Let's have a look at how growth in shareholders' equity, return on equity, and cost of equity impact the market value of equity. First, let's consider that we're given only the beginning shareholders' equity and the growth in shareholders' equity of 100 and 3% respectively. Could we start to construct a base analysis for shareholders equity? Well, we could establish that the beginning shareholders equity is 100, and since growth is 3%, then ending equity must be 103. And if we had the return on equity, in addition to the beginning equity, we could figure out the net income. If return on equity is 11% and beginning shareholders equity is 100, and the net income must be 11. So now all we are missing in our base analysis is the dividends which we can calculate as the plug, which must be eight. So now we've completed our base analysis and we have our shareholders equity at book value, can we move into the market value of equity? Well, we already know that net income is 11, and we know some of that net income has been reinvested for growth, which we previously calculated as three. This means that shareholders could have eight as a dividend. If we assume that the dividend grows at 3% in perpetuity, then we could apply the Gordon Growth Model. But for that, we'd need the cost of equity. So if we apply the Gordon Growth Formula, we arrive at a market value of equity of 114.3.

Let's take that structure and sensitize our model. Let's increase the growth to 6%. Intuitively, it feels like the market value of equity should increase, but let's see if that holds true. We know that if beginning equity remains at 100 and the growth increases to 6%, then the ending equity must be revised to 106. So if ending shareholders' equity increases to 106 but the company generates the same net income, then dividends must decrease. In fact, our plug is dividends of five. Let's apply that to our valuation. If we now need growth of six, then shareholders are looking at receiving five as a dividend. If we pump our revised dividend and growth numbers into our Gordon Growth Formula, then we get a higher market value of 125. Our focus here is on the red line, highlighting the market value of equity under various scenarios. you'll notice that the base case has an equity value of 114.3, and the high growth case has a market value of 125. Hopefully, you'll recall that these were the numbers we arrived at in the two previous slides. It's also worth noting that for each of the scenarios presented here, we have the price earnings ratio being equity value, in our red, line divided by net income, and the price to book being, again, the market value of equity on the red line, but now divided by the beginning shareholders equity at book value, which is right at the top of this table. So what happens if we increase the return on equity to 15%? Well, intuitively, it feels like it should increase the market value of equity? And indeed, you can see this has increased to 171.4. What happens if we reduce the cost of equity? Well, this reduces the denominator in the Gordon Growth Formula, again, increasing the market value of equity. Finally, what happens if we make return on equity equal to cost of equity? Well, in this instance, the return being generated only just meets the hurdle rate required by shareholders, which is a depressing effect on the market value of equity.