Present Value with Constant Perpetual Growth Rate

Present Value with Constant Perpetual Growth Rate

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Present value with constant perpetual growth rate is often applied to find present value or current price of ordinary share (common stock).

Time Line

Which

• C₀ : base amount at the beginning of period 1 (Period 0) for constant perpetual growth rate
• g: constant perpetual growth rate

Question

The XYZ  Co. has just paid a cash dividend of $2 per share. Potential investors require a 16 percent return from investments. If the dividend is expected to grow at a steady 8 percent per year, what is the current value of the stock? What will the stock be worth in five years?

Solution

• The current value of the stock

          Do=$2

Po=D1/(r-g)=[D0*(1+g)]/(r-g)

=[2*(1+0.08)]/(0.16-0.08)=$27

So current price =$27

• Stock price at the next five years

          Dividend in five year

=> D₅ =Do*(1+g)⁵ =$2*(1+0.08)⁵ =$2.9387, so price of stock in five years:

=>P₅ = D₅ *(1+g)/(r-g)

= $2.9387 *(1+0.08)/(0.16-0.08)=$39.67 or

        P₅  = Po*(1+g)⁵ =$27 *(1+0.08)⁵ =$39.67