Question

Crisp Cookware's common stock is expected to pay a dividend of $1.5 a share at the end of this year (D₁ = $1.50); its beta is 0.75; the risk-free rate is 5.1%; and the market risk premium is 5%. The dividend is expected to grow at some constant rate g, and the stock currently sells for $30 a share. Assuming the market is in equilibrium, what does the market believe will be the stock's price at the end of 3 years (i.e., what is  )? Do not round intermediate steps. Round your answer to the nearest cent

Answer 1

Actual Value of share at the end of year 3 = present value of dividend + present value of share

Workings -

1. Calculation of cost of capital ( K_e)

cost of capital = R_f + Beta ( )

Where

(R_f ) Risk free rate of Return = 5.1%

Market risk premium  = 5 %

Beta = 0.75

cost of capital = 5.1 % + 0.75 ( 5%)

= 8.85 %

2. Calculation of growth rate (g)

share value = dividend per share (D₁) / ( K_e - g)

$ 30 =$1.5/ ( 0.0885 - g)

$ 2.655 - $ 30 g = $ 1.5

( $ 2.655 - $ 1.5 ) / $ 30 = g

g = 0.0385

or 3.85 %

3. Calculation of present value of dividend

year	dividend	PVF @ 8.85%	Present Value
1	1.5 + 3.85% = 1.557	0.9187	1.430
2	1.557 +3.85% = 1.6177	0.8440	1.365
3	1.617 + 3.85% = 1.680	0.7754	1.303
		Total PV	4.098

new value of share at the end of year 3 = 1.303 / (0.0885 -0.0385 )

= $ 26.06

Actual Value of share at the end of year 3 = present value of dividend + present value of share

= $ 4.098 + 0.7754 * $ 26.06

= $ 24.30

or

if we consider value of share $ 30 then -

= $ 4.098 + 0.7754 * $ 30

= $ 27.36