Assume that financial markets are competitive and have no taxes or transactions costs but that the firm knows more about its value than the market does. The firm has cash worth $200.$ The firm also has existing product lines which both the firm and the market value at $500.$ The firm is an all$-$equity firm with $100$ shares outstanding.

a$)$ What is firm value?

b$)$ What is the share price?

Now a new opportunity arrives. The market realizes the firm knows more than the market about the value of the new project. Accordingly, the stock market takes the magnitude of external financing into consideration when assessing the project$$s NPV$.$

For firms similar to this one, the market's experience has been that, if the firm seeks $100$ in new capital, the NPV of the project is $1000$ on average. The following table contains data on what the market's assessment of the new project's NPV will be for different levels of all$-$equity externa financing.

External Financing Market's NPV Assessment

$01020$

$1001000$

$200960$

$300925$

$400875$

Suppose the firm knows for certain that the NPV of the new project is $900$ and does not need any external financing. It has enough in$-$house cash to fund the new opportunity without raising additional funds but it might use this new business opportunity as an excuse to raise financing.

Solve parts $($c$)$ to $($g$)$ below for each level of external financing from $100$ to $400$ dollars.

Before you move ahead to solve parts $($c$)$ to $($g$)$ below, the following will be helpful in determining the price the stock will be sold for in the new issue.

The price that the new shares will be sold for will come from the following expression:

P $=$

In this problem, the firm has no debt and the number of old shares is $100$:

P $=$

Market's Assessment of the

value of ALL Firm assets

including the new product line

MV of Debt

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

number of old shares $+$ number of new shares

$-$

Market's Assessment of the value of ALL Firm

assets including the new product line$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$100+$ number of new shares

The market's assessment of the value of all the firm's assets will be

Value of its old assets $($including cash holdings$)$

$+$ Cash raised in the new issue

$-$ Cash spent to create the new product line

$+$ Market's assessment of the value of the new product line.

The value of the new product line is not provided, but have the following relationship:

Market assessment of the value of the new product line $=$

Cash spent to create new product line

$+$ Market's assessment of the NPV of the new product line

While the amount needed to create the new product line is not given, from the last two

relationships, it is straight forward to see that you can determine the market's assessment of the

value of all the firm's asset $($including the new product line$)$ even without this information.

Once you've determined the numerical value for market's assessment of the value of the all the

firm's assets $($including the new project$),$ one can determine the number of new shares issued

from the following relationship:

Funds Raised $=$

For example if the firm issues $200$ dollars of new shares, then once you calculate the market's

assessment of the value of all the firm's assets $($including the new product line$)$ given that it is raising $200$ of external equity finance, you can solve for the number of new shares from the

following equation:

$200=$

Once you have a number of "Market's Assessment of the value of ALL Firm assets including the new product line, the expression above gives you one equation in one unknown and the number of new shares can be determined. From this, one can determine the share price P at the time of the new issue.With these expression in hand, please solve parts $($c$)$ to $($g$)$ below for each possible level of

external financing listed in the following table:

External Financing Market's NPV Assessment

$01020$

$1001000$

$200960$

$300925$

$400875$

c$)$ What will be the price at which the new shares are sold and how many new shares will the

firm issue?

d$)$ When the project is over, everyone including the market will realize that the new product

line's NPV is $900.$ What will be the share price when this happens?

e$)$ How much will the old shareholders have gained from the project?

f$)$ How much will the new shareholders have gained from the project?

g$)$ How much would the old shareholders have gained from the project if there were no lemons

problem? How much is the old shareholders loss due to lemons? $($The lemons loss may be

negative in which case it is really a gain from superior information.$)$

Once you have answered $($c$)-($g$)$ for all for possible levels of financing, then answer part $($h$)$

below:

h$)$ Which level of external financing, if any, will the firm choose?