Assignment #2_Spring2024_Solutions

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Corporate Finance (BFIN 2036) Spring 2024 Problem Set #2 SOLUTIONS Classes 4-5: Corporate Valuation & Capital Structure Format: Turn in hard copy of Answers at beginning of class on 21-Feb-2024 . Special Instructions: This is an individual assignment meant to evaluate your understanding of concepts covered in the course. You are not to seek help from others (whether or not they are currently enrolled in this course); nor offer help to others. Content: • This 11-question, 100-point problem set in conjunction with the text and class discussion Assignment: This is the second problem set for Corporate Finance. Your goal in working through these problems is threefold: 1. Ensure understanding of the topics covered so far this semester 2. Application of analytical skills to problems that may be stated in unfamiliar ways 3. Preparation for the Mid-Term and Final Exams You can solve these problems with a calculator or spreadsheets, but depending on the then-prevailing University status, the exams may be calculator-only. You should have facility with the solution process unaided by spreadsheets and their accompanying built-in formulas. Write directly on the sheets and show your work. Feel free to attach additional sheets if you like. Please print out single-sided .

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 1 Problem Set #2 Name: Answer Key

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 2 #1 Finding the Beta ( 8 points ) ReliaForge was a private company and so had no way to easily discern the beta of its equity. But ReliaForge participated in the brass forging industry where there were a few competitors that were publicly traded. Unfortunately, each of the competitors had considerably different debt-to-total capital levels than ReliaForge, whose Debt-to-Total Capital target was 30%. Nonetheless, with the following data, ReliaForge was sure that it could calculate its own beta. Brass Fabrication ($ 000s) MV of Enterprise Listed Unlevered Sales Debt Equity Value β β LiteCo $350,000 $51,000 $176,000 $227,000 1.30 1.06 StrongCo $183,000 $26,000 $100,000 $126,000 1.51 1.25 RecyclableCo $110,000 $5,000 $85,000 $90,000 1.74 1.66 Marginal Tax Rate 21% What is ReliaForge ’s levered Equity Beta ? (Hint: Make sure that, when you find the averages, you weight the averages by the respective enterprise values.) Brass Fabrication ($ 000s) MV of Enterprise Listed Unlevered Sales Debt Equity Value β β LiteCo $350,000 $51,000 $176,000 $227,000 1.30 1.06 StrongCo $183,000 $26,000 $100,000 $126,000 1.51 1.25 RecyclableCo $110,000 $5,000 $85,000 $90,000 1.74 1.66 Marginal Tax Rate 21% Weighted Average 1.24 b u (est.) 1.24 (industry average) b L 1.65 (assumes target leverage of 30% for ReliaForge) =1.24*(1+3*(1-0.21)/7)

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BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 3 #2 Cost of Capital Mechanics ( 10 points ) It is October 1, 2023, and Reliant Systems is trying to determine the WACC it should use in discounting its projects. It issued 25-year debt 10 years ago (at par of $1,000), so it has 15 years remaining until maturity. Here are the relevant facts for the company: • Unlevered Equity Beta 0.89 • Debt-to-Equity Ratio Target 0.30 • Rm-Rf (market risk premium) 5.5% • Rf (risk-free rate) 2.2% • Coupon on 30-year bonds 6.50% • Today's Date 2/1/2020 • Bond Maturity Date 2/1/2035 • Today's Bond Price $1,080 • Coupons per year 2 • Tax Rate 21% What is the current WACC of Reliant? (Hint: You will have to calculate the levered cost of equity and you will also have to estimate the cost of debt by determining the YTM of the bond .) D/D+E 0.231 E/D+E 0.769 Cost of Equity:Unlevered 7.10% Levered Beta 1.10 Cost of Equity Levered 8.26% Cost of Debt (YTM) 5.70% WACC 7.39%

