risk asks for finding a firm that specializes in the product or service that we are considering. If all the assumptions behind the Modigliani and Miller theorems are true, whenever the firm decreases its use of debt and increase its use of equity by the same amount cost of equity decreases stock price does not change. What would happen to the expected return of Portfolio P that holds $1 million of Stock A and $1.5 million of Stock B, if the correlation between the two stocks changes from 0 to 1? Stock A has an expected return of 12% and a standard deviation of its return of 20%. Stock B has an Which of these securities has had the highest historical risk (measured as variability in returns)? Small-company stocks Which one of the following statements is correct concerning market efficiency? In a semi-strong efficient market, market participants with insider information will have an advantage over others. You have calculated that the project accounting break-even point is 23,467 units. This means that at this level of production your project’s: NPV is negative Theresa is analyzing a project that currently has a projected positive NPV. What will be the effect of increqasing in the corporate tax rate? Decrease the NPV of the project. You bought one of Great White Shark Repellant Co.'s 7 percent coupon bonds one year ago for $1,100. The bond makes annual payments, matures 10 years from now, and has a face value of $1,000. Suppose you decide to sell your bonds today when the required return on the bonds is 8 percent. What was your total return on investment? -8.9%; N=10, I/Y=8, PMT=70, FV=1000, CPT PV=-932; return=(932+70-1,100)/1,100 Suppose that a firm has a corporate bond issue currently outstanding that has 20 years left to maturity. The coupon rate is 4%, and coupons are paid semiannually. The bond is currently selling for $850 and has a face value of $1,000. What is the firm cost of debt based on this bond? 5.22%; N=40, PMT=20, FV=1,000, PV=-850, CPT I/Y=2.608, Annual yield=2*2.61=5.22% Last year you bought a stock for $32. A year later you received dividends of $3. The stock is now selling for $35. What is your total percentage return for the year on this investment? 18.75%; Return=(35+3-32)/32 Sixx AM Manufacturing has a debt to debt plus equity (D/(D+E)) ratio of 0.25. Its cost of equity is 13 percent, and its cost of debt is 6 percent. If the tax rate is 25 percent, what is the company's after-tax WACC? 10.88%, WACC=(1-0.25)*0.25*6%+0.75*13% What is the portfolio weights for Stock A in a portfolio that has 105 shares of Stock A that sell for $25 per share and 95 shares of Stock B that sell for $45 per share? 0.38; 105*25/(105*25+95*45) Assume you prefer a portfolio with an expected standard deviation of 40%. You can invest in the market and at the same time invest/borrow money at the risk-free rate. The expected return on the market portfolio is 15% with a standard deviation of 20%. The current risk-free rate is 5%. If you want to invest $5,000 of your own money, how much do you borrow at the risk-free rate to achieve a portfolio standard deviation of 40%? 5,000 Suppose Spin Corp.’s equity beta is 0.7 and the historical average of the market risk premium is 8%. Last year’s stock return was -12% and last year's Spin Corp.’s bond return was 3.6%. The risk-free rate is 1%. What

 Present Value: PV 0 = FV t ( 1 + r ) t  Ordinary Perpetuity: PV 0 = C 1 r  Perpetuity “due now”: PV 0 = C 0 + C 1 r  Growing Perpetuity PV 0 = C 1 ( r − g )  Annuity: PV 0 = C 1 r ∙ [ 1 − 1 ( 1 + r ) t ] 19. A. 0.2*12%+0.8*18%=0.168=16.8% 20. E. sqrt(0.2^2*20^2+0.8^2*40^2+2*0.2*0.8*20* 40*0.2)=33.03 21. A. (0.5/1.2)*10-4.17% 22. C. N=10, PMT=20, I/Y=4, FV=0, CPT PV=- 162.2 23. D. 0.3333*100,000*0.34/1.1+0.4445*100,000*0 .34/1.1^2+0.1481*100,000*0.34/1.1^3+0.074 1*10 0,000*0.34/1.1^4 = $28,296 24. D. 20- 11-0.3*(20-11-4)-(0-12)+10-0.3*(10-2)=27.1 25. D. RA=(40/110)*6% +(70/110)*13%=10.455%, RE=10.455+(60/50)*(10.455-7)=14.60% 26. B. Old Price=4,000/100=$40, PV(Tax Shield)=0.2*500=100, New Price=(4,000+100)/100=$41 Consider a portfolio containing two stocks with equal weights (w = w =50%). Stock A’s expected return is 20% with a standard deviation of 30%; stock B’s expected return is 15% with a standard deviation of 25%. The correlation between the two stocks is 0.5. How much would the portfolio standard deviation be reduced if the correlation dropped from 0.5 to 0? 