Question

This​ year, Midland Light and Gas​ (ML&G) paid its stockholders an annual dividend of

​$2.50

a share. A major brokerage firm recently put out a report on​ ML&G predicting that the​ company's annual dividends should grow at the rate of

5​%

per year for each of the next seven years and then level off and grow at the rate of

3​%

a year thereafter.

​(Note​:

Use four decimal places for all numbers in your intermediate​ calculations.)a. Use the​ variable-growth DVM and a required rate of return of

8.60​%

to find the maximum price you should be willing to pay for this stock.b. Redo the​ ML&G problem in part ​a, this time assuming that after year​ 7, dividends stop growing altogether​ (for year 8 and​ beyond,

g=0​).

Use all the other information given to find the​ stock's intrinsic value.

c. Contrast your two answers and comment on your findings. How important is growth to this valuation​ model?

a. Using the​ variable-growth DVM and a required rate of return of

8.60​%,

the maximum price you should be willing to pay for the stock is

​$nothing.

​(Round to the nearest​ cent.)

Answer 1

Under DVM, price of the stock is the present value future dividends

In the given case, there are 2 stages of growth: first for 7 years at the rate of 5% (growing annuity) and infinitely at 3% thereafter (growing perpetuity).

Also given, last dividend= $2.50

Part (a):

Given, required rate of return (r ) = 8.6%

Present value of first stage dividend= (P/(r-g1))*(1-((1+g1)/(1+r))^n)

Where

P= First year dividend= $2.5*(1+5%)= $2.625,

n= Number of payments (7),

r= Rate of interest per period in decimals (0.086) and g1= Growth rate per period in decimals (0.05)

Plugging the values,

PV= (2.625/(0.086-0.05))*(1-((1+0.05)/(1+0.086))^7)=15.3271911

PV of second stage= (D8/(r-g2))/(1+r)^7

Where g2= growth rate after 7 years (given as 3%)

Where D8= Dividend for year 8 = 2.50*(1+5%)^7*(1+3%) = $3.62328

PV= ($3.62328/(0.086-0.03))/(1+0.086)^7 = $36.3166

Current price of the stock= 15.3272 + 36.3166 = $51.64

Part (b):

With g=0 for year 8 and beyond, Dividend after 7 years is a perpetuity. PV at year 7= D8/r

PV of dividends after 7 years, now= (3.62328/0.086)/(1+0.086)^7 = $22.9593

Current price= 15.3271911 + 22.9593 = $38.29

This shows that growth, after year 7 has contributed $13.35 (about 35%) of the current value of the stock.