Question

"The company will pay a dividend of $15 per share 10 years from today and will increase the dividend by 5 percent per year thereafter. If the required return on this stock is 15 percent, what is the current share price?"

Answer 1

Answer:

Current Share price= $114.21

Explanation:

The Dividend Valuation Model is a technique adopted to detremine the value of an asset. According to this model, the value of an asset is the sum of the present values of the future cash flows that would arise from the asset discounted at the required rate of return (discount rate)

The model is premised on the concept of the time value of money. The idea that $1 today is not the same as $1 tomorrow. The $1 of today is worth more than that of tomorrow; because of the opportunity to earn interest. So to determine the worth of a future cash flow, we compute its worth today- its present value.

The Present Value of a future cash flow is the amount that needs to be invested today at a particular rate of return to equal the same cash flow in the future. Present value means the value in year 0 or now

The process of calculating the present value of a future sum is called discounting. So to calculate the current stock price in this question, we shall discount the future dividends using the required rate of return and then add them together.

So if an asset (e.g a stock) promises some cash flows in the future, those cash flows need to be brought to their present values and then be added to arrive at the value of the asset

In this question, the cash flows are the dividends as given and the rate of return (discount rate) is 15%

So we apply this model as follows:

Step 1 : PV of div from year 1 to 10  =  15× ((1-1.15)^(-10))/0.15)  =  75.282

Step 2:PV (in year 10)of div from year 11 onward=(15×1.05)/(0.15-0.05)=  157.5

Step 3:PV(in year 0) of div from year 11 onward =  157.5 × (1.15)^ (-10) =  38.93

Current Share price= $75.282 + $38.93 = $114.21

Note: step 3 is important because the the cash flows from year 11 onward were discounted to arrive at their values in year 10. Since we are interested in the current price i.e year 0 value, it is important that we re-discount again to bring them to their PV in year 0.