Question

4. You are the CEO of Valu-Added Industries, Inc. (VAI). Your firm has 10,000 shares of common stock outstanding, and the current price of the stock is $100 per share. There is no debt; thus, the “market value” balance sheet of VAI looks like:

VAI Market Value Balance Sheet
Assets $1,000,000 Equity $1,000,000

You then discover an opportunity to invest in a new project that produces positive cash flows with a present value of $210,000. Your total initial costs for investing and developing this project are only $110,000. You will raise the necessary capital for this investment by issuing new equity. All potential purchasers of your common stock will be fully aware of the project’s value and cost, and are willing to pay “fair value” for the new shares of VAI common.

• What is the Net Present Value of this project?

• How many shares of common stock must be issued (at what price) to raise the required

  capital?

• What is the effect of this new project on the value of the stock of the existing shareholders, if any?

Answer 1

Solution :-

(A) NPV of this project =

= Present value of cash inflow - Present value of cash outflows

= $210000 - $110000 = $100000

(B) Total assets of the company before this project = $1000000

To. Assets after this project =

= $1000000 + $100000 = $1100000

No. Of shares before new issue = 10000

Now assume new number of shares to be issue = N

And the price of share after the issue = P

Therefore total new shares = 10000+N

Now P = (old equity + NPV of project) / old no. Of shares.

= P = (1000000 + 100000) / 10000 = $110

Now N*P = 110000 (as we want to raise this capital from new shares).

Now N = 110000/P = 110000/110 = 1000 shares

Therefore we want to issue 1000 shares at price $110

(C)

The effect of this new project on the existing shareholder is that his price increases to $110 from $100

They will get $10 per share

Total assets = $1000000(old assets) + $110000(new introduced) + $100000(NPV) = $1210000

new shares = 10000 + 1000 = 11000

new share price = 1210000/11000 = $110

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