Question

Ostea Inc. is a publicly traded beverage company with 20 million shares, trading

at $50 a share, and $400 million in debt.
The current cost of capital is 11%.

Ostea plans to borrow $300 million and buy back stock.
It expects its cost of capital to drop to 9%, if it does so.
Assuming that investors are rational and that savings from the lower cost of capital will grow 2.75% a year in perpetuity, how many shares will Ostea be able to buy back with $300 million.

Answer 1

• Old cost of capital = 11%
• New cost of capital = 9%
• Reduction in cost of capital = 2% (11%-9%)
• Growth rate of savings = 2.75%

Total savings value = Reduction in cost 2% * (1+Growth Rate 2.75%) / (New cost of capital 9% - Growth Rate 2.75%)

Total savings value = 32.88%

The rational equity share holder will incorporate this savings value into their valuation and the price will increase to = Current price $50 * (1+Savings 32.88%)

New equity value = $66.44 / share

Number of shares bought back = Total amount $300 million / Price per share $66.44

Number of shares bought back = 4,515,352 shares