Question

Q1. A firm is currently paying a dividend of $2.50. A stock analyst expects the dividend growth rate to decline linearly over the next seven years from 22% in the short run to 4% in the long run. If the required rate of return on the stock is 13%, the value of the stock is closest to:

options:

1) $42.94

2) $44.14

3) $46.39

4) $48.09

Q2. Which of the following is true regarding the residual income valuation model?
I- Can be applied to any firm regardless of the dividend policy.
II- They can only be applied to firm with positive free cash flows
III- Valuation with residual income models is relatively less sensitive to terminal value
estimates.
IV- These models focus on accounting profitability rather than just economic profitability

options:

1)
I and II

2)
II, III and IV

3)
I and III

4)
All of the above

Answer 1

Answers-

Q 1)

Dividend paid = D0 = $ 2.50
Dvidend growth rate to decline from 22 % (gs) to 4 % (gL)  in long run in a span of 7 years
required rate of return = r = 13 % - 0.13
H = 7/2 = 3.5

V0 = [ D0 x ( 1+gL) + D0 x H x (gs - gL) ] / (r - gL)

V0 = [ $ 2.50 x ( 1+ 0.04) + $ 2.50 x 3.5 x ( 0.22 - 0.04) ] / (0.13 - 0.04)

V0 = [ $ 2.50 x 1.04 + $ 2.50 x  3.5 x 0.18 ] / 0.09

V0 = [ $ 2.6 + $ 1.575 ] / 0.09

V0 = $ 4.175 / 0.09

V0 = $ 46.39

Therefore the correct Option is 3. $ 46.39

Q 2)

The ccorrect option is 3) I and III

The residual income valuation model is applicable to any firm regardless of the dividend policy and  is relatively less sensitive to terminal value estimates.

The Options II and IV are incorrect as the resiidual income can be applied with negative free cash flow as well.