Question

You are valuing the stock of the Northgate Company. The firm is going to pay a dividend of ​ $5 per share one year from now. Dividends are expected to grow at​ 6% a year for the next 11 years​ (i.e., year 1 through​ 11). Starting from year 12 and​ beyond, the dividend growth rate will drop to​ 1% per year. Northgate Company has a​ 7% WACC, and a ​ 8% cost of equity. Please use an appropriate model to calculate the fair value of​ Northgate’s stock today.

a. The present value​ (measured by dollar​ now) of the dividends for the first 11 years is $___. (Round to the nearest​ cent.)

b. The present value​ (measured by dollar​ now) of the stream of dividends starting from year 12 and beyond is $___. ​(Round to the nearest​ cent.)

c. The fair value of​ Northgate’s stock today $___.

Answer 1

a. PV of dividends from year 1 to year 11 =5/(1+8%)+5*(1+6%)/(1+8%)^2+5*(1+6%)^2/(1+8%)^3+5*(1+6%)^3/(1+8%)^4+5*(1+6%)^4/(1+8%)^5+5*(1+6%)^5/(1+8%)^6+5*(1+6%)^6/(1+8%)^7+5*(1+6%)^7/(1+8%)^8+5*(1+6%)^8/(1+8%)^9+5*(1+6%)^9/(1+8%)^10+5*(1+6%)^10/(1+8%)^11=46.4631 or 46.46
b. Terminal Value =Dividend year 1*(1+g)^10*(1+g2)/(Cost of Equity-growth) =5*(1+6%)^10*(1+1%)/(8%-1%) =129.1969
PV of terminal value =129.1969/(1+8%)^11 =55.4103 or 55.41
c. Fair Value of Stock =46.4631+55.4103 =101.87