Question

A stock has an expected return of 18.00%. The risk-free rate is 1.58% and the market risk premium is 8.24%. What is the β of the stock?

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

The risk-free rate is 1.64% and the market risk premium is 6.38%. A stock with a β of 1.65 just paid a dividend of $1.29. The dividend is expected to grow at 21.18% for three years and then grow at 3.15% forever. What is the value of the stock?

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

Unsure if I'm doing the process right. Thanks!

Answer 1

Answer to the first question

As per Capital Asset Pricing Model (CAPM)

Re = Rf + (Rm-Rf) β

Where Re = Expected Return

Rf = Risk free rate of return

Rm – Market Return

Rm – Rf = Market Risk Premium

β – Beta of the stock

Calculation of Expected Return of stock

Rf = 1.58%

Rm – Rf = 8.24%

Re = 18.00%

Using the formula Re = Rf + (Rm-Rf) β

18.00 = 1.58 + 8.24 * β

18.00 - 1.58 = 8.24 * β

16.42 = 8.24 * β

β = 16.42 / 8.24

= 1.99 (Rounded to two decimal places)

Answer to the second question

Step 1 - Calculation of Re

Re = Rf + (Rm-Rf) β

= 1.64 + 6.38 * 1.65

= 1.64 + 10.527

= 12.17 % (Rounded to two decimal places)

Step 2 - Calculation of D1, D2 and D3

Company just paid a dividend of $1.29 means D0 or current dividend.

Therefore D1 = D0 * (1+g)

where g represents growth rate

D1 = $1.29 * (1 + 0.2118)

D1 = $1.29 * 1.2118

D1 = 1.56 (rounded to two decimals)

D2 = D1*(1+g)

D2 = $1.56 * 1.2118

=$1.89 (rounded to two decimals)

D3 = D2*(1+g)

D3 = $1.89 * 1.2118

= $2.29 (rounded to two decimals)

Step 3 - Calculation of Explicit Forecast Period

Step 4 - Beyond 3 years

Expected Dividend for the 4th year or D4 = D3 * 1.0315

Why did we take 1.0315 since growth rate is now 3.15% after 3 years

D4 = 2.29 * 1.0315

D4 = $2.36 (rounded to two decimals)

Horizon Period i.e. P3= D4 / (Re - g)

P3 = $2.36 / (0.1217 - 0.0315)

P3 = $2.36 / 0.0902

P3 = $26.16 (rounded to two decimals)

Present Value of P3 = P3 * Discounting factor(12.17%,3 years)

= $26.16 * 0.7085

= $18.54 (rounded to two decimals)

Therefore Value of Stock = $4.52 + $18.54

= $23.06 (rounded to two decimals)

Notes-

• 12.17% can be written as 0.1217.
• 3.15% an be written as 0.0315.
• How did we calculate the discounting factors @ 12.17 %

Year 1 = 1/1.1217

=0.8915

Year 2 = 0.8915 / 1.1217

= 0.7948

Year 3 = 0.7948 / 1.1217

= 0.7085