The last dividend paid by Wilden Corporation was $1.55. The dividend growth rate is expected to be constant at 1.5% for 2 years, after which dividends are expected to grow at a rate of 8.0% forever. The firm's required return (rs) is 12.0%. What is the best estimate of the current stock price?

a. $38.16
b. $41.70
c. $40.48
d. $39.30
e. $37.05

Using the dividend growth model, the value of a stock is the present value of the future dividends receivable discounted at the required rate of return . The required rate of return is given as 12%.

So we discount the year 3 dividend using the dividend growth model formula

P = D (1+g)/r-g

r- rate of return, g = growth rate

Present value of the future dividends:

PV of Year 1 = 1.55(1.015)m × 1.12^(-1)

= 1.4047

PV of Year 2 = 1.55 (1.015)(1.015) × 1.12^(-2)

= 1.27

PV of Year 3 (this will be done in two steps)

Step 1; PV (in yr 2) of year 3 dividend

= (1.55)(1.015)^2×(1.08)/(0.12-0.08)

=43.114

Step 2 : PV (in yr 2) of year 3 dividend

=43.114 × (1.12^(-2))

= 34.37

Best estimate of stock = 1.40 + 1.27 +34.37

= $37.05

Note

To discount the year 3 dividend, we use two steps. The first stp helps get the PV in year 2, and step 3 helps to take it further to the PV in year 0