4.3% St. dev if corr=0.5: sqrt(0.5^2*0.3^2+0.5^2*0.25^2+2*0.5*0.5*0.3*0.25* 0.5)=0.238 St. dev if corr=0: sqrt(0.5^2*0.3^2+0.5^2*0.25^2+2*0.5*0.5*0.3*0.25* 0)=0.195 Suppose you can borrow and lend at a risk-free rate. You want to construct a portfolio with higher returns than the return of the market portfolio. You can achieve this by buying stocks with a beta of less than 1 as long as you can borrow at the risk-free True. A firm is fully equity (100% equity) financed with a cost of equity of 9%. The risk-free rate is 2%, the market risk premium is 7% and the cost of debt is 6%. The firm’s corporate tax rate is 20%. What’s the firm’s WACC? 9% (=1*0.09) Assume the firm peet.edu has a debt-ratio (D/(D+E)) of 30%. peet.edu’s marginal tax rate is zero and it can borrow at 8%. Its CEO (Mr. Peet) has calculated that its WACC is 11%. What’s the current cost of equity (rE)? 12.3%; 0.11=0.7*x+0.3*0.08, x=(0.11-0.3*0.08)/0.7 =0.123 What will be the new cost of equity (r ) if peet.edu increases its debt-ratio (D/(D+E)) to 60% (assuming its cost of debt does not change)? 15.5%; 0.11=0.4*x+0.6*0.08, x=(0.11-0.6*0.08)/0.4 =0.155 Suppose that a firm has a corporate bond issue currently outstanding that has 10 years left to maturity. The coupon rate is 6%, and coupons are paid semiannually. The bond is currently selling for $850, and has a face value of $1,000. What is the firm's annual cost of debt based on this bond? 8.23% N=20, PMT=30, PV=-850, FV=1,000, CPT I/Y=4.115% (multiply by 2 to get 8.23%) The trade-off theory of optimal capital structure predicts that when choosing the optimal level of debt, firms will compare the tax benefits of debt financing to the potential bankruptcy costs if the firm cannot meet its interest payments. Assume a corporate tax rate of 35%. Debt financing provides a tax shield that increases the value of the firm . False If a firm borrows $50 million for two years at 9%, what is the present value of the interest tax shield? Assume the firm pays interest at the end of each of the two years and the interest tax shield falls in the same risk class as the firm’s debt. The corporate tax rate is 35%. $2.8 million PMT=1.575(=50*0.09*0.35) N=2 I/Y=9 FV=0 Cpt PV=-2.77 Rally, Inc. is an all-equity firm with assets worth $25 billion, and 10 billion shares outstanding. Rally plans to borrow $10 billion and use the funds to repurchase Theresa is analyzing a project that currently has a projected NPV of zero. Which of the following changes that she is considering will help that project produce a positive NPV instead? Depreciate initial investment to lower end bookvalue Quick depreciation increases tax savings early in the project and hence improves NPV. HW #9 Last year you bought a stock for $35. A year later you received dividends of $1.25. The stock is now selling for $30. What is your one-year return on this investment? ($30+$1.25-$35)/$35=-0.107=-10.7% Last year you bought a bond for $1,050. It was a 20-year 7% coupon rate bond with a yield-to-maturity of 6.54%. Its face value is $1,000. This year you want to sell the bond. Bonds with similar maturity and risk profile now trade at a 7.5% yield-to-maturity. What is your one-year return from investing in this bond? N=19, I/Y=7.5%, PMT=70, FV-1,000 CPT PV=-950.2 (this is price of bond this year) One year return=(950.2+70-1050)/(1050)=-2.8% Which of these asset classes has exhibited the highest historical risk (measured as standard deviation of its annual returns)? Large-company stocks You are convinced the efficient market hypothesis is