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

Birdie Golf, Inc., 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 $352 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:
2012 2013 2014 2015 2016 Sales $512,000,000 $576,000,000 $640,000,000 $720,000,000 $800,000,000 Production costs 359,200,000 403,200,000 448,000,000 505,600,000 564,000,000 Depreciation 48,000,000 51,200,000 52,800,000 53,120,000 53,600,000 Other expenses 51,200,000 57,600,000 64,000,000 72,320,000 77,600,000 EBIT $ 53,600,000 $ 64,000,000 $ 75,200,000 $ 88,960,000 $104,800,000 Interest 12,160,000 14,080,000 15,360,000 16,000,000 17,280,000 Taxable income $ 41,440,000 $ 49,920,000 $ 59,840,000 $ 72,960,000 $ 87,520,000 Taxes (40%) 16,576,000 19,968,000 23,936,000 29,184,000 35,008,000 Net income $ 24,864,000 $ 29,952,000 $ 35,904,000 $ 43,776,000 $ 52,512,000 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:
2012 2013 2014 2015 2016 Investments:
Net working capital $12,800,000 $16,000,000 $16,000,000 $19,200,000 $19,200,000 Fixed assets 9,600,000 16,000,000 11,520,000 76,800,000 4,480,000 Total $22,400,000 $32,000,000 $27,520,000 $96,000,000 $23,680,000 Sources of financing:
New debt $22,400,000 $10,240,000 $10,240,000 $ 9,600,000 $ 7,680,000 Profit retention 0 21,760,000 17,280,000 17,280,000 16,000,000 Total $22,400,000 $32,000,000 $27,520,000 $26,880,000 $23,680,000 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 $71 million debt issue, which would be followed by a $96 million dividend payment to Birdie Golf. This will increase Hybrid’s debt-to-equity ratio from .50 to 1.00. Birdie Golf will also be able to use a $16 million tax loss carryforward in 2013 and 2014 from Hybrid Golf’s previous operations. The total value of Hybrid Golf is expected to be $576 million in five years, and the company will have $192 million in debt at that time.