A question regarding valuation

My question is regarding valuation, raising capital, and the price you pay. Assume a project that requires a 5000 initial investment with cash flows that look like the following: Year 0: -5000 Year 1: 750 Year 2: 810 Year 3: 875 Year 4: 945 Year 5: 1,020 Year 6: 1,102 Year 7: 1,190 Year 8: 1,285 Year 9: 1,388 Year 10: 1,499 Year 11 and beyond = 0 cash flow; project terminates after year 10 cash flow. (I rounded the above numbers; the first cash flow is 750 flat with 8% growth every year if you want to get detailed.) The project is financed entirely with equity, and the cost of equity is 9%. NPV = 1,603.51 PV of cash flows = 6,603.51 irr = 15% The number of shares currently outstanding is 1,000. Thusly, the price of stock for this company/project is \$6.60 per share (pv of cash flows discounted at 9% divided by shares outstanding). Perhaps I am getting confused in my own logic here, but my question is the following: If you wanted to raise additional capital for this project or you wanted to sell your shares of stock in this project (prior to the first cash flow), how would you do so and at what price would you sell it? The value of the stock is easily and clearly calculated to be \$6.60 per share. But at \$6.60 a share the investor will receive no return on their investment. What value is there for an investor who purchases the stock at this price? The cash flows are known outright so there is no speculation. How would you calculate the cost of stock to sell to an outsider in this situation? Hopefully, I’ve just been up too late and am misunderstanding something really obvious and simple. If anyone can help explain this for me I will greatly appreciate it. It just seems like the cost of the shares that are priced as the cost of equity will exactly negate any potential gain the shareholder will receive by paying that price.

> If you wanted to raise additional capital for this > project or you wanted to sell your shares of stock > in this project (prior to the first cash flow), > how would you do so and at what price would you > sell it? The value of the stock is easily and > clearly calculated to be \$6.60 per share. But at > \$6.60 a share the investor will receive no return > on their investment. What value is there for an > investor who purchases the stock at this price? > The cash flows are known outright so there is no > speculation. How would you calculate the cost of > stock to sell to an outsider in this situation? The cost to the stock will remain at \$6.6 and the investor will realise the value at the rate with which you have discounted your cash flows. Essentially, the value of the stock will increase over a period of time assuming the cash flows received by the investor are reinvested. If the cash flows are not re invested the sum of all the received cash flows consumed will be higher than invested and that will represent the benefit to the investor. Ofcourse, in the latter case investor will not have realized return on re-investment of cash flows. > > Hopefully, I’ve just been up too late and am > misunderstanding something really obvious and > simple. If anyone can help explain this for me I > will greatly appreciate it. It just seems like > the cost of the shares that are priced as the cost > of equity will exactly negate any potential gain > the shareholder will receive by paying that price.

There are different ways of raising capital. I assume you are talking only about selling stocks. As you sell stocks, price can not stay at \$6.6. Can you see someone buying 100,000 shares for \$6.6 to make less than \$6,600? As new shares are issued their value is dilluted and they will be sold cheaper than initial price. If the company issues n new shares, their price should be \$6,603.51/(1,000+n). If the company only sells 1 share, its price will be very close to \$6.6. However, if the company sells 1,000 shares, their price will be close to \$3.3. This situations is identical to stock split.

Thanks for the help, guys. I realized the crux of my problem was that for some reason I was overlooking the fact that they would make a 9% return on their investment (assuming discount rate was 9% in the DCF analysis). For some reason I had it in my head that because the required rate of return and the cost of capital were equal then profit would be zero. Dumb mistake on my part. Maratikus: When you raise capital by issuing new shares, does the market price of current shares get automatically recalculated (as in a stock split) or does the market naturally trade the price to its new equilibrium?

Also, When you issue new shares, how do you determine how many shares you want to issue if both the price of shares and value of shares are functions of the number of shares you issue? For example, Say I want to raise \$5,000. The current price is \$6.60, and current shares o/s are 1,000. Price = shares outstanding / PV of cash flows New shares issued = Total amount of new capital / price of stock per share Everytime you change the amount of new shares you issue, the price of the stock per share changes! But the number of new shares you issue to arrive at \$5,000 is a function of the price of the stock! It’s a neverending loop.