Final answer:
The estimated dividend in the third year with a growth rate of 10% is $3.33. To determine what an investor will pay for a share, the present value of future dividends from Babble, Inc. should be calculated, which requires the rate of return.
Step-by-step explanation:
To estimate the dividend in the third year with a growth rate of 10%, we use the formula for future value of a growing dividend: D3 = D0 × (1 + g)^n, where D3 is the dividend in the third year, D0 is the initial dividend, g is the growth rate, and n is the number of years. Plugging in the values given in the question:
D3 = $2.50 × (1 + 0.10)^3 = $2.50 × 1.331 = $3.33
Thus, the estimated dividend in the third year is $3.33. Regarding the case of Babble, Inc., to calculate what an investor would pay for a share of this company, we would need to discount the future dividends to their present value. This involves summing the present value of each dividend payment:
PV = D1 / (1 + r) + D2 / (1 + r)^2 + ... + Dn / (1 + r)^n
Without the required rate of return (r), we cannot compute the present value of those dividends to determine what an investor will pay for a share.