Question

(a) Union Pacific currently does not pay a dividend. You expect that the company will begin paying a dividend of $2 per share in 6 years, and you expect dividends to grow indefinitely at a 3.5% rate per year thereafter. If the required rate of return is 12 percent, how much is the stock currently worth? [8 Points) (b) Walmart Inc. just paid a dividend of do = $2.08 per share. The dividends are expected to grow at a rate of 6 percent for the next four years and then level off to a 3 percent growth rate indefinitely. If the required rate of return is 12 percent, what is the value of the stock today? [12 Points]

Answer 1

Value of stock is equal to the present value of all future dividends

Value of stock in 5 years = Dividend in Year 6/(Required return - growth rate)

= 2/(12%-3.5%)

= $23.53 per share

Value of stock today = 23.53/(1.12)^5

= $13.35 per share

b)Value of stock = 2.08(1.06)/(1.12) + 2.08(1.06)^2/(1.12)^2 + 2.08(1.06)^3/(1.12)^3 + 2.08(1.06)^4/(1.12)^4 + 2.08(1.06)^4(1.03)/(1.12)^4(12%-3%)

= $26.36 per share

Answer 2

Solution :

a.

D0 = D1 = D2 = D3 = D4 = D5 = 0

D6 = 2 ($)

g = 3.5% = 0.035 = constant for ever from year 6 onwards.

r = 12% = 0.12

=> 1 + r = 1.12

So,

P5 = D6/(r - g)

=> P5 = 2/(0.12 - 0.035) = 23.53 ($) 

=> P0 = P5/(1 + r)^5 = 23.53/1.12^5 = 13.35 ($)

Hence, 

Worth of the stock today = $13.35  (ANSWER)

b.

D0 = 2.08 ($)

g = 6% for 4 years 

So,

D1 = 2.08*1.06 = 2.2048 ($)

D2 = 2.2048*1.06 = 2.3371 ($)

D3 = 2.3371*1.06 = 2.4773 ($)

D4 = 2.4773*1.06 = 2.6260 ($)

g = 3% from year 5 onwards = 0.03

D5 = 2.6260*1.03 = 2.7047 ($)

r = 12% = 0.12

=> 1 + r = 1.12 

So,

P4 = D5/(r -g) = 2.7047/(0.12 - 0.06) = 45.08 ($)

P0 = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + (D4 + P4)/(1+r)^4

= 2.2048/1.12 + 2.3371/1.12^2 + 2.4773/1.12^3 + (2.6260+45.08)/1.12^4

= 35.91 ($)

Hence,

Value of the stock today = $35.91 (ANSWER)