Question

If a certain corporation just recently paid a dividend of $3.70, and the dividend is expected to grow at 4% for a long time into the future, calculate the price of this company’s stock at required returns of 8%, 10% and 12%. Then using a 10% required return, calculate the price at growth rates of 2%, 5% and 8%. Discuss what you see in the behavior of the prices in response to changes in the growth rate and changes in the required return. Using the price you calculated with a 4% growth rate and a 10% required return, what would be the expected dividend and price five years from today

Answer 1

a) Computation of Share Price if Required Return (Re) = 8% / 10% / 12%

Key Data

Expected Dividend (D₁) = $3.70 + 4% = $ 3.848

Required Return (Re) = 8% / 10% / 12%

Growth Rate (g) = 4%

Solution:

As per dividend discount model

Price of the Share (P₀) = D₁/(Re-g)

i) If Re = 8

Price of the Share (P₀)    = $3.848 / (8%-4%)

                                        = $ 96.2

ii) If Re = 10%

Price of the Share (P₀)    = $3.848 / (10%-4%)

                                        = $ 64.13

iii) If Re = 12%

Price of the Share (P₀)    = $3.848 / (12%-4%)

                                        = $ 48.1

b) Computation of Share Price if Growth Rate (g) = 2% / 5% / 8%

Key Data:

Expected Dividend (D₁) = D_0­ + g

                       If g = 2% = $3.70 + 2% = $ 3.774

                       If g = 5% = $3.70 + 5% = $ 3.885

                       If g = 8% = $ 3.70 + 8% = $ 3.996

Required Return (Re) = 10%

Growth Rate (g) = 2% , 5%, 8%

Solution:

As per dividend discount model

Price of the Share (P₀) = D₁/(Re-g)

i) If g = 2%

Price of the Share (P₀)    = $3.774 / (10%-2%)

                                        = $ 47.175

ii) If g = 5%

Price of the Share (P₀)    = $3.885 / (10%-5%)

                                        = $ 77.7

iii) If g = 8%

Price of the Share (P₀)    = $3.996 / (10%-8%)

                                        = $ 199.8

c)Discussion of behavior in prices

i) In case increase in required rate of return

We observe that as the rate of return increases price of the stock is falling as there is an inverse relationship between price and required rate of return.

As the investors wants higher return from the stock the stock price shall reduce in order to get the desired return

ii)In case of increase in growth Rate

We observe the price of the stock increases as the growth rate increases , therefore there is an direct relationship between stock price and growth rate.

As the dividends of the firm are growing , investors are getting more return on their stock and hence price of the share is also increasing.

d) Expected Price 5 years from now if growth rate is 4% and required rate is 10 %

As growth rate is 4 % share price will grow by 4 % every year

Price of the share today (P₀)= $ 64.13 [Calculated in working note a) sub point ii)]

Price at the end of 5^th Year = P₀(1+r)ⁿ

                                                       = $64.13(1.04)⁵

                                                          = $ 78.02 approx