Question

Investors require a 7% rate of return on Mather Company's stock (i.e., r_s = 7%).

1. What is its value if the previous dividend was D₀ = $1.75 and investors expect dividends to grow at a constant annual rate of (1) -3%, (2) 0%, (3) 3%, or (4) 5%? Do not round intermediate calculations. Round your answers to the nearest cent.

2. Using data from part a, what would the Gordon (constant growth) model value be if the required rate of return was 8% and the expected growth rate was (1) 8% or (2) 12%? Round your answers to the nearest cent. If the value is undefined, enter N/A.

Answer 1

Ans:- (a) Value of the stock by Gordon Model is given by P0 = D0 * (1+g) / (rs -g), where D0 is the last dividend paid, rs is the required rate of return and g is the growth rate,

D0 = $1.75, rs = 7%

(1) If g =-3%, then P0 =$1.75*(1-0.03) / [ 0.07 - (-0.03)] = $16.98

(2) If g= 0%, then P0 = $1.75*(1-0) / (0.07 - 0) = $25

(3) If g= 3%, then P0 = $1.75*(1+0.03) / (0.07 - 0.03) =$45

(4) If g = 5%, then P0= $1.75 * (1+0.05) / (0.07 - 0.05) = $92

Ans:-(b) If rs = 8%, g=8%, and D0 = $1.75, then P0 = $1.75 * (1+0.08) / (0.08 - 0.08) = N/A or undefined

If g = 12%, then P0 = $1.75 * (1+0.12) / (0.08 - 0.12) = -$49, which is not appicable.

Gordon Model is based on the assumption that the required rate of return (rs) is greater than growth rate ( rs > g) but in part (b) rs is not greater than g, therefore Gordon model will not be applicable when g = 8% and g =12% and hence the prices cannot be determined.

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