Navel County Choppers, Inc., is experiencing rapid growth. The company expects dividends to grow at 23 percent per year for the next 10 years before leveling off at 7 percent into perpetuity. The required return on the company’s stock is 15 percent. If the dividend per share just paid was $1.89, what is the stock price? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

P0 = $77.397794 rounded off to $77.40

Explanation:

The two stage growth model of DDM will be used to calculate the price of the stock today. The DDM values a stock based on the present value of the expected future dividends from the stock. The formula for price today under this model is,

P0 = D0 * (1+g1) / (1+r)  +  D0 * (1+g1)^2 / (1+r)^2  +  ...  +  D0 * (1+g1)^n / (1+r)^n  + [(D0 * (1+g1)^n  *  (1+g2) /  (r - g2))  /  (1+r)^n]

Where,

P0 = 1.89 * (1+0.23) / (1+0.15)  +  1.89 * (1+0.23)^2 / (1+0.15)^2  +  

1.89 * (1+0.23)^3 / (1+0.15)^3  +   1.89 * (1+0.23)^4 / (1+0.15)^4  +  

1.89 * (1+0.23)^5 / (1+0.15)^5  +  1.89 * (1+0.23)^6 / (1+0.15)^6  +  

1.89 * (1+0.23)^7 / (1+0.15)^7  +  1.89 * (1+0.23)^8 / (1+0.15)^8  +  

1.89 * (1+0.23)^9 / (1+0.15)^9  +  1.89 * (1+0.23)^10 / (1+0.15)^10  +  

[(1.89 * (1+0.23)^10  *  (1+0.07)  / (0.15- 0.07))  /  (1+0.15)^10]

P0 = $77.397794 rounded off to $77.40