Question

Problem 7-05
Nonconstant Growth Valuation

A company currently pays a dividend of $1.25 per share (D₀ = $1.25). It is estimated that the company's dividend will grow at a rate of 22% per year for the next 2 years, and then at a constant rate of 8% thereafter. The company's stock has a beta of 1.4, the risk-free rate is 4%, and the market risk premium is 4%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

$

Answer 1

Step-1, Calculation of the Required Rate of Return (Ke)

As per CAPM Approach, the Required Rate of Return is calculated as follows

Required Rate of Return = Risk-free Rate + (Beta x Market Risk Premium)

= 4.00% + (1.4 x 4.00%)

= 4.00% + 5.60%

= 9.60%

Step-2, Dividend for the next 2 years

Dividend per share in Year 0 (D0) = $1.25 per share

Dividend per share in Year 1 (D1) = $1.5250 per share [$1.25 x 122%]

Dividend per share in Year 2 (D2) = $1.8605 per share [$1.5250 x 122%]

Step-3, Share Price in Year 2

Dividend Growth Rate after Year 2 (g) = 8.00% per year

Required Rate of Return (Ke) = 9.60%

Share Price in Year 2 (P2) = D2(1 + g) / (Ke – g)

= $1.8605(1 + 0.08) / (0.0960 – 0.08)

= $2.0093 / 0.0160

= $125.58 per share

Step-4, The Current Stock Price

As per Dividend Discount Model, Current Stock Price the aggregate of the Present Value of the future dividend payments and the present value the share price in year 2

Year	Cash flow ($)	Present Value factor at 9.60%	Present Value of cash flows ($)
1.5250	0.91241	1.39	1.5250
1.8605	0.83249	1.55	1.8605
125.58	0.83249	104.55	125.58
TOTAL			107.49

“Therefore, the estimate of the stock's current price = $107.49”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.