Final answer:
To estimate the price of one share of Admiral Plumbing, we need to calculate the present value of its future cash flows and divide it by the number of shares. The cash flows for the next three years are $75 million, $95 million, and $100 million per year, growing at a constant rate of 4% after three years. The present value of these cash flows is then summed up and divided by 50 million shares.
Step-by-step explanation:
To estimate the price of one share of Admiral Plumbing, we need to calculate the present value of its future cash flows and divide it by the number of shares. The formula for present value is PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods.
In this case, the future cash flows are $75 million, $95 million, and $100 million per year, growing at a constant rate of 4% after three years. The discount rate is 9.50%. We can calculate the present value of these cash flows and then sum them up.
Using the formula, we can calculate the present value for each year:
- Year 1: PV = $75 million / (1 + 9.50%)^1 = $68.81 million
- Year 2: PV = $95 million / (1 + 9.50%)^2 = $80.10 million
- Year 3: PV = $100 million / (1 + 9.50%)^3 = $80.70 million
After three years, the cash flows will grow at a constant rate of 4%. We can calculate the present value of this growing cash flow using the formula:
Year 4 onwards: PV = CF / (r - g), where CF is the cash flow, r is the discount rate, and g is the growth rate.
In this case, CF = $100 million, r = 9.50%, and g = 4%. Using the formula:
Year 4 onwards: PV = $100 million / (9.50% - 4%) = $2.27 billion
Now, we can sum up the present values:
Total Present Value = $68.81 million + $80.10 million + $80.70 million + $2.27 billion = $2.50 billion
Finally, we divide the total present value by the number of shares to estimate the price of one share:
Price per Share = $2.50 billion / 50 million shares = $50