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 4 #3 Determining Cost of Capital I ( 6 points ) Lycera Corporation (NYSE:LYC) was evaluating several small capital projects but didn’t know what discount rate to use. It had the following data: • The 10-year Treasury was trading at about 1.9%. • The tax rate is 21% • LYC’s stock price was $49/share, and it had 9 million shares outstanding • According to its investment banker, LYC stock (equity) had a levered beta of 1.65. • Three years ago, LYC issued 20-year bonds with a coupon of 6.5%, but the current yield to maturity on the bonds was about 5.5%, giving the bonds a market value of $190 million. • Ibbotson Associates indicated that, for the past 50 years, equity returns exceeded bond returns by 6.0%. What discount rate should LYC use? Inputs Shares Outstanding 9,000,000 Share Price $ 49.00 MV of Equity $441,000,000 MV of Debt $190,000,000 Interest Cost 5.50% Stock Beta 1.65 Tax Rate 21% 10-Year Treasury 1.90% Market Risk Premium 6.0% Outputs Cost of Equity 11.80% Total Capital $631,000,000 Debt-to-Total Capital 30% Equity-to-Total Capital 70% Calculation WACC 9.56%

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 5 #4 Determining Cost of Capital II ( 6 points ) Using the following data, determine the Weighted Average Cost of Capital (WACC) for Sortac Corporation: • Asset (unlevered) Beta: 1.02 • Debt: $450 million • Average Interest Rate on indebtedness: 6.95% • Shares Outstanding: 110 million • Recent Share Price: $8.50/share • Market Risk Premium: 5.5% • 10-Year U.S. Government Bond Yield: 1.9% • Corporate Tax Rate: 21% Asset Beta 1.02 Debt $ 450,000,000 Average Interest Rate 6.95% Shares Outstanding 110,000,000 Price/Share $8.50 Market Risk Premium 5.5% Risk Free Rate 1.900% Tax Rate 21% Equity $935,000,000 Equity Beta 1.41 Total Capitalization $ 1,385,000,000 Cost of Equity 9.6% WACC= 8.29%

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BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 6 #5 Debt Levels and WACC ( 8 points ) Debt is cheaper than equity, primarily because it has a superior claim on a firm’s assets; and secondarily because the cost of debt (interest expense) is subsidized by the government via the interest tax shield. As a result, it would seem that increasing debt as a part of the total firm capital structure would reduce the cost of capital. (a) Calculate the WACC for each of the ten combinations of debt and equity below. D-TC Ke Kd Tax Rate WACC 0% 8.0% 6.0% 21% 8.00% 10% 8.3% 6.3% 21% 7.97% 20% 8.6% 6.7% 21% 7.94% 30% 9.0% 7.0% 21% 7.96% 40% 12.1% 8.0% 21% 9.79% 50% 13.9% 9.0% 21% 10.51% 60% 16.2% 11.0% 21% 11.69% 70% 18.7% 16.0% 21% 14.46% 80% 23.0% 21.0% 21% 17.87% 90% 28.5% 25.5% 21% 20.98% (b) In this particular example, what debt level minimizes the Cost of Capital? 20% Debt-to-Total Capital gives the lowest WACC at 7.94%. (Note that this is for this example only; different fact sets and circumstances may lead to many different outcomes.) (c) How would you explain the fact that, at high debt levels, the WACC actually increases even as the proportion of lower-cost-than-equity debt rises? In other words, what cost increases with increasing levels of debt? Even though debt is always cheaper than equity at any given level of indebtedness, increasing amounts of debt increase the financial risk (that is, the risk of distress that can lead to insolvency). To offset that growing risk, lenders charge higher and higher interest rates as leverage grows. A financially risky firm, as a result, faces a higher return requirement for all of its capital providers and, therefore, a higher hurdle rate.

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 7 #6 Terminal Value ( 7 points ) SignalClear is thinking of building a factory in Lisbon that will have an estimated life of at least 50 years. SignalClear is trying to do a valuation of the project: The factory project will have a significant upfront capital cost, but it will allow SignalClear to add incremental business, since Eurozone import restrictions block SignalClear from importing its products made in its Taiwanese factory. There will be rapid growth in sales and margin in the early years, but the growth will level out after seven years and subsequently grow at the pace of the overall market. Economists project that inflation will be 2% at that time, and overall unit demand should grow at 1% p.a. The SignalClear WACC is 11.3%, In Year 7 the EBIT will be $2,165,000, capex will exceed annual depreciation of $210,000 by $17,000, the tax rate is 30%, and working capital will increase by $37,000. Subsequently, EBIT, capex, depreciation, and working capital will all grow at the same rate as Revenue. SignalClear will forecast actual cash flows for 7 years. What present value should SignalClear use to represent years 8 and forward? SignalClear WACC 11.30% a Inflation 2% b GDP Growth 1% c Terminal Growth Rate 3% d=b+c Year 7 Cash Flow EBIT 2,165,000 Less Taxes (649,500) 30% Net Income 1,515,500 Add Back: Depreciation 210,000 Less Capital Expend. (227,000) Less Incr. in W/C (37,000) Free Cash Flow 1,461,500 e Year 8 CF increased by g 1,505,345 f=e*(1+d) Divisor 8.30% g=a-d Perpetuity 18,136,687 h=f/g Discount Factor 2.116 i=(1+a)^7 Present Value of TV 8,572,190 j=h/i

