Nachman Industries just paid a dividend of D₀ = $3.75.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?

Question

Quizplus · Accepted Answer

Using the dividend discount model, we can calculate the current market value of the stock:

Year 1 dividend = $3.75
Expected growth rate in Year 1 = 30%
Expected dividend in Year 2 = $3.75 x (1 + 0.30) = $4.88
Expected growth rate in Year 2 = 10%
Expected dividend in Year 3 = $4.88 x (1 + 0.10) = $5.37
Expected growth rate in Year 3 and thereafter = 5%
Required return = 9%

Using the formula:
PV = D1 / (1 + r) + D2 / (1 + r)^2 + D3 / (1 + r)^3 + ... + Dn / (1 + r)^n
where PV = present value of stock, D1 = dividend in Year 1, r = required return, and n = number of years

PV = $3.75 / (1 + 0.09) + $4.88 / (1 + 0.09)^2 + $5.37 / (1 + 0.09)^3 + ($5.37 x 0.05) / (0.09 - 0.05) / (1 + 0.09)^3

PV = $127.47

Therefore, the best choice is C, $127.47.

Nachman Industries Just Paid a Dividend of D0 = $3

Nachman Industries Just Paid a Dividend of D₀ = $3