true. Suppose that you are offered to invest in two mutual funds. Fund Dud is a plain–vanilla index fund that tracks the S&P 500, and you can buy into it for free. Fund Ace also invests in S&P 500 companies, but has performed exceptionally over the last 2 years and has beaten the S&P 500 return by 10%. Because of this stellar performance, Fund Ace charges 2% of your investment irrespective of performance. Choose to invest in Dud; In an efficient market, both have the same expected returns so it is better to go with low fees If the efficient markets hypothesis is true, then investors that put money into well diversified and low-cost ETFs will do better than investors that invest in actively managed mutual funds that charge high fees for their stock-picking ability. True If the efficient markets hypothesis is true, then all investors should predict stock price movements and trade actively based on their predictions. True. Active trading will incur costs without extra expected benefits Stock A has a beta of 1.3, dividend yield of 4%, and trades at $37 per share. Stock B has a beta of 1.5, does not pay dividends and trades at $57 per share. Last year stock A had a total return of 12.7% and stock B had a total return of -1.3%. The market equity premium is 7.6% and the risk- free rate is 4%. The expected return on A (using CAPM) is 0.04+1.3*0.076=0.139; The expected return on B (using CAPM) is 0.04+1.5*0.076=0.154 Consider the following securities What is the expected return on HW #8 A manager can choose between depreciating the full value of an investment with straight-line depreciation over three, four or five years. To maximize the value of the related project, the manager should choose three year depreciation Quicker depreciation schedules lead to larger savings early on and therefore have a higher present value of the tax savings. Your boss asks you about the effect of a 50% decrease in all account payables on a proposed project. Your answer is that this will: Decrease the NPV of the project A decrease in accounts payables will increase the net working capital (as NWC=AR+Inventory-AP) and therefore will increase the investment in NWC. This reduces the cash flows early on and increases them by the same amount later in project life. The net effect on the project NPV is, therefore, negative . Sound Inc. is developing a 3 generation network music player. You have been asked to complete the capital budget for this project. So far, you have compiled the following information:  The project will last for four years.  The initial investment in equipment is $12 million.  The salvage value of the equipment will be $4 million.  The equipment will be depreciated to $2 million over the next four years using straight-line depreciation.  The project needs an initial investment in net working capital of $0.5 million.  The corporate tax rate is 30%.  The cost of capital is 10%.  Assume that the firm’s other projects yield a positive income before tax Additionally, you receive the following project-related information from the accounting and marketing departments (in $ million): Year 0 1 2 3 4 Net working capital 0.5 0.8 1.2 0.8 0 Sales 6 8 10 9 Cost of goods sold 3 4 5 4 Depreciation 2.5 2.5 2.5 2.5 What’s the after-tax salvage value in year 4 (in $ million)? After-tax Salvage Value = 4-0.3*(4-2) = $3.4 mil How big is the present value of the total depreciation tax shield? The depreciation tax shield (savings) each period = 0.3*2.5=0.75 Using the annuity formula in the calculator, the PV of the tax shield is: N=4, I/Y=10, PMT=0.75, FV=0, CPT PV=-2.38 , , , , Answer: $2.38 million Suppose Sound Inc. decides to depreciate the equipment straight-line to $4 million over the next four years (instead of depreciating the equipment to $2 million as in the base case). How does this new depreciation plan change the project’s NPV, assuming everything else remains constant (in $ million)? NPV decreases

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