Question

Jack owns 1,000 shares of ABC company stock. He expects to receive a total of $3 in dividend/share
next year (D1) with a growth rate of 4% a year in dividend. The market discount rate (r) is 10%. (Note: Round
up answers in 2 decimal points)
(a) If Jack wants to sell the stock at the end of year 5, what is the price he can sell (P5)?
(b) What is the intrinsic value of the stock [E(P0)] if Jack plans to sell the stock at year 5? (Use CFs & P5 to
calculate)
(c) What is the intrinsic value of the stock [E(P0)] if Jack plans to sell the stock at year 5? (Use DDM constant
formula to calculate)
(d) What should Jack do if the market price (P0) is now selling at $40? Why?
(e) What is the rate of return (%) of Jack if he buys the stock at [E(P0)] in (b) and sells it at P0 (price in (d))?

Answer 1

a. Share price, P5=D6/(market discount rate-growth rate)

D6=D1*(1+growth rate)^5=3*((1+4%)^5)=3.65

Share price, P5=3.65/(10%-4%)=$60.83

b. D2=D1*(1+4%)=3*1.04=3.120

D3=D2*(1+4%)=3.120*1.04=3.245

D4=3.245*(1+4%)=3.375

D5=3.375*(1+4%)=3.510

P5=60.83

Expected share price(EP0)=((D1/(1+10%))+((D2/(1+10%)^2)+((D3/(1+10%)^3)+((D4/(1+10%)^4)+((D5+P5)/(1+10%)^5)

=(3/1.1)+(3.12/1.1^2)+(3.245/1.1^3)+(3.375/1.1^4)+((3.510+60.83)/1.1^5)

=2.73+2.58+2.44+2.30+39.95

EP0=$50.0

c. EP0=D1/(discount rate-growth rate)=3/(10%-4%)=$50.0

d. The intrinsic value is $50 which is higher than the market value of $40. Therefore Jack has to buy to make profits

e. The rate of return=(50-40)/40=10/40=25%