Question

BBB has a steady dividend of $2.00 and be maintained indefinitely. Currently their cost of capital is 5%, and they expect that they can lock into that cost for the next 2 years. Cost of capital will increase to 8% and remain at that level for 2 years. In year 5 they will be subject to a 10% cost of capital, which is expected to hold indefinitely.

Find the Value of BBB's stock in years 3 and 5 and find the value of stock today.

Answer 1

Constant Dividend, D = $2.00

Cost of Capital for next 2 years, r1 = 5%
Cost of Capital for next 2 years, r2 = 8%
Cost of Capital thereafter, r = 10%

Value of stock in year 5, P5 = D / r
Value of stock in year 5, P5 = $2.00 / 0.10
Value of stock in year 5, P5 = $20.00

Value of stock in year 4, P4 = (D + P5) / (1 + r)
Value of stock in year 4, P4 = ($2.00 + $20.00) / (1 + 0.10)
Value of stock in year 4, P4 = $20.00

Value of stock in year 3, P3 = (D + P4) / (1 + r2)
Value of stock in year 3, P3 = ($2.00 + $20.00) / (1 + 0.08)
Value of stock in year 3, P3 = 20.37

Value of stock in year 2, P2 = (D + P3) / (1 + r2)
Value of stock in year 2, P2 = ($2.00 + $20.37) / (1 + 0.08)
Value of stock in year 2, P2 = $20.713

Value of stock today, P0 = D / (1 + r1) + (D + P2) / (1 + r1)^2
Value of stock today, P0 = $2.00 / (1 + 0.05) + ($2.00 + $20.713) / (1 + 0.05)^2
Value of stock today, P0 = $22.51