Navel County Choppers, Inc., is experiencing rapid growth. The company expects dividends to grow at 19 percent per year for the next 8 years before leveling off at 5 percent into perpetuity. The required return on the company’s stock is 10 percent. If the dividend per share just paid was $1.52, what is the stock price?

Price of stock = $74.636

Explanation:

The Dividend Valuation Model is a technique used to value the worth of an asset. According to this model, the worth of an asset is the sum of the present values of its future cash flows discounted at the required rate of return.  

The price of the stock will the sum of the present value of the growing annuity and the growing perpetuity

Present value of dividend  from year 1 to 8

The PV of the growing annuity  = A/r-g) ( 1- (1+g)/(1+r)^n   )

A- dividend payable now , r- required of return, g-growth rate, number of years

PV  = 1.52×(1.19)/(0.1-0.19) × (1 -(1.19/1.1)^8)= 17.605

PV of Dividend from year 9 and beyond:

P = D× g/(r-g)

This will be done in two steps:

Step 1: PV(in year 8)of dividend = (1.52× 1.19^8× 1.05)/(0.1-0.05)= 122.250

Step 2 : PV in year 0 = 122.25× 1.1^(-8)= 57.030

Price of stock = 17.60 +  57.030= 74.63

Price of stock = $74.636

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