A fast-growing firm recently paid a dividend of $0.20 per share. The dividend is

Question

A fast-growing firm recently paid a dividend of $0.20 per share. The dividend is expected to increase at a 20 percent rate for the next three years. Afterwards, a more stable 11 percent growth rate can be assumed.

If a 12 percent discount rate is appropriate for this stock, what is its value today? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

A fast-growing firm recently paid a dividend of $0.20 per share. The dividend is expected to increase at a 20 percent rate for the next three years. Afterwards, a more stable 11 percent growth rate can be assumed.

Explanation / Answer

This can be solved using two stage griwth model.

For first three years, dividend will increase at the rate 20% per annum. After that, it will increase by 11% every year.

Discount Rate= 12%

Divident for current year Do= $ 0.20

Dividend for the First Year D1= 0.20 x(1+0.20) = $ 0.24

Dividend for the second Year D2= 0.24 x(1+0.20) = $ 0.288

Dividend for the third Year D3= 0.288 x (1+0.20) = $ 0.3456

After year three, dividend will increase at a constant rate of 11% per annum. Considering the dicsount rate of 12%, the terminal value at the end of year 3 can be given as:

T3= D3/(1-1.11/1.12) = $ 38.7072 . This includes the dividend for the Year-3 as well.

Present value of the stock= D1/(1.12)^1 + D2/(1.12)^2 + T3/(1.12)3

Do will not be added to present value of stock as it has been already paid out.

= 0.2142 + 0.2295 + 27.5510

= 27.9949

or rounding to last two decimal places, Present Value of Stock= $ 27.99

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