Question

A company currently pays a dividend of $2.8 per share (D₀ = $2.8). 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 5% thereafter. The company's stock has a beta of 1.6, the risk-free rate is 6.5%, and the market risk premium is 2%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Solution:

Given:

Current Dividend = $ 2.8 per share or D0 = $ 2.8

Dividend Growth Rate for the next 2 years = 22 % per year

Dividend Growth Rate After 2 years = 5 % Constant Rate

Stock Beta of Company = 1.6

Risk-Free Rate of Return = 6.5 %

Market Risk Premium = 2 %

To Calculate:

Estimate of the Stock’s Current Price.

Process: Calculations:

Step: 1 Calculation of Expected Return of Stock:

Expected Return of Stock: - ERs= Rf + (βs × MRP)

Where:

ERs = Expected Return of Stock

Rf = Risk Free Interest Rate

βs = Beta of Stock

MRP = Market Risk Premium

Here:

Rf = 6.5 %, βs = 1.6, MRP = 2 %

On putting the values, in the formula, we get,

Expected Return of Stock = 6.5 % + (1.6 × 2 %)

= 6.5 + 3.2 = 9.7 %

Expected Return of Stock = 9.7 %

Step: 2 Calculation of Dividends:

Dividend = Current Dividend (1 + Growth Rate of Dividend)

On putting the Values in the formula, Dividends for First 2 Year can be calculated as:

For First Year: Current Dividend = $ 2.8, Growth Rate of Dividend = 22 %

D1 = D0 (1 + G)

D1 = $ 2.8 (1 + 22 %)

D1 = $ 2.8 (1 + 0.22)

D1 = $ 2.8 × 1.22 = $ 3.416

D1 = $ 3.416

For Second Year: Current Dividend = $ 3.416, Growth Rate of Dividend = 22 %

D2 = D1 (1 + G)

D2 = $ 3.416 (1 + 22 %)

D2 = $ 3.416 (1 + 0.22)

D2 = $ 3.416 × 1.22 = $ 4.16752

D2 = $ 4.16752

Step: 3 Value of Shares After 2 Years:

Value of Shares After 2 Years = (D2 (1 +Growth Rate After 2 Years)) / (Expected Return of Stock – Growth Rate After 2 Years)

= (4.16752 (1 + 5 %)) / (9.7 % – 5 %)

= (4.16752 (1 + 0.05)) / (0.097 – 0.05)

= (4.16752 × 1.05) / 0.047

= 4.375896 / 0.047

= 93.1041702128

Value of Share After 2 Years = $ 93.1041702128

Step: 4 Calculation of the Stock’s Current Price:

Current Price = D1 / (1+ Expected Return) + D2 / (1+ Expected Return) ^2 + Value of Share After 2 Year / (1+ Expected Return) ^2

Here:

D1 = 3.416, D2 = 4.16752, Expected Return = 9.7 % and

Value of Share After 2 Years = $ 93.1041702128

On putting these values in the formula, we get,

(3.416 / (1 + 0.097)) + (4.16752 / (1 + 0.097) ^2) + (93.1041702128 / (1 + 0.097) ^2)

= (3.416 / 1.097) + (4.16752 / (1.097 ^2)) + (93.1041702128 / (1.097 ^2))

= 3.1139471285 + 3.4630952569 + 77.367021697

= 83.9440640824 ≈ 83.94

Current Price of Share = $ 83.94

Ans: The Stock’s Current Price = $ 83.94