Calculating the cost of equity can be tricky since there are two different types of equity. Firms have retained earnings (the money left over after dividends are paid) as the first type of equity. The second form of equity comes from issuing new shares of stock. Don't fear, we'll discuss both of these types of equity in this tutorial!
Let's talk about retained earnings first. So in the course of business, a firm will generate some sales or revenue. They pay cost of goods sold, taxes, interest expense, and so on. The final amount then is their net income. So what do they do with net income? The firm either pays a dividend to their shareholders, or they keep that money for themselves. The portion that the firm keeps is called their retained earnings!
Retained earnings have a cost, so to find that cost, we use the following equation:
In this equation, D1 is the next dividend the firm will pay, P0 is the current price of a share of stock, and g is the growth rate. In most problems, P0 will be given to you. However, we will usually have to find the growth rate, g, on our own.
There are three different ways to get the growth rate, g. The first way is that it will simply be given to you in the problem. Easy enough! The second way to find growth is to use the equation:
In this equation, ROE is the return on equity which will be given to you in the problem. The lowercase r is the retention rate. Remember before when we said that companies have two options with their net income? They can either pay a dividend or retain the money for themselves. The percentage that they keep for themselves is their retention rate or r in our equation. Let's try a quick practice problem to illustrate this point.
Practice Problem 1--Finding The Growth Rate
Busboy Corporation has a return on equity of 18% and pays out 40% of their net income in the form of a dividend. What is Busboy Corporation's growth rate?
Solution
The problem tells us that ROE is 18%. They tell us that they pay out 40% of net income as a dividend. If they pay out 40%, they must retain the rest! So we know that r is 60%. So to find growth, our equation looks like:
In our practice problem, we find that growth equals 10.8%.
The third and final way to find growth is by using the time value of money. To better illustrate this point, let's try another problem.
Practice Problem 2--Finding Growth Through Time Value of Money
File Incorporated paid a dividend of $2.18 nine years ago. The firm recently paid a dividend of $4.36. What is File Inc.'s growth rate?
Solution
Take a look at this problem on a timeline.
When using the time value of money to find the growth rate, we just solve for the interest. In this example, we set the present value to -$2.18, the future value to $4.36, n=9, and we solve for I. You'll get 8% if all went well. That's our growth rate!
So now that we understand how to find the growth rate in a number of ways, let's go ahead and try to find the cost of retained earnings with this practice problem.
Practice Problem 3--Finding the Cost of Retained Earnings
Baseball Bats & Bags Corporation's common stock currently sells for $50 per share. The firm will pay a dividend of $2.00 per share next year, and their earnings are expected to grow at 10% annually. What is their cost of retained earnings?
Solution
Sounds tough, but it really isn't. We are given the stock price, P0 and the growth rate of 10%. Now, remember that D1 is the next dividend that the firm will pay. Clearly in this problem, they tell us that the next dividend will be $2.00. Putting it all together, your equation looks like this:
That's it! You should have found that their cost of retained earnings is 14%. Now let's take a look at the cost of new common stock.
When a firm decides they're going to issue new common stock, they will have to pay something called floatation costs to the bank that handles their stock issue. To account for these floatation costs, we simply deduct them from the current stock price. Here's the equation for the cost of new common stock:
Notice that this equation is almost identical to the cost of retained earnings. The only difference is that the denominator is NP0 instead of simply P0. Not a big deal... NP0 is just price - floatation costs.
Practice Problem 4
Cookie Company has decided to raise money by issuing new shares of common stock. The firm recently paid a dividend of $3.25 and their common stock currently sells for $30 per share. Dividends are expected to grow at 12% per year for the foreseeable future and the company will have to pay $5 per share in floatation costs. What is Cookie Company's cost of new common stock?
Solution
Right away, you should recognize that the dividend we are given is D0 but we need D1. Any time you see terms such as recently paid, you know you're dealing with D0. To find D1, use this simple equation:
Finally, we have to find NP0. We know that the price of the shares are $30 and the floatation costs are $5. So, NP0 is $25. Putting this all together with the cost of new common stock equation, we get:
So the cost of new common stock for Cookie Company is 26.56%. Try some practice problems on your own to make sure you've got it!
Practice Problem 5
Bill's Blinds is building a new curtain factory and needs to issue some new common stock. Their stock sells for $45 per share and they will pay floatation costs of $2.50 on each new share they sell. The company's return on equity is 12% and they retain 75% of their net income. The most recent dividend paid was $1.25 per share. What will be their cost of new common stock?
Solution
Did you get 12.21%? Make sure you calculate D1 for this one since you're given D0 in the problem!
Practice Problem 6
Sunglass World is trying to determine their cost of internal equity. Five years ago, the firm paid a dividend of $3.40 and their most recent dividend was $4.55. Current shares of stock sell for $65, but if they issue new shares, they will have to pay floatation costs of $2.75 per share. What is their cost of retained earnings?
Solution
If you got 13.42%, you have mastered cost of equity! If not, there are a couple of tricks to this one. Since you're looking for the cost of retained earnings, ignore flotation costs! Those only come into play when you're issuing new stock! Also, you know that D0 is $4.55 so make sure you find D1.
That was one long tutorial! If you have any questions whatsoever, please post to our forums. You'll get some quick help from our other members!