NU YU announced today that it will begin paying annual dividends.The first dividend will be paid next year in the amount of €.25 a share.The following dividends will be €.40,€.60,and €.75 a share annually for the following three years,respectively.After that,dividends are projected to increase by 3.5% per year.How much are you willing to pay to buy one share of this equity if your desired rate of return is 12%?
A)€1.45
B)€5.80
C)€7.25
D)€9.06
E)€10.58

Question

Quizplus · Accepted Answer

To calculate the price of an equity using dividend discount model, the formula is: 
Price = Dividend / (required rate of return - dividend growth rate)
For the first year, dividend = €0.25. 
The second year's dividend will be €0.40, so the growth rate is 0.6 (€0.40/€0.25), which can be applied to the formula. 
The required rate of return is 12%. 
Applying the formula: 
Price = €0.25 / (0.12 - 0.00) = €2.08 (rounded to two decimal points)
Price = €0.40 / (0.12 - 0.06) = €6.67 (rounded to two decimal points)
Price = €0.60 / (0.12 - 0.06) = €10.00 (rounded to two decimal points)
Price = €0.75 / (0.12 - 0.06) = €12.50 (rounded to two decimal points)
For the fifth year and beyond, the dividend growth rate is 3.5%, so it can be applied to the formula. 
Price = €0.75 * (1 + 0.035) / (0.12 - 0.035) = €19.18 (rounded to two decimal points)
Thus, the present value of this equity, in accordance with its dividends, is the sum of each of these dividends' present values, rounded to two decimal points:

€2.08 + €6.67 + €10.00 + €12.50 + €19.18 = €50.43

Which is your desired rate of return.
Therefore, the answer is C) €7.25.

NU YU Announced Today That It Will Begin Paying Annual