Question

1. A stock paid a dividend of $1 per share in 2019. Dividend will increase by 3% for the next two years and remain the same for the next three years. Thereafter, dividend will grow by 2% each year forever. Assume that the beta of the stock is 1.3, the equity risk premium is 5%, and the market return is 6.5%.

1. Find the risk-free rate
2. All things being equal, do you expect the stock to outperform the market? Why?
3. Estimate equity cost of capital
4. Determine the terminal value
5. What does the terminal value represent?
6. What type of model would you use to determine the value of the stock?
7. Determine the intrinsic value of the stock
8. If the stock is currently trading at $60, what would be your recommendation?

Answer 1

A. Given equity risk premium is 5%= (Rm-Rf)

market return is 6.5%=(Rm)

equity risk premium is the extra return that you will receive by investing in the market rather than investing in risk free assets .

Return from risk free assets= Rf

so subsitution Rm in Rm-Rf

=6.5%-Rf=5%

Return from risk free assets= Rf= 1.5%

B I expect the stock to outperform the market. Beacause Beta of the stock explains how the stock will perform in relation to changes in the market. Beta of the market is 1 but the beta of the stock is given as 1.3. This 1.3 tells that the when the market changes by 1% the stock changes by 1.30% so if the market is upward by 1% then the stock will be upward by 1.30%. Thus the stock will outperform the market

C. Estimate equity cost of capital Ke

As per Capital asset pricing model CAPM Ke= Rf+(Beta*(Rm-Rf))

We know that Rf from A=1.5%

Beta of the stock=1.3

Rm-Rf=5%

so Ke=1.5%+1.3(5%)=1.5%+6.5%=8%

So  Estimate equity cost of capital Ke =8%

d.  terminal value=

Terminal value of the perpectual cash flow= C*(1+g)/(WACC-g)

=Since the cashflow is the dividend and divident grows perpetually from year 6 so the C= Divident paid in year 5

Given divident paid in the 2019= 1$ considered as D0

Then the dividends for the future years = Dividend of the last year (1+growth rate (g))

Dividends are calculated as follows

Growth in dividend(g)		3%	3%	0	0	0	2%
Year	0	1	2	3	4	5	6
Dividend amount	1.000	1.030	1.061	1.061	1.061	1.061	1.082
Explaination	given in question	=1*(1+3%)	=(1.030*(1+3%)	1.061*(1+0)	1.061*(1+0)	1.061*(1+0)	1.061*(1+2%)

Terminal value= C*(1+g)/(WACC-g)

WACC= Ke = 8%

g is the constant growth rate 2%

C= dividend in year 5

=1.061*(1+2%)(8%-2%)=1.082/6%

so terminal value=18.0353$

e. The terminal value reperesents the price of the stock at the end of the 5 th year if the constant growth in dividend is 2% and cost of capital is 8%

f I would Didivdend growth model  to determine the value of the stock

g intrinsic value of the stock

= d1/(1+ke)+ d2/(1+ke)^2+ d3/(1+ke)^3+ d4/(1+ke)^4+d5/(1+ke)^5+P5/(1+ke)^5

year	Dividend amount & price at 5 th year (A)	Present value factor@ ke 8%(B)	Present value(A*B)
1	1.030	0.925926=1/(1.08)^1	0.953704
2	1.061	0.857339=1/(1.08)^2	0.909551
3	1.061	0.793832=1/(1.08)^3	0.842177
4	1.061	0.73503=1/(1.08)^4	0.779793
5	1.061	0.680583=1/(1.08)^5	0.722031
6	18.0353(price)	0.680583=1/(1.08)^5	12.27452
		Total	16.48178

intrinsic value of the stock=16.48178$

h if the stock is trading at 60$ then it means stock is trading and premium and hence not recommend to buy. Because it is not worthy