Stockholm School of Economics in Riga Financial Economics, Spring 2010 Tālis Putniņš

Problem Set XI: Capital budgeting/valuation with leverage; and mergers and acquisitions Exercise 1: Capital budgeting and valuation Walter Corp (WC) has the opportunity to invest $1 million now (t = 0) and expects after-tax returns of $600,000 at t = 1 and $700,000 at t = 2. The project will last for two years only. The appropriate cost of capital is 12% with all equity financing, the borrowing rate is 8% and WC will borrow $300,000 against the project. The debt must be repaid in two equal instalments. The corporate tax rate is 30%. Calculate the project’s APV.

Exercise 2: Capital budgeting and valuation In year 1 Kimmel Corp. will earn $2000 before interest and taxes. The market expects these earnings to grow at 3% per year. The firm will make no net investments or changes to net working capital. The corporate tax rate equals 40% and the firm has $5000 debt, which is effectively risk free. Kimmel plans to keep a constant D/E ratio, so that on average the debt will grow at a rate of 3% per year. The risk free rate is 5% and expected return on the market is 11%. The asset beta for this industry is 1.11. a) If Kimmel were an all-equity (unlevered) firm, what would its market value be? b) Assuming the debt is fairly priced, what how much interest will Kimmel pay in year 1? c) Even though Kimmel’s debt is risk free, the future growth of the debt is uncertain because it depends on the value of the firm. What is the present value of the tax shields? d) Using the APV method, what is Kimmel’s total levered market value? What is Kimmel’s market value of equity? e) What is Kimmel’s WACC? f) From WACC calculate Kimmel’s cost of equity?

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g) Assuming that proceeds from increases in debt are paid out to equity holders, use the FCF to equity method to find the market value of equity. How does that compare to your answer in (d)?

Exercise 3: Capital budgeting and valuation Consider a perpetual project that requires an initial investment of $1 million and produces a pre-tax cash inflow of $95,000 per year in perpetuity. The cost of capital with all-equity financing is 10% and the project allows the firm to firm to borrow at 7%. The corporate tax rate is 35%. Use APV to calculate the project’s value under the following two scenarios: a) The project will be partly financed with $400,000 of debt which is fixed in perpetuity. b) The initial borrowing of $400,000 will be increased or reduced in proportion to changes in the future market value of the equity to maintain a target D/E ratio. Explain the difference between your answers to (a) and (b).

Exercise 4: Capital budgeting and valuation Now suppose that the project described in the previous exercise will be undertaken by a university. Funds for the project will be withdrawn from the university’s endowment, which is invested in a widely diversified portfolio of stocks and bonds. However, the university can also borrow at 7%. The university is tax exempt. The university treasurer proposes to finance the project by issuing $400,000 of perpetual bonds at 7% and by selling $600,000 worth of common stocks from the endowment. The expected return on common stocks is 10%. He therefore proposes to evaluate the project by discounting at a weighted average cost of capital, calculated as: E D  rE V V  400,000   600,000   0.07   0.10   1,000,000   1,000,000 

WACC  rD

 8 .8 %

What is right or wrong about the treasurer’s approach? Should the university invest in the project? Would the project’s value to the university change if the treasurer financed the project entirely by selling common stocks from the endowment?

Exercise 5: Capital budgeting and valuation Gulbenes Corp. is assessing its capital structure. In January 2010 its equity had a market value of $24.27 billion, its debt had a market value of $2.8 billion and an AAA rating. Its equity beta is 1.47 and it faces a corporate tax rate of 40%. The Treasury bond yield is 6.5% and corporate AAA bonds are trading at a spread of

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0.30% over the Treasury rate. The expected stock market premium is 5.5%. Gulbenes Corp. has a policy of rebalancing its capital structure to maintain a target D/E ratio and its bonds are frequently refinanced at market rates. a) Estimate the current cost of capital for Gulbenes Corp. b) If Gulbenes Corp. moves to a debt-to-equity ratio of 30% it is estimated its bonds will have a BBB rating. BBB bonds have a spread of 2% over the Treasury rate. Estimate the cost of capital if Gulbenes Corp. moves to this new debt-to-equity ratio. c) Assuming a constant growth rate of 6% in the firm’s value, how much will firm value change if management decides to move to the debt-to-equity ratio of 30%? What will the effect be on the stock price?