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 8 #7 Capital Budget Decision-Making ( 12 points ) SafeTraffic, Inc. is considering the $321,000 purchase of a machine that will allow it to produce aluminum red light camera enclosures for 5 years, after which the machine will no longer be serviceable. The production data, discount rate, and tax rate are shown below: Should SafeTraffic purchase the machine? (Show why or why not.) Since the NPV is negative, this indicates that the company should not purchase the machine given the forecasted operating parameters. Initial investment 321,000 $ Depreciation straight-line over life (Years) 5 Units sold Annually 3,600 Cost per unit 23.89 $ Price per unit 49.95 $ Tax rate 21% Required return 14% 0 1 2 3 4 5 Revenue 179,820 179,820 179,820 179,820 179,820 Costs 86,004 86,004 86,004 86,004 86,004 Depreciation 64,200 64,200 64,200 64,200 64,200 IBT 29,616 29,616 29,616 29,616 29,616 Taxes 6,219 6,219 6,219 6,219 6,219 IAT 23,397 23,397 23,397 23,397 23,397 Depreciation 64,200 64,200 64,200 64,200 64,200 OCF 87,597 87,597 87,597 87,597 87,597 Init. Investment (321,000) $ CF (321,000) $ 87,597 $ 87,597 $ 87,597 $ 87,597 $ 87,597 $ Discount Factor 1.000 0.877 0.769 0.675 0.592 0.519 Discounted Cash Flows (321,000) $ 76,839 $ 67,403 $ 59,125 $ 51,864 $ 45,495 $ Sum of DCF (20,274) $

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BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 9 #8 Firm Valuation ( 7 points ) The following is a forecast for a potential acquisition. You think you will need to offer $48 million and that you will immediately have to invest an additional $7 million in working capital to keep the company running. You create a forecast for five years and include an estimate of the terminal value. In addition, there are some key assumptions used in building this pro forma forecast: • Discount rate: 11.1% • Terminal growth rate: 2.0% A. Should you make this investment (i.e., what is the NPV)? B. What is the IRR of the cash flows? C. Show how the nominal (FV) terminal value of $67.1 million was calculated. (Final Year Cash Flow * (1 + 2%)) ÷ (11.1 % ˗ 2%) ($5,985,892 * (1.02) ÷ (9.1%) = $67,094,619 Year 0 1 2 3 4 5 Sales 42,237,000 $ 61,873,500 $ 71,877,000 $ 78,175,500 $ 79,287,000 $ Variable costs 37,050,000 54,275,000 63,050,000 68,575,000 69,550,000 Fixed costs 2,500,000 2,575,000 2,652,250 2,731,818 2,813,772 Depreciation 6,240,000 11,760,000 8,400,000 6,000,000 4,272,000 EBIT (3,553,000) (6,736,500) (2,225,250) 868,683 2,651,228 Taxes (746,130) (1,414,665) (467,303) 182,423 556,758 Net income (2,806,870) (5,321,835) (1,757,948) 686,259 2,094,470 Depreciation 6,240,000 11,760,000 8,400,000 6,000,000 4,272,000 Operating cash flow 3,433,130 $ 6,438,165 $ 6,642,053 $ 6,686,259 $ 6,366,470 $ Net cash flows Operating cash flow - $ 3,433,130 $ 6,438,165 $ 6,642,053 $ 6,686,259 $ 6,366,470 $ Change in Net Working Cap (7,000,000) (3,141,840) (1,600,560) (1,007,760) (177,840) (380,578) Acquisition Price (48,000,000) - - - - - Terminal Value 67,094,619 Total cash flow (55,000,000) $ 291,290 $ 4,837,605 $ 5,634,293 $ 6,508,419 $ 73,080,512 $ Discount Factor 1.00 1.11 1.23 1.37 1.52 1.69 PV of Cash Flow (55,000,000) $ 262,187 $ 3,919,244 $ 4,108,632 $ 4,271,882 $ 43,174,895 $ Net present value 736,840 $ Total cash flow (55,000,000) $ 291,290 $ 4,837,605 $ 5,634,293 $ 6,508,419 $ 73,080,512 $ Internal rate of return 11.43%

