Question

Whited Inc.'s stock currently sells for $34.92 per share. The dividend is projected to increase at a constant rate of 3.2% per year. The required rate of return on the stock, rs, is 9.9%. What is the stock's expected price 6 years from now?

Answer 1

Current Stock Price (P₀) = $ 34.92

Dividend growth rate (g) = 3.2% per year

Required rate of return (R_e) = 9.9%

We need expected price of stock 6 years from now.

Using Dividend Discount Model, we know that P₀ = D₁ / (R_e - g), where

• P₀ = Current price of stock
• D₁ = Dividend expected in next year
• g = Growth rate
• R_e = Required rate of return

Using the given details, we need to calculate:

1. Dividend expected to be paid in the next year, then
2. Calculate the dividend for year 7 using growth rate
3. Apply dividend discount model to calculate price at the end of Year 6

Step 1: Calculation of D₁

P₀ = D₁ / (R_e - g)

34.92 = D₁ / (0.099 - 0.032)

D₁ = 34.92* 0.067

D₁ = $ 2.34

Step 2: Calculation of D₇

D1	D2	D3	D4	D5	D6	D7
2.34	2.41	2.49	2.57	2.65	2.74	2.83

The above table is calculated using growth rate. For your reference, D₂ = D₁ + (D1*3.2%) = 2.34 + 0.07 = $ 2.41

Step 3: Calculation of P6

Using Dividend Dicount Model, we know P₀ = D₁ / (R_e - g)

Therefore, for calculating P₆, formula will be P₆ = D₇ / (R_e - g)

P₆ = 2.83 / (0.099 -0.032)

P₆ = 2.83 / 0.067

P₆ = $42.18

The stock's expected price 6 years from now will be $ 42.18.