Exercise 6: Capital budgeting and valuation Lāčplēsis Corp. is assessing whether it should increase its leverage and you have been hired as a consultant. The firm has $527 million in market value of debt and $1.76 billion in market value of equity. The firm has EBIT of $131 million and faces a corporate tax rate of 36%. The company’s bonds are rated BBB and the cost of debt is 8%. At this rating the firm has a probability of default of 2.30% and the present value of bankruptcy costs is 30% of the firm’s value without its tax shields. The Tbond rate is 6%. Lāčplēsis Corp. has a policy of holding the level of its debt fixed in perpetuity, and the debt is frequently refinanced at market rates. a) Estimate the unlevered value of the firm. b) Estimate the levered value of the firm at a debt-to-equity ratio of 50%. At that level of leverage the firm’s bond rating would be CCC with a default probability of 46.61%. c) Would you recommend Lāčplēsis Corp. moves to the higher debt-to-equity ratio?

Exercise 7: Mergers and acquisitions Aldaris Corp. currently has EPS = $2.00, but management are keen to report EPS = $2.67. Management therefore decides to acquire Cēsu Corp. even though there are no economic gains form the merger. Aldaris Corp. issues just enough of its own shares to ensure its $2.67 EPS objective. You are given the following data on the companies:

EPS Price per share P/E ratio Number of shares Total earnings Total market value

Aldaris Corp $2.00 $40 20 100,000 $200,000 $4m 3

Cēsu Corp $2.50 $25 10 200,000 $500,000 $5m

Merged firm $2.67 ? ? ? ? ?

a) Complete the table above for the merged firm. b) How many shares of Aldaris Corp. are exchanged for each share of Cēsu Corp.? c) What is the cost of the merger to Aldaris Corp.? d) What is the change in the total market value of the Cēsu Corp. shares that were outstanding before the merger?

Exercise 8: Mergers and acquisitions Consider two small firms, Jubilejas Corp. and Senču Corp., that operate independently and have the following financial characteristics:

Revenue - COGS EBIT Expected growth rate Cost of capital

Jubilejas Corp. $8,000 $6,000 $2,000 4% 9%

Senču Corp. $4,000 $2,400 $1,600 6% 10%

Both firms are in steady state, with capital spending offset by depreciation. No working capital is required, and both firms face a tax rate of 50% a) Find the value of the combined (merged) firm if no synergies are realized. b) Now assume that combining the firms will create economies of scale in the form of shared distribution and advertising costs, which will reduce the cost of goods sold (COGS) from 70% of combined revenues ($8,400/$12,000) to 65% of combined revenues. This synergy is as risky as the combined enterprise. Estimate the value of the synergy. c) Now consider an alternative synergy. Suppose that as a result of the merger the combined firm is able to enter new markets and is expected to increase the future growth in the revenue of the combined entity to 6%. Also assume that the cost of goods sold is expected to remain at 70% of revenues. Estimate the value of the revenue enhancement synergy assuming it is as risky as the combined enterprise.

Exercise 9: Mergers and acquisitions Inčukalna Corp. and Lodiņa Corp. have agreed to merge in response to increased competition in the industry. The merger is of strategic significance in that the combined group will have a stronger global business presence. The feasibility of the merger, however, hinges on potential revenue enhancements that would come from increased pricing power. The CFOs of both firms have agreed that incremental revenues equal to 6% of existing annual revenue could be achieved due to crossselling of products to each customer base. To achieve this, $40 million would have to 4

be spent initially in restructuring the company (no ongoing expenses) and the restructuring expense could be used to offset the company’s tax liability. The sum of Inčukalna Corp’s and Lodiņa Corp’s revenues (not including the revenue enhancement) was expected to grow from $300 million currently at a nominal rate of 5% p.a. The merged company is expected to have a cost of debt of 8%, cost of equity of 13% and a WACC of 9.5%. The tax rate is 30%. The risk-free rate is 5.5%. What is the expected value of the synergy?

Exercise 10: Mergers and acquisitions The fixed exchange ratio in an acquisition of Līvu Corp. by Latgales Corp. is 1.4:1. The buyer and seller agree to a floating collar, which has a low trigger of $20 and a high trigger of $40, i.e.: the exchange ratio is 1.4 to 1, unless the buyer’s stock price falls below $20, in which case the exchange ratio is equal to $28 divided by the buyer’s share price; if the buyer’s share price is greater than $40, the exchange ratio is equal to $56 divided by the buyer’s share price. Calculate and graph the number of shares issued for one share of the seller’s stock, assuming the following share prices for the buyer: $0.01, $10.00, $15.00, $20.00, $30.00, $40.00 and $50.00. Also calculate and graph the value of the bid at these prices.

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