Question

7. Perry, Inc., paid a dividend of $2.50 yesterday. You are interested in investing in this company, which has forecasted a constant-growth rate of 7 percent for its dividends, forever. The required rate of return is 18 percent. (14 points)

a. Calculate D1, D2, D3, and D4. (2 points)

b. Compute the present value of these four dividends. (3 points)

c. What is the expected value of the stock four years from now (P4)? (3 points)

d. What is the value of the stock today based on the answers to parts b, and c? (3 points) e. Use the constant growth model to compute the value of the stock today. (3 points)

Answer 1

1.
Di=D0*(1+g)

D1:
=2.5*1.07=2.675

D2:
=2.5*1.07^2=2.86225

D3:
=2.5*1.07^3=3.0626075

D4:
=2.5*1.07^4=3.276990025

2.
PV of Di=Di/(1+r)^i

PV of
D1:
=2.5*(1.07/1.18)=2.26694915254237

D2:
=2.5*(1.07/1.18)^2=2.05562338408503

D3:
=2.5*(1.07/1.18)^3=1.86399747539914

D4:
=2.5*(1.07/1.18)^4=1.69023499887888

Total PV=Sum of PV of Di
Total PV=7.88

3.
P4=D4*(1+g)/(r-g)=2.5*1.07^4*1.07/(18%-7%)=31.8761757

4.
Value of the stock today=31.8761757/1.18^4+7.88=24.31818182

5.
P0=D0*(1+g)/(r-g)=2.5*1.07/(18%-7%)=24.31818182