Question

Church Inc. is presently enjoying relatively high growth because of a surge in the demand for its new product. Management expects earnings and dividends to grow at a rate of 22% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends to zero, i.e., g = 0. The company’s last dividend, D0, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. What is the current price of the common stock?

                a.            $26.57

                b.            $32.69

                c.             $28.97

                d.            $23.39

                e.            $27.37

Excel in detail please

Answer 1

Given about Church Inc.,

Risk free rate Rf = 3%

Market risk premium MRP = 5.5%

Beta of stock = 1.2

Using CAPM, cost of equity Ke = Rf + MRP*Beta

=> Ke = 3 + 5.5*1.2 = 9.6%

last dividend D0 = $1.25

dividend growth rate for 4 years = 22%

So, D1 = D0*1.22 = 1.25*1.22 = $1.53

D2 = 1.53*1.22 = $1.86

D3 = 1.86*1.22 = $2.27

D4 = 2.27*1.22 = $2.77

thereafter growth rate is 0

Value of perpetuity at year 4 is

P4(TV) = D4/Ke = 2.77/0.096 = $28.85

Stock price today is sum of PV of all future dividends and P4 discounted at Ke

So, P4 = D1/(1+Ke) + D2/(1+Ke)^2 + D3/(1+Ke)^3 + D4/(1+Ke)^4 + TV/(1+Ke)^4

All the calculations are shown in excel below.

final value of stock today is $26.57. So option A is correct.