Practice Question
Planner Corp. pays a \$2.00 a share dividend every other year, and their most recent dividend was paid today. Five years from now, the company will repurchase all of the outstanding shares at \$50 per share. What is the stock worth today at an 8% rate of return?
To determine the stock worth today, we need to calculate the present value of all future cash flows, including the dividends and the repurchase price. Here are the steps:
Step 1: Identify the Cash Flows
- Dividend payments: \$2.00 every other year.
- Repurchase price: \$50 in year 5.
Step 2: Calculate the Present Value of Dividends
Since dividends are paid every other year, the next dividend will be paid in year 2 and then in year 4.
We use the present value formula: \[ PV = \frac{D}{(1 + r)^t} \]
- Year 2: \( \frac{2}{(1 + 0.08)^2} = \frac{2}{1.1664} = 1.715 \)
- Year 4: \( \frac{2}{(1 + 0.08)^4} = \frac{2}{1.3605} = 1.470 \)
Step 3: Calculate the Present Value of Repurchase Price
Repurchase price in year 5: \[ PV = \frac{50}{(1 + 0.08)^5} = \frac{50}{1.4693} = 34.034 \]
Step 4: Sum the Present Values
Total Present Value = \[ 1.715 + 1.470 + 34.034 = 37.219 \]
Final Answer
The stock worth today at an 8% rate of return is \$37.219.