3 Suppose Birdie is unwilling to pay cash for the merger but will consider an equity exchange. What exchange ratio would make the merger terms equivalent to the original merger price of €68.75 per share?

Birdie Golf has been in merger talks with Hybrid Golf Company for the past six months. After several rounds of negotiations, the offer under discussion is a cash offer of €550 million for Hybrid Golf. Both companies have niche markets in the golf club industry, and the companies believe a merger will result in significant synergies due to economies of scale in manufacturing and marketing, as well as significant savings in general and administrative expenses.
Bryce Bichon, the financial officer for Birdie, has been instrumental in the merger negotiations. Bryce has prepared the following pro forma financial statements for Hybrid Golf assuming the merger takes place.
The financial statements include all synergistic benefits from the merger:
2020 (€) 2021 (€) 2022 (€) 2023 (€) 2024 (€)
Sales 800,000,000 900,000,000 1,000,000,000 1,125,000,000 1,250,000,000 Production costs 562,000,000 630,000,000 700,000,000 790,000,000 875,000,000 Depreciation 75,000,000 80,000,000 82,000,000 83,000,000 83,000,000 Other expenses 80,000,000 90,000,000 100,000,000 113,000,000 125,000,000 EBIT 83,000,000 100,000,000 118,000,000 139,000,000 167,000,000 Interest 19,000,000 22,000,000 24,000,000 25,000,000 27,000,000 Taxable income 64,000,000 78,000,000 94,000,000 114,000,000 140,000,000 Taxes (40%) 25,600,000 31,200,000 37,600,000 45,600,000 56,000,000 Net income 38,400,000 46,800,000 56,400,000 68,400,000 84,000,000 Bryce is also aware that the Hybrid Golf division will require investments each year for continuing operations, along with sources of financing. The following table outlines the required investments and sources of financing:
2020 (€) 2021 (€) 2022 (€) 2023 (€) 2024 (€)
Investments:
Net working capital 20,000,000 25,000,000 25,000,000 30,000,000 30,000,000 Non-current assets 15,000,000 25,000,000 18,000,000 12,000,000 7,000,000 Total 35,000,000 50,000,000 43,000,000 42,000,000 37,000,000 Sources of financing:
New debt 35,000,000 16,000,000 16,000,000 15,000,000 12,000,000 Profit retention 0 34,000,000 27,000,000 27,000,000 25,000,000 Total 35,000,000 50,000,000 43,000,000 42,000,000 37,000,000 The management of Birdie Golf feels that the capital structure at Hybrid Golf is not optimal. If the merger takes place, Hybrid Golf will immediately increase its leverage with a €110 million debt issue, which would be followed by a €150 million dividend payment to Birdie Golf. This will increase Hybrid’s debt-to-equity ratio from 0.50 to 1.00. Birdie Golf will also be able to use a €25 million tax loss carry-forward in 2021 and 2022 from Hybrid Golf’s previous operations. The total value of Hybrid Golf is expected to be €900 million in five years, and the company will have €300 million in debt at that time.
Equity in Birdie Golf currently sells for €94 per share, and the company has 18 million shares of equity outstanding. Hybrid Golf has 8 million shares of equity outstanding. Both companies can borrow at an 8 per cent interest rate. The risk-free rate is 6 per cent, and the expected return on the market is 13 per cent.
Bryce believes the current cost of capital for Birdie Golf is 11 per cent. The beta for Hybrid Golf equity at its current capital structure is 1.30.