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 10 #9 Costs of Capital in an Acquisition ( 8 points ) Copernicus Corporation is trying to decide how to evaluate an acquisition. The market value of its equity is $1.2 billion and it has no debt. Its investment bank, Moneydollar Capital, has told management that the beta of Copernicus stock is 1.48; that the risk-free rate is 2.5%; and that the long-term market returns for all stocks are averaging 8%. Moneydollar Capital is urging Copernicus to buy Callisto for $465 million. Moneydollar’s plan is for Copernicus to borrow the $465 million in the bond market and that the bonds would have a yield of 5.7%. The expected corporate tax rate is 21%. a) What is the current (pre-borrowing) Weighted Average Cost of Capital for Copernicus? b) What discount rate should Copernicus use in assessing the combined cash flows of Copernicus and Callisto if Copernicus uses the cash from its bond offering to buy Callisto and then intends to maintain that new debt-to-equity ratio indefinitely? HINT: β levered = β Unlevered *(1 + (D*(1-T c ) / E)) #1 Current Equity 1,200 Unlevered (asset) beta 1.48 Market expected return 8.0% Risk-free rate 2.5% Market Risk Premium 5.5% Cost of equity (Unlevered) 10.64% Cost of Debt n/a WACC 10.64% #2 with Callisto Acquisition/Debt Issuance Equity 1,200 Debt 465 Unlevered (asset) beta 1.48 Levered Beta 1.93 Market expected return 8.0% Risk-free rate 2.5% Market Risk Premium 5.5% Levered cost of equity 13.13% Cost of Debt 5.70% WACC 10.72%

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 11 #10 Impact of Required Return ( 10 points ) EZ-Pro, Inc. has the opportunity to engage in a 5-year marketing agreement with a Chilean distributor. The license fee it must pay is $45 million. In exchange, it will have the opportunity to earn after-tax cash flows of $11.3 million annually for the life of the agreement. The company will finance the opportunity using the same capital structure (debt-to-total capital ratio) that it has today, which management also considers EZ-Pro ’s target capital structure. These are the relevant data for EZ-Pro: Shares outstanding: 10.5 million Current price per share: $12.50 per share Bonds outstanding: $21.0 million @ 7% Stock beta: 1.15 Treasury Bill rate: 2.5% Current Market Risk Premium 6.0% Tax Rate: 21% (a) What is the NPV of the project for EZ-Pro? Input Area: Year 0 1 2 3 4 5 ($000s) Cash Flow (45,000) $ 11,300 $ 11,300 $ 11,300 $ 11,300 $ 11,300 $ Discount Factor 1.000 1.089 1.185 1.290 1.405 1.529 Beta of Stock 1.15 Market risk premium 6.00% Present Value (45,000) $ 10,380 $ 9,534 $ 8,758 $ 8,045 $ 7,389 $ Bond value 21,000 $ Bond YTM 7% Sum of PV (894) $ Shares outstanding 10,500,000 Price per share 12.50 $ Tax rate 21% Treasury bill rate 2.5% Project cost 45,000 $ Unlevered cash flows 11,300 $ Project length 5 Output Area: Market value of equity 131,250 $ Total enterprise value 152,250 $ Weight of debt 0.1379 Weight of equity 0.8621 Beta of stock 1.15 Expected return on stock 9.40% WACC 8.87% NPV (893.93) $

