Consider a publicly traded firm which is currently financed by equity

only. Due to the poor performance of the company, a group of investors plan to buy

up all shares of the firm and reorganize the company to make it profitable again.

Currently, the company has $150000$ shares outstanding, and the share price at the

moment is $$35.$ The firm currently has a required return on equity of $15\%.$ For the

next five years after taking over the firm, the investors have the following estimates:

Year $1$ Year $2$ Year $3$ Year $4$ Year $5$

Sales $$2\mathrm{.}5$M $$2\mathrm{.}7$M $$2\mathrm{.}9$M $$3$M $$3\mathrm{.}1$M

Costs $$0\mathrm{.}6$M $$0\mathrm{.}8$M $$0\mathrm{.}9$M $$1$M $$1\mathrm{.}1$M

Depreciation $$0\mathrm{.}4$M $$0\mathrm{.}45$M $$0\mathrm{.}49$M $$0\mathrm{.}5$M $$0\mathrm{.}55$M

Capital expenditures $$0\mathrm{.}25$M $$0\mathrm{.}25$M $$0\mathrm{.}2$M $$0\mathrm{.}2$M $$0\mathrm{.}25$M

Change in net working capital $-$$$0\mathrm{.}1$M $-$$$0\mathrm{.}15$M $$0\mathrm{.}1$M $$0\mathrm{.}1$M $$0\mathrm{.}1$M

Asset sales$*$ $$1\mathrm{.}5$M $$1$M $$0\mathrm{.}5$M

After the $5$th year, the company$$s cash flow is expected to grow at a rate of $4\%$ per

year. As part of the reorganization, the investors plan to change the capital

structure of the company as well. Namely, from the all$-$equity capital structure

they plan to switch to a partial debt financing. In the first five years, the firm will

pay the following annual interests: $$150,000$; $$180,000$; $$200,000$; $$195,000$;

$$210,000.$ These correspond to an interest rate of $12\%.$ Starting from the $6$th year,

the firm will have a debt$-$equity ratio of $50\%,$ and the interest rate on debt from the

$6$th year will be $8\%,$ according to the forecasts. The tax rate is $25\%.$

Although the current stock price is $$35$ per share, the investors are very optimistic

about the company and they are willing to pay an even higher price for the shares.

What is the highest price they should be willing to pay per share, based on their

forecasts above?

$*$Asset sales$$ refers to the revenue earned by selling certain fixed assets. These

are after$-$tax values.