Nachman Industries just paid a dividend of D₀ = $2.50.Analysts expect the company's dividend to grow by 30% this year,by 10% in Year 2,and at a constant rate of 5% in Year 3 and thereafter.The required return on this low-risk stock is 9.00%.What is the best estimate of the stock's current market value? Do not round intermediate calculations.

Question

Quizplus · Accepted Answer

Using the dividend discount model:
D1 = $2.50 x (1 + 0.30) = $3.25
D2 = $3.25 x (1 + 0.10) = $3.58
D3 = $3.58 x 1.05 = $3.76
Next, we need to find the present value of these future dividends. Using the formula for the present value of a growing annuity:
PV = D1 / (r-g) + D2 / (1+r)^2 / (r-g) + D3 / (1+r)^3 / (r-g)
PV = $3.25 / (0.09-0.30) + $3.58 / (1+0.09)^2 / (0.09-0.10) + $3.76 / (1+0.09)^3 / (0.09-0.05)
PV = $46.42 + $45.81 + $92.75
PV = $185.98
Therefore, the best estimate of the stock's current market value is $84.98. (Choice C)

Nachman Industries Just Paid a Dividend of D0 = $2

Nachman Industries Just Paid a Dividend of D₀ = $2