Question

Following table is the data of past dividend payments.



　 dividend (in millions)
2012 $1.00
2013 $1.50
2014 $2.00
2015 $2.35
2016 $3.15
2017 $4.00
2018 $4.65
2019 $5.25
2020 $5.96


Using the past dividend data, you will forecast the future growth rate.

The most recent dividend paid by New Technologies was an annual dividend of $5.96 million in total and there are 20 million shares outstanding .

Assume T-bill rate is 3%, S&P500 market return is 7%, beta of New Technologies is 0.88.



#1. What is the appropriate discount rate (required rate of return)?

#2. You forecast that future dividends will grow for 3 years at the geometric average of historical dividend growth rate using the data given. What is the geometric average of historical dividend growth rate?

#3. You assume that dividends for the next 3 years will be increased at the rate you just calculated from #2. After that, you assume dividends are expected to increase by 4% each year forever. What should be today’s stock price per share?

#4. If the H-model is applied to the above question, at what rate should the growth rate decline each year to reach the constant growth rate of 4%?

#5. Using the H-model, what should be the stock price per share today?




#1. k = 5.54%


#1. k = 6.52%


#1. k = 9.24%


#2. geometric avg growth rate = approx. 25%


#2. geometric avg growth rate = approx. 21%


#2. geometric avg growth rate = approx. 28%


#3. approx. $15.50 per share


#3. approx. $40.30 per share


#3. approx. $21.10 per share


#4. each year it should decline by 5% per year


#4. each year it should decline by 7% per year


#4. each year it should decline by 9% per year


#5. approx. $17.80 per share


#5. approx. $20.90 per share


#5. approx. $15.20 per share

Answer 1

1. The appropriate required/discount rate (r) is determined from CAPM model

Required rate = risk free rate + beta *( market rate of return - risk free rate)

T- bills rate can be taken as risk free rate

So, Required rate (r) = 3%+0.88*(7%-3%) = 6.52%

2. The geometric average return = (last year value/1st year value) ^ (1/no. of periods) - 1

There are 9 values given for 8 periods (2012-13 is one period and so on)

Geometric average return = (5.96/1)^(1/8) -1 = 0.249988 = 25%

3. Here

Last dividend per share = C0 = $5.96 million/20million shares = $0.298

C1= 0.298*1.25 =$0.3725

C2 = 0.3725*1.25 = $0.465625

C3 = 0.465625*1.25 = $0.582031

C4 = 0.582031*1.04 = $0.605313

So, Terminal value of share at the end of 3rd year (as per constant growth model)

V3 = C4/(r-g) where C4 is the 4th year dividend , r is the required rate and g is the constant growth rate

= 0.605313/0.0252 = $24.02034

So value of share today

V0 = C1/1.0652+ C2/1.0652^2+C3/1.0652^3 + V3/1.0652^3

= 0.3497+0.410368+0.481563+19.87402

=$ 21.10

4) If the H model is to be applied. the growth rate declines every year from 25% to reach 4%in 3 years

So, it should decline by (25%-4%)/3 =7% each year