Question

In: Finance

The dividend for Should I, Inc., is currently $1.70 per share. It is expected to grow...

The dividend for Should I, Inc., is currently $1.70 per share. It is expected to grow at 12 percent next year and then decline linearly to a perpetual rate of 3 percent beginning in four years. If you required a return of 16 percent on the stock, what is the most you would pay per share?

Solutions

Expert Solution

Explanation:
Given that the company is expected to grow at 12% in the next year. Then the growth rate will decline linearly (like 12%, 9%,and 6%) to a perpetual growth rate of 3% beginning in four years.

So, the growth rates will be 12%, 9%, and 6% in 1-3 years, then it will grow at a stable growth rate of 3% forever (or perpetuity).
The dividend for the company is currently $1.70 per share.
Dividend in the coming (or next) year that is D1=$1.7*(1+12%)=$1.7*(1.12)=$1.904
Similarly, in coming years, dividends will be:

D2=$1.904*(1+9%)=$2.07536
D3=$2.07536*(1+6%)=$2.1998816
D4=$2.1998816*(1+3%)=$2.265878048
The growth becomes stable (equal to 3%) beginning in four years. So, we need to calculate the terminal value.

Price at year 3 (or P3)=D3*(1+ stable or perpetual growth rate)/(Required rate of return-Perpetual growth rate)
Given that, the required rate of return is 16%.

Price at year 3 (or P3)=$2.1998816*(1+3%)/(16%-3%)=$2.265878048/(16%-3%)=$17.42983114
Now, we need to discount the values D1, D2, D3 and P3 to present value using the discount rate of 16% (which is the required rate of return here) to get the price today that we would pay.
So, Price=$1.904/(1+16%)^1+$2.07536/(1+16%)^2+$2.1998816/(1+16%)^3+$17.42983114/(1+16%)^3
=$1.904/(1.16)^1+$2.07536/(1.16)^2+$2.1998816/(1.16)^3+$17.42983114/(1.16)^3
=$1.904/(1.16)+$2.07536/1.3456+$2.1998816/1.560896+$17.42983114/1.560896

=$1.6413793+$1.542330559+$1.409371028+$11.16655507
=$15.7596 or $15.76 (rounded upto two decimal places)
So, we would pay $15.76 per share.


Related Solutions

The dividend for Should I, Inc., is currently $1.70 per share. It is expected to grow...
The dividend for Should I, Inc., is currently $1.70 per share. It is expected to grow at 12 percent next year and then decline linearly to a 3 percent perpetual rate in four years. If you require a 16 percent return on the stock, what is the most you would pay per share? Price per share: $_______
The dividend for Should I, Inc., is currently $1.67 per share. It is expected to grow...
The dividend for Should I, Inc., is currently $1.67 per share. It is expected to grow at 16 percent next year and then decline linearly to a perpetual rate of 4 percent beginning in four years. If you required a return of 11 percent on the stock, what is the most you would pay per share?
ABC, Inc. just paid a dividend of $2.50 per share. The dividends are expected to grow...
ABC, Inc. just paid a dividend of $2.50 per share. The dividends are expected to grow for the next 3 years at 8% per year, then grow at 3% per year forever. The required rate of return for ABC stock is 12% per year. a) What should the market price of ABC stock be? b) What should the ex-dividend stock price of ABC be in year 2? c) If you purchased the share of ABC at time 2, at the...
ABZ Corp. just paid a dividend of $1.00 per share. The dividend is expected to grow...
ABZ Corp. just paid a dividend of $1.00 per share. The dividend is expected to grow 6% per year in perpetuity.  The stock's beta is 0.85.  The risk-free rate is 3%, and the market risk premium is 7%. The current stock price is $37 per share.  Assume that one year from now the stock will be correctly valued. What are the dividend yield, capital gain yield and expected return for the coming year? Draw the Security Market Line and plot the stock on...
MMM Co. just paid a dividend of $1.10 per share. The dividend is expected to grow...
MMM Co. just paid a dividend of $1.10 per share. The dividend is expected to grow by 30% next year, 90% in both Years 2 & 3, 20% in Year 4, and then grow at a constant rate of 4% thereafter. The required rate of return is 5%. Compute the selling price of the stock.
The Portheus Corp. currently pays a dividend of $3.00 per share. This dividend is expected to...
The Portheus Corp. currently pays a dividend of $3.00 per share. This dividend is expected to grow at a rate of 14% per year for the next 5 years and at a constant rate of 4% per year thereafter. If Portheus’ stock has a required return of 8% per year, what should the current price of the stock be?
A company recently paid a $3 per share dividend, which is expected to grow at a...
A company recently paid a $3 per share dividend, which is expected to grow at a constant rate forever. The company’s stock, has a beta coefficient equal to 1.1, is selling for $40.50 per share. Currently, the risk-free rate of return is 3 percent and the return on an average stock is 10 percent. If the stock is selling at its equilibrium price, what is its growth rate?
Apple, Inc. just paid a dividend of $2.28 a share. Dividends are expected to grow at...
Apple, Inc. just paid a dividend of $2.28 a share. Dividends are expected to grow at a rate of 12% per year for the next three years and then at a rate of 3.5% thereafter. If your required rate of return is 9%, what is the most that you should be willing to pay for a share of Apple stock today?
Kai Zen Motors currently pays a dividend of $2 per share, and this dividend is expected...
Kai Zen Motors currently pays a dividend of $2 per share, and this dividend is expected to grow at a 20 percent annual rate for three years, and then at a 11 percent rate for the next two years, after which it is expected to grow at a 6 percent rate forever. What value would you place on the stock if a 16 percent rate of return were required? [5
A stock is selling for $40 per share currently. The next dividend will be $1 per share, and will grow at 12% per year forever.
A stock is selling for $40 per share currently. The next dividend will be $1 per share, and will grow at 12% per year forever. What is the rate of return required by investors? Answer: 14.5%
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT