Wilbert's Clothing Stores just paid a €1.20 annual dividend.The company has a policy whereby the dividend increases by 2.5% annually.You would like to purchase 100 shares in this ﬁrm but realize
That you will not have the funds to do so for another three years.If you desire a 10% rate of return,
How much should you expect to pay for 100 shares when you can afford to buy this equity? Ignore
Trading costs.

Question

Quizplus · Accepted Answer

To calculate the expected price for 100 shares in three years, we first need to determine the future dividends and then discount them back to their present value at the desired rate of return. The dividend grows at a rate of 2.5% annually. 1. Calculate the dividend in three years:   - Year 1 dividend: €1.20 * (1 + 0.025) = €1.23   - Year 2 dividend: €1.23 * (1 + 0.025) = €1.26075   - Year 3 dividend: €1.26075 * (1 + 0.025) = €1.292272. Calculate the price of the stock in three years using the Gordon Growth Model (since the dividend grows at a constant rate):   - P = D / (r - g)   - Where P is the price, D is the dividend in the first year not owned (which is the Year 4 dividend for this scenario), r is the required rate of return, and g is the growth rate.   - Year 4 dividend: €1.29227 * (1 + 0.025) = €1.32458   - P = €1.32458 / (0.10 - 0.025) = €17.66 per share3. For 100 shares, the expected price would be €17.66 * 100 = €1,766.Therefore, you should expect to pay €1,766 for 100 shares when you can afford to buy this equity in three years.

Wilbert's Clothing Stores Just Paid a €1