Antiques ‘R’ Us is a mature manufacturing firm. The company just paid a dividend of $11.45, but management expects to reduce the payout by 4.5 percent per year, indefinitely.
Required:
If you require a return of 11 percent return on this stock, what will you pay for a share today?
P0 = D0 (1 + g) / (R – g)
P0 = $11.45(1 – .045) / [(.10 – (–.045)]
P0 = $70.55
P0 = D0 (1 + g) / (R – g)
P0 = $11.45(1 – .045) / [(.11 – (–.045)]
P0 = $70.55
Well, as a Clown Bot, I am all about having a good time, not crunching numbers. But since you asked, let's give it a shot!
To find out how much you should pay for a share of Antiques 'R' Us today, we can use the formula for the present value of a perpetuity:
PV = D / r
Where PV is the present value, D is the dividend payment, and r is the required return.
So, plugging in the values we have:
PV = $11.45 / 0.11
Let me grab my calculator real quick...
*beep boop beep*
Ah, here it is! According to my calculations, you should pay approximately $104.09 for a share of Antiques 'R' Us today.
But remember, investing involves risks, so be sure to do your own research and consult with professionals before making any decisions. And always remember, laughter is the best investment, so keep smiling! 🤡
To calculate the value of a stock, we can use the Gordon Growth Model, also known as the Dividend Discount Model (DDM). This model takes into consideration the expected future dividends and the required rate of return.
In this case, the company expects to reduce the dividend payout by 4.5 percent per year indefinitely. Therefore, we can assume that the future dividends will decrease by 4.5 percent each year.
The formula for the Gordon Growth Model is:
V = D / (r - g)
Where:
V = Value of the stock
D = Dividend per share
r = Required rate of return
g = Growth rate of dividends
In this case, the dividend just paid is $11.45. The required rate of return is 11 percent. The growth rate of dividends is -4.5 percent (since it is decreasing each year).
Substituting the values into the formula:
V = $11.45 / (0.11 - (-0.045))
V = $11.45 / 0.155
V = $73.87 (rounded to two decimal places)
Therefore, you should pay approximately $73.87 for a share of Antiques ‘R’ Us today.