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BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 12 (b) EZ-Pro ’s main competitor, MultiStar, is also in talks with the same Chilean distributor. MultiStar is identical in all regards to EZ-Pro with one exception: MultiStar ’s levered stock beta is 0.93. What is the NPV of the project for MultiStar? Since it is exactly the same project, why does MultiStar reach a different conclusion than EZ-Pro? (To show the difference you will have to complete an NPV analysis as you did for Part (a).) EZ-Pro reaches a different conclusion because its investors are demanding a higher return than MultiStar investors (i.e., EZ- Pro’s hurdle rate is higher than MultiStar’s) because the inherent operating risk of its assets is apparently higher. Even though the project has the same financial outcomes for both firms, the returns provided by the project are acceptable to MultiStar’s less demanding investors, whereas EZ- Pro’s investors, facing higher firm risk, are not similarly satisfied. Input Area: Year 0 1 2 3 4 5 ($000s) Cash Flow (45,000) $ 11,300 $ 11,300 $ 11,300 $ 11,300 $ 11,300 $ Discount Factor 1.000 1.077 1.161 1.250 1.347 1.451 Beta of Stock 0.93 Market risk premium 6.00% Present Value (45,000) $ 10,489 $ 9,737 $ 9,038 $ 8,390 $ 7,788 $ Bond value 21,000 $ Bond YTM 7% Sum of PV 443 $ Shares outstanding 10,500,000 Price per share 12.50 $ Tax rate 21% Treasury bill rate 2.5% Project cost 45,000 $ Unlevered cash flows 11,300 $ Project length 5 Output Area: Market value of equity 131,250 $ Total enterprise value 152,250 $ Weight of debt 0.1379 Weight of equity 0.8621 Beta of stock 0.93 Expected return on stock 8.08% WACC 7.73% NPV 442.59 $

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 13 #11 Synergy and Acquisitions ( 18 points ) SoyGen Corporation, a 100%-equity capitalized soy bean processing company, wants to diversify into the corn wet milling business by buying Fructalore Corporation, also 100%-equity capitalized. SoyGen estimates that by reducing overhead and combining marketing efforts, it could increase after-tax cash flow by $2,925,000 per year in perpetuity above the standalone cash flow of the two companies on their own. The current stock market value of Fructalore (which you consider to be its fair value as well) is $70,200,000 and the current market value of SoyGen is $202,500,000. SoyGen has calculated that its cost of capital is 10%. Fructalore has tentatively agreed to be acquired for either an all-cash offer of $99,000,000; or for 30% of SoyGen stock. (Assume that SoyGen has more than enough cash on its balance sheet if it pays cash; and that it would exchange newly-issued shares of the combined company for a stock purchase. HINT: You do not need to make a multi-year pro forma forecast, since you can assume that the market values of the two companies equal the NPV of the forecasted cash flows of the two companies on a standalone basis.) a) What is the synergy value of the merger? b) What is the total value of Fructalore to SoyGen? c) What is the cost of the cash purchase? What is the NPV to SoyGen of the cash purchase? d) What is the cost of the stock purchase? What is the NPV to SoyGen of the stock purchase? e) Which alternative form of payment should SoyGen pick? f) Say that, for tax reasons, Fructalore withdraws its current proposal and instead demands 35% of the stock of the combined company. What does this do to SoyGen ’s NPV? Should SoyGen meet the new demand? Input Area: Incremental aftertax cash flows 2,925,000 $ (a) Fructalore 70,200,000 $ (b) SoyGen 202,500,000 $ (c) Discount rate 10.0% (d) Stock offer 30% (e) Cash offer 99,000,000 $ (f) Output Area: a. Synergy value 29,250,000 $ (g) = a/d b. Value to acquirer 99,450,000 $ (h) = b+g c. Cost of cash acquisition 99,000,000 $ (i) = f NPV of cash acquisition 450,000 $ = h-i d. Cost of stock acquisition 90,585,000 $ (j) = e*(c+h) NPV of stock acquisition 8,865,000 $ = h-j e. Choice? Aquire the company for stock.

BFIN 2036 Corporate Finance- Spring 2024 MBA/MS Page 14 #11 Synergy and Acquisitions (Additional workspace) Input Area: Incremental aftertax cash flows 2,925,000 $ (a) Fructalore 70,200,000 $ (b) SoyGen 202,500,000 $ (c) Discount rate 10.0% (d) Stock offer 35% (e) Cash offer 99,000,000 $ (f) Output Area: a. Synergy value 29,250,000 $ (g) = a/d b. Value to acquirer 99,450,000 $ (h) = b+g c. Cost of cash acquisition 99,000,000 $ (i) = f NPV of cash acquisition 450,000 $ = h-i d. Cost of stock acquisition 105,682,500 $ (j) = e*(c+h) NPV of stock acquisition (6,232,500) $ = h-j f. Choice? Decline the Counteroffer.

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