 In contemporary open economies with efficient capital markets, if any firm exploits investment opportunities efficiently, the firm's stock market value can be increased substantially. Now how it can happen to understand this? Let's see an example. We have a two company sample in our example with certain information where expected earning per share is $5, dividend payout is 100%. This means that there is no retention or flow back. This means that the B in this particular case is equal to 0. Dividend payout is 100%. Then reinvestment is 0%. The perpetual dividend per share is $5. Rate capitalization rate is 12.5%. So the share price is equal to the simply D1 over K. We have no G. This means that there is no dividend growth rate because there is no reinvestment policy. The resulting value is $40. This $40 says that no growth in the company's value. This means that no change in capital stock and earning power over the time to come. Therefore, there is no growth in the dividend. This particular strategy is termed as a no growth strategy or zero growth strategy because we don't see any growth rate in our example. All of the earnings are paid out as dividends without any retention or flowing back. So in this particular case, dividend cash flows are the simple perpetuity. Now we have the opposite of no growth strategy. This means we have reinvestment plans that we have growth strategy in this particular case. Now assume that one company starts a project with ROI of 15%. This means that the return on investment on this particular project is equal to 15%. This is greater than our cost of capital or K which is 12.5%. Now low dividend payouts that shows that the company will reduce the dividend payouts in order to have some reinvestment plans. So there will be some retention, there will be some flow back. So the dividend payout is low, then the 15% return on investment for the owners. And if full dividend payout is there, then 5% by shareholders on their individual investment. This means that if there is low dividend payout, the company has certain reinvestment plans inside the company, inside that particular project. And that project will earn 15% ROI for the company's shareholders. And if the company pays full earnings at the dividend, shareholders will have no choice but to earn only the 12.5% as the K. Now we have new retention policy by this company which is 60%. This means that dividend payout will be 40%. So the new dividend per share will be equal to $2 per share. Now what will be the effect of this growth strategy on the company's share price? Definitely the stock price of this particular company will go high. Now we have two types of reinvestment plans, low reinvestment plan, low reinvestment rate plan and high reinvestment rate plan. What is the implication of these two? Let's see, under low reinvestment rate plans, there are higher dividends in the initial period and low dividend growth rates. Under higher reinvestment rate plans, there are higher dividends, higher dividend growth rates backed by the higher reinvestment of the earnings. And that reinvestment of earnings enhances the stock value more high. If we see the graphical application of these two reinvestment plan, we can see in our example where the black upward curve shows the higher reinvestment plan and the lower blue upward curve shows the lower reinvestment plan. We see that the dividend per share is higher in the higher reinvestment plan and that is increasing over the lower reinvestment plan by a higher rate. Now how much growth can be there if the company has a certain reinvestment plan? We have an example in continuation of our earlier example. Now we have outstanding shares in number of three million, initial investment of hundred million dollars, return on investment or return on equity of fifteen percent. We have total earnings of fifteen million. So the earnings per share we have five dollars, reinvestment at the rate of sixty percent means we have a nine million profit to be reinvested or plow back in the company. This means that percentage increase in the asset would be equal to fifteen point one five into six million and that is again equal to nine percent. With this nine percent more asset the company will earn more profit by nine percent and it will pay out nine percent dividend more to its shareholders. Now what will be the dividend growth rate which is G? To determine dividend growth rate we need to multiply return on equity with the plowing back ratio which is equal to sixty percent and the return on equity is equal to fifteen percent. So the value of G or the growth rate is equal to nine percent. Now we can determine the stock price of this firm. We have formula of D1 over K minus G, now we have D1 of equal to two dollars, so we have K of twelve point five percent and we have now determined the G that is nine percent. The resulting value is fifty seven point one four dollars. So we see that under no growth strategy the value of the firm stock was equal to forty dollars per share and under growth strategy the value of the firm is equal to fifty seven point one four dollars per share. So with the inception of the growth strategy the per share stock price of this company has increased by seventeen point one four dollars. Present value of growth opportunities, we see that the decreased payouts and the higher flowbacks increases stock price by seventeen point one four dollars as we have earlier seen. This means that the planned reinvestment provide expected return greater than the K. The investment opportunities with positive net present value raise the company's worth. This NPV is also called as the present value of growth