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Mastercard Inc
Mastercard Inc.'s stock has a required return of 8% and the stock is currently priced at $125 per share. Mastercard just paid a dividend of $2.00, and they have announced that they plan to increase its dividend payment at a rate of 30% per year for the next 4 years. After Year 4, they expect the dividend growth rate to slow down from the 20% to a more modest constant growth rate of X% per year going forward forever. What is the constant growth rate that Mastercard is expecting after Year 4 (i.e., what is X)?
Expert Solution
Required rate of Return(Ke) = 8%
Current Price(P0) = $125 per share
Dividend just paid(D0) = $2
Growth rate of Dividend for next 4 years(g) = 30%
Constant Growth rate thereafter(g1)= X
P0= (((D0*(1+ g)^1))/(1+ ke)^1)+ (((D0*(1+ g)^2))/(1+ ke)^2)+ (((D0*(1+ g)^3))/(1+ ke)^3)+ (((D0*(1+ g)^4))/(1+ ke)^4)+ ((((D0*(1+ g)^4)*(1+X))/(1+ ke)^4)* (1/ ( ke- g1))
125 = (((2* (1+30%)^1))/(1+8%)^1)+ (((2* (1+30%)^2))/(1+8%)^2)+ (((2* (1+30%)^3))/(1+8%)^3)+ (((2* (1+30%)^4))/(1+8%)^4)+ (((2* (1+30%)^4)* (1+ X))/(1+8%)^4) *(1/ ( 8%- g1))
125= 2.4074+ 2.8978+ 3.4881+ 4.1986+ 4.1986*(1+X)/(0.13-X)
125= 12.9919+ 4.1986*(1+X)/(0.13-X)
112.0081= 4.1986*(1+X)/(0.13-X)
112.0081* (0.13-X)= 4.1986+ 4.1986 X
14.56105- 112.0081 X=4.1986+ 4.1986 X
10.36245= 116.2067 X
X= 10.36245/ 116.2067
= 0.08917 or 8.92%
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