Question

XYZ was founded 10 years ago. It has been profitable for the last 5 years, but it has needed all of its earnings to support growth and thus has never paid a dividend. Management has indicated that it plans to pay a $1 dividend 3 years from today, then to increase it at a relatively rapid rate of 20% for 3 years, and then to increase it at a constant rate of 8% thereafter. Assuming a required return of 12%, what is your estimate of the stock's intrinsic value today?

a) Calculate the firm's non-constant dividends.

b) Calculate the firm's horizon value.

c) What is the firm's intrinsic value today, P̂ 0?

Answer 1

According to Dividend discount model, intrinsic value of stock is given by present value of all future cash flows.

According to Gordon Growth model, present value of dividend growing at constant rate g is given as under

P0 = D1/(r-g) where D1 next year dividend, P0 is price today and r is discount rate.

a. D3 =$1

D4= 3*1.2 = $1.2

D5 = D4*1.2 = 1.2*1.2 = $1.44

D6 = D5*1.2 = $1.728

D7 = D6*1.08 = 1.86624

Where D3,D4...D7 represent dividend in year 3,4..7 respectively.

b. Horizon value or terminal value is present value of future dividends but at a future time period.

Here horizon value would give present value of constant growth rate period till infinity at time period 6.

P6 = D7/(r-g) = 1.86624/(0.12-0.08) = $46.656

Thus, terminal or horizon value of dividends is $ 46.656.

c. Intrinsic value today would be present value of all future cash flows. Thus,

P0 = D3/(1+r)^3 +..D6/(1+r)^6 + P6/(1+r)^6

= 1/(1.12^3) + 1.2/(1.12^4) + 1.44/(1.12^5) + 1.728/(1.12^6) + 46.656/(1.12^6)

= 0.71178 + 0.76262 + 0.8171 + 0.87546 + 23.63738

= $26.8043

Thus, intrinsic value of stock today is $26.80.

Kindly comment in case of any query.