Final answer:
To determine the maximum price an investor should pay for Pharm stock today, we calculate the present value of dividends and stock price using a discount rate of 8%. After calculation, the total present value of the stock is $47.39, which is the maximum price a prudent investor should consider paying.
Step-by-step explanation:
To calculate the maximum price a prudent investor would be willing to pay for a share of Pharm stock today, we need to consider the present value of the expected future cash flows, which include dividends and the stock price after two years. The equity cost of capital is given as 8%, which we use as the discount rate.
The present value (PV) of the dividends and stock price is calculated using the formula:
- PV of Year 1 Dividend = Dividend in Year 1 / (1 + r)^1
- PV of Year 2 Dividend = Dividend in Year 2 / (1 + r)^2
- PV of Stock Price in Year 2 = Stock Price in Year 2 / (1 + r)^2
Where 'r' is the equity cost of capital (8% in this case).
Inserting the given dividends and stock price:
- PV of Year 1 Dividend = $2.20 / (1 + 0.08)^1
- PV of Year 2 Dividend = $2.90 / (1 + 0.08)^2
- PV of Stock Price in Year 2 = $50 / (1 + 0.08)^2
After performing these calculations:
- PV of Year 1 Dividend = $2.04
- PV of Year 2 Dividend = $2.48
- PV of Stock Price in Year 2 = $42.88
Adding up all the present values:
- Total PV = PV of Year 1 Dividend + PV of Year 2 Dividend + PV of Stock Price in Year 2
- Total PV = $2.04 + $2.48 + $42.88
- Total PV = $47.39
In conclusion, a prudent investor would not want to pay more than the total present value for a share of Pharm stock, which is $47.39.