The company plans to dissolve in two years. At the present time, dividends at each date are set equal to the cash flow of $18,000. There are 100 shares outstanding, so the dividend per share is $180. Assume an 8% required rate of return. What is the present value of a share of stock?
Question
The company plans to dissolve in two years. At the present time, dividends at each date are set equal to the cash flow of 180. Assume an 8% required rate of return. What is the present value of a share of stock?
Solution
To calculate the present value of a share of stock, we need to discount the dividends back to the present using the required rate of return.
Step 1: Identify the dividends per share, which is $180.
Step 2: Identify the required rate of return, which is 8% or 0.08.
Step 3: Since the company plans to dissolve in two years, we will receive dividends for two years.
Step 4: Calculate the present value of the dividends for each year and sum them up. The formula for the present value of a future cash flow is:
PV = CF / (1 + r)^n
where:
- PV is the present value
- CF is the cash flow (dividends per share in this case)
- r is the required rate of return
- n is the number of periods (years in this case)
For the first year: PV1 = 166.67
For the second year: PV2 = 154.32
Step 5: Sum up the present values of the dividends for each year to get the present value of the stock:
PV of stock = PV1 + PV2 = 154.32 = $320.99
So, the present value of a share of stock is approximately $320.99.
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