Question

Question text Roadrunner Enterprises is expected to grow its dividends and earnings at various rates. The company just paid a cash dividend of $2.50 per share. The company expects to grow its dividend at 14% for the next two years, then at 12% for the following three years, after which the company expects to grow at a constant rate of 10% per year indefinitely. The required rate of return on Roadrunner's common stock is 15%.

What are the dividends in years 1 through 5?

What is the Fair Market Value of the stock at the end of year 5?

What is the Fair Market Value of the stock now?

If the stock trades at $50 per share, is the stock rich or cheap?

Answer 1

- Cash Dividend just paid (D0) = $2.50

Growth rate for next 2 years (g) = 14%

Growth rate for the following three years(g1) = 12%

After which growth rate(g2) will be 10% per year indefinately

Required rate of Return(Ke) = 15%

a). Calculating the dividends in years 1 through 5:-

D1 = D0(1+g) = $2.50*(1+0.14)

=$2.85

D2 = D0(1+g)^2 = $2.50*(1+0.14)^2

=$3.249

D3 = D2(1+g1) = $3.249*(1+0.12)

=$3.64

D4 = D2(1+g1)^2 = $3.249*(1+0.12)^2

=$4.0755

D5 = D2(1+g1)^3 = $3.249*(1+0.12)^3

=$4.5646

b). Calculating the Fair Market Value of the stock at the end of year 5:-

P5 = D5(1+g2)/(ke-g2)

=$4.5646(1+0.10)/(0.15-0.10)

= $100.4214

So, the Fair Market Value at the end of year 5 is $100.4214

c). Calculating the Fair Market Value of the stock now:-

P0 = 2.4783 + 2.4567 + 2.3934 + 2.3302 + 2.2694 + 49.9272

P0 = $61.8552

So, the Fair Market Value now is $61.8552

d). Stock is trading at $50

While, the Fair Market Value is $61.8552

Since, the Fair market value is less than the current Stock Price.

Thus, the Stock is trading at Cheaper price

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