Question

The risk-free rate is 2.43% and the market risk premium is 8.12%. A stock with a β of 1.56 just paid a dividend of $1.36. The dividend is expected to grow at 23.91% for five years and then grow at 3.26% forever. What is the value of the stock?

Answer format: Currency: Round to: 2 decimal places.

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)

= 2.43% + [1.56 x 8.12%]

= 2.43% + 12.6672%

= $15.0972%

Step-2, Dividend for the next 5 years

Dividend in Year 0 (D0) = $1.36 per share

Dividend in Year 1 (D1) = $1.6852 per share [$1.36 x 123.91%]

Dividend in Year 2 (D2) = $2.0881 per share [$1.6852 x 123.91%]

Dividend in Year 3 (D3) = $2.5874 per share [$2.0881 x 123.91%]

Dividend in Year 4 (D4) = $3.2060 per share [$2.5874 x 123.91%]

Dividend in Year 5 (D5) = $3.9726 per share [$3.2060 x 123.91%]

Step-3, Share Price in Year 5 (P5)

Dividend in Year 5 (D5) = $3.9726 per share [$3.2060 x 123.91%]

Dividend Growth Rate after Year 5 (g) = 3.26% per year

Required Rate of Return (Ke) = 15.0972%

Share Price in Year 5 (P5) = D5(1 + g) / (Ke – g)

= $3.9726(1 + 0.0326) / (0.150972 – 0.0326)

= $4.1021 / 0.118372

= $34.65 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 5

Year	Cash flow ($)	Present Value Factor (PVF) at 15.0972%	Present Value of cash flows ($) [Cash flows x PVF]
1	1.6852	0.868831	1.46
2	2.0881	0.754867	1.58
3	2.5874	0.655852	1.70
4	3.2060	0.569824	1.83
5	3.9726	0.495081	1.97
5	34.65	0.495081	17.16
TOTAL	25.69

“Hence, the value of the stock will be $25.69”

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.