Question

The risk-free rate is 2.37% and the market risk premium is 6.39%. A stock with a β of 1.60 just paid a dividend of $2.67. The dividend is expected to grow at 21.99% for three years and then grow at 3.53% forever. What is the value of the stock?

The answer is $48.21 but not sure how to get that answer. Please show the finance calculator steps if possible and not excel! Thanks

Answer 1

If CAPM holds, we have following formula to calculate company's required return

Required rate of Return of the stock = risk free rate + β* the market risk premium

Where,                

Risk free rate = 2.37%

The market risk premium = 6.39%

And β of stock = 1.60

Putting all the values in the equation we can get

Required rate of Return of stock = 2.37%+ 1.60* 6.39%

= 12.594%

Therefore the required return of stock or cost of equity is 12.594%

Now we have following information

D0 = current dividend paid = $2.67 per share

k = required rate of return = cost of equity =12.594%

g = growth rate of dividends = 21.99% for year 1, year 2 and year 3 and 3.53% after that

With the given dividend growth rate, we can calculate the actual dividends for year 1 to 3.

D1 = $2.67 * 1.2199 = $3.257

D2 = $3.257 *1.2199 = $3.973

D3 = $3.973 *1.2199 = $4.847

The dividends occurring in the stable growth period of 3.53% from fourth year's dividend:

D4 = $4.847 *1.0353 = $5.018

Now we can calculate the present value of each dividend; where required rate of return is 12.594%.

PV1 = $3.257/ 1.12594 = $2.89

PV2 = $3.973 / (1.12594) ^2 = $3.13

PV3 = $4.847/ (1.12594) ^3 = $3.40

We can apply the stable-growth Gordon Growth Model formula to these dividends to determine their residual value in the terminal year

=D4 / (k-g)

= $5.018/ (0.12594 -0.0353) = $55.364

The present value of these stable growth period dividends (residual value) are

$55.364 / (1.12594) ^3 = $38.79

Now add the present values of all future dividends to get current stock price

$2.89 +$3.13 +$3.40 + $38.79 = $48.21 (rounding off to two decimal points)

The company’s stock is worth $48.21 per share.