Cheek Products, Inc. $($CPI$),$ was founded $53$ years ago by Joe Cheek and originally sold snack foods such as potato chips and pretzels. Through acquisitions, the company has grown into a conglomerate with major divisions in the snack food, home security systems, cosmetics$,$ and plastics industries. Additionally, the company has several smaller divisions. In recent years, the company has been underperforming, but the company$$s management doesn$$t seem to be aggressively pursuing opportunities to improve operations $($or the stock price$).$

Meg Whalen is a financial analyst specializing in identifying potential buyout targets. She believes that two major changes are needed at CPI. First, she thinks that the company would be better off if it sold several divisions and concentrated on its core competencies in snack foods and home security systems. Second, the company is financed entirely with equity. Because the cash flows of the company are relatively steady, Meg thinks the company$$s debt$-$equity ratio should be $25$ percent. She believes these changes would significantly enhance shareholder wealth, but she also believes that the existing board and company management are unlikely to take the necessary actions. As a result, Meg thinks the company is a good candidate for a leveraged buyout.

A leveraged buyout $($LBO$)$ is the acquisition by a small group of equity investors of a public or private company. Generally, an LBO is financed primarily with debt. The new shareholders service the heavy interest and principal payments with cash from operations and$/$or asset sales. Shareholders generally hope to reverse the LBO within three to seven years by way of a public offering or sale of the company to another firm. A buyout is therefore likely to be successful only if the firm generates enough cash to service the debt in the early years and if the company is attractive to other buyers a few years down the road.

Meg has suggested the potential LBO to her partners, Ben Feller and Brenton Flynn$.$ Ben and Brenton have asked Meg to provide projections of the cash flows for the company. Meg has provided the following estimates $($in millions$)$:

At the end of five years, Meg estimates that the growth rate in cash flows will be $3\mathrm{.}5$ percent per year. The capital expenditures are for new projects and the replacement of equipment that wears out. Additionally, the company would realize cash flow from the sale of several divisions. Even though the company will sell these divisions, overall sales should increase because of a more concentrated effort on the remaining divisions.

After plowing through the company$$s financials and various pro forma scenarios, Ben and Brenton feel that, in five years, they will be able to sell the company to another party or take it public again. They also are aware that they will have to borrow a considerable amount of the purchase price. The interest payments on the debt for each of the next five years if the LBO is undertaken will be $($in millions$)$:

$20222023202420252026$

Interest payments $$1,690$ $$1,935$ $$2,280$ $$2,225$ $$2,300$

The company currently has a required return on assets of $14$ percent. Because of the high debt level, the debt will carry a yield to maturity of $12\mathrm{.}5$ percent for the next five years. When the debt is refinanced in five years, they believe the new yield to maturity will be $8$ percent.

CPI currently has $215$ million shares of stock outstanding that sell for $$29$ per share. The corporate tax rate is $21$ percent. If Meg, Ben, and Brenton decide to undertake the LBO, what is the most they should offer per share?