Question

Mexican Motors stock sells for 200 pesos per share and next year's dividend is 8.5 pesos. Security analysts are forecasting earnings growth of 7.5% per year for the next five years. a) Assume that earnings and dividends are expected to grow at 7.5% in perpetuity. What rate of return are investors expecting?

Answer 1

a..
Div. for Yr.	0	1
Div. CF		8.5
Price P1=8.5*1.075/(r-0.075)		9.1375/(r-0.075)
P0=200=	(8.5/(1+r)^1)+(((9.1375/(r-0.075))/(1+r)^1)

As the dividends grow at the rate of 7.5% ,right from Year 2 to perpetuity,using   Discounted cash flows of dividends ,

Current share price= sum of PV of dividend cash flows including the present value of constant growth -dividends,

Proceeding as above ,

equating the current price of the Mexican Motors Stock to the sum of the present values of the dividend cash flows , discounted at the investors' required return, r

200=(8.5/(1+r)^1)+(((9.1375/(r-0.075))/(1+r)^1)

Solving the above,

the reqd. rate of return, r= 11.75%

ANSWER: The investors are expecting 11.75% return.

b. g= the sustainable growth rate(SGR)=

ROE*Retention ratio

ie.g=12%*(1-50%)=

6%

The growth rate is 6% (as compared to the above 7.5% forecasted.

Div. for Yr.	0	1
Div. CF		8.5
Price P1=8.5*1.06/(r-0.06)		9.01/(r-0.06)
P0=200=	(8.5/(1+r)^1)+(((9.06/(r-0.06))/(1+r)^1)

As growth rate ,g of dividends changes,

The above answer needs to be revised as now, the investors'reqd. return will differ.

So, reworking on a.

equating the current price of the Mexican Motors Stock to the sum of the present values of the dividend cash flows , discounted at the investors' required return, r

200=(8.5/(1+r)^1)+(((9.01/(r-0.06))/(1+r)^1)

Solving the above,

the reqd. rate of return, r= 10.25%

ANSWER: The investors are expecting 10.25% return.