Step-by-step explanation:
To calculate the current value of the company's stock, we need to find the present value of all the future cash flows, including the regular dividends for the next four years and the liquidating dividend at the end of the fourth year.
Let's break down the calculation:
Step 1: Calculate the present value of the regular dividends for the next four years.
PV of regular dividends = D1 / (1 + r)^1 + D2 / (1 + r)^2 + D3 / (1 + r)^3 + D4 / (1 + r)^4
where,
D1 = Regular dividend in the first year = $0.80 per share
D2 = Regular dividend in the second year = $0.80 per share
D3 = Regular dividend in the third year = $0.80 per share
D4 = Regular dividend in the fourth year = $0.80 per share
r = Discount rate = 7% = 0.07
PV of regular dividends = 0.80 / (1 + 0.07)^1 + 0.80 / (1 + 0.07)^2 + 0.80 / (1 + 0.07)^3 + 0.80 / (1 + 0.07)^4
PV of regular dividends ≈ 0.7476 + 0.6988 + 0.6537 + 0.6116
PV of regular dividends ≈ 2.7117
Step 2: Calculate the present value of the liquidating dividend at the end of the fourth year.
PV of liquidating dividend = D5 / (1 + r)^4
where,
D5 = Liquidating dividend at the end of the fourth year = $77 per share
PV of liquidating dividend = 77 / (1 + 0.07)^4
PV of liquidating dividend ≈ 77 / 1.3108
PV of liquidating dividend ≈ 58.6901
Step 3: Calculate the current value of the company's stock (total present value of all cash flows).
Current value of stock = PV of regular dividends + PV of liquidating dividend
Current value of stock ≈ 2.7117 + 58.6901
Current value of stock ≈ 61.4018
The current value of the company's stock is approximately $61.40 per share.