Question

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.

Please show work

Answer 1

This question is based on multiple period dividend discount model.

Calculation of Dividend for Year 1 and 2 .

Dividend for Year 1 - D0*(1+g)

= $2.50 * (1+0.30)

= $2.50 * 1.30

= $3.25

Dividend for Year 2 - D1*(1+g)

= $3.25 * (1+0.10)

= $3.25 * 1.10

= $3.575

Stage 1 - Calculation of Explicit Forecast period

Stage 2- Beyond 2 years

Expected dividend for the 3rd year i.e. D3 = D2 * (1+g). Growth rate now is 5%.

= $3.575 * (1 + 0.05)

= $3.575 * 1.05

= $3.75375

Horizon Price i.e. P2 = D3 / (Re-g)

= $3.75375 / (0.09 - 0.05)

= $3.75375 / 0.04

= $93.84375

Present Value of P2 = $93.84375 * 0.84167999

= $78.986407

Value of Stock = Stage 1 + Stage 2

= $5.99065735 + $78.986407

= $84.977064

Note - How did we calculate the discounting factors @9%

Year 1 = 1/1.09

= 0.91743119

Year 2 = 0.91743119/1.1189

= 0.84167999