opportunities and how to determine present value of growth opportunities we have a formula that is the value of a firm is equal to value of a firm having no growth plus the present value of growth opportunity or PV go. So when we add up these two variables the resulting value comes to the value of the firm. If we put our numeric values in these in this model we see that P naught is equal to E one over K here E one is the earnings per share and K is the capitalization rate plus we will be adding their present value of growth opportunities. We see that our earnings per share are equal to five dollar and our K is equal to twelve point five percent and the present value of growth opportunities we had just computed that is seventeen point four zero dollars. So solving this model it gives us the value of fifteen point fifty seven point one four dollars and again this is the value over the value if the firm has no reinvestment plans or the no growth plan. Now one thing to be noted that the growth is not the investor's desire. The growth raises firm value only in a case where the project's return on investment is greater than the firm's cost of capital. Now to understand this we have another example the sister concern of our recent company in the example has an ROE of twelve point five percent which is equal to K that is twelve point five percent and that K is the cost of capital of the company in our example. So the company's cost of capital is equal to its sister concerns return on equity. So in this in that particular case the present value of growth opportunity is equal to zero because the flowing bag is equal to zero and the growth rate is also equal to zero. Therefore the present value of this company will be computed using the perpetuity phenomena and that is even over K even is five dollar and K is equal to twelve point five percent this is this gives us the value of forty dollars now assume that there is a certain amount of flowing bag of the profit and that is sixty percent. Now to determine G we again need to multiply return on equity of the project with the project's firm's cost of projects flow back ratio and the return on equity of the sister concern is twelve point five percent and its flowing bag ratio is sixty percent. So the growth rate for the sister's concern or the sister company is seven point five percent. Now we can determine the present stock price of this sister company using the constant growth dividend discount model which is D1 over K minus G. Now again D1 is equal to two and K is equal to twelve point five percent whereas in now the company has growth rate of seven point five percent and the resulting figure is forty dollars per share. We again see that if we determine the present value of growth opportunities of this sister company we need to determine the even over K from P naught this means that the value under both the variables is the same that is forty dollars the resulting value is zero. So in that particular case the present value of growth opportunities for this sister concern is equal to zero. The reason is that the ROE of the sister company is equal to its parent company's cost of capital. Now reinvestment just maintains the stock price then there is no increase in the firm value. Why? Because this project's ROI is just equal to the firm's cost of capital that is K. Reinvestment can only be justified if the project's return on investment is greater than the firm's cost of capital. Flowing back is non-beneficial if the present value of growth opportunity is equal to zero this means the firm has no growth strategy or it is equal to a no growth strategy. The implication of no growth strategy is certain that is the mature age firms with considerable cash flows but limited investment opportunities are termed as the cash cost because at this stage with no profitable opportunities the mature firms raised cash flows are available for the shareholders for a certain period of time and that is the reason that without any new investment these cash flows are milking by the shareholders. So the firm is termed as the cash cow for its owners. To understand this we have another example where earning per share is $5 and earnings flowing back ratio is 60% ROE is 10% capital capitalization rate is 15%. The expected dividend per share is $2 and present value of growth opportunities we need to determine. Now for that purpose we need to have the value of G we put the very a value of ROE and B into the computation of G model we have 6% growth rate now with this we can determine the present value of the stock using D1 over K minus G resulting value is 22.22 dollars per share now now we can determine the present value of growth opportunity and if we see that P naught is equal to 1222.22 dollars per share and the value of growth opportunity is equal to 5 divided by 15 the sum of this model is equal to negative 11.10%. So this firm has negative present value of growth opportunities this means the company's ROE is lesser than its cost of capital or K so what is the implication for this negative present value of growth opportunities such firm is subject to the takeover policy by another firm and the buying firm's management will do what it will takeover the firm it will have no retention plane and in this way the firm value will be increased because there will be some perpetuity of the earnings because all of the earnings will be paid out as dividend so the value of the firm will be equal to E1 plus K which is equal to 5 dollars per share over the capitalization rate of 15% and that is the value per share comes to 33 dollars per share so this way the new buyer has increased the value of the firm