This year, Midland Light and
This year, Midland Light and Gas (ML&G) paid itsstockholders an annual dividend of
$2.50
a share. A major brokerage firm recently put out a report onML&G predicting that the company’s annual dividends shouldgrow at the rate of
5%
per year for each of the next seven years and then level off andgrow at the rate of
3%
a year thereafter.
(Note:
Use four decimal places for all numbers in your intermediatecalculations.)a. Use the variable-growth DVM and a required rateof return of
8.60%
to find the maximum price you should be willing to pay for thisstock.b. Redo the ML&G problem in part a, this time assumingthat after year 7, dividends stop growing altogether (for year 8and beyond,
g=0).
Use all the other information given to find the stock’sintrinsic value.
c. Contrast your two answers and comment on your findings. Howimportant is growth to this valuation model?
a. Using the variable-growth DVM and a required rate of returnof
8.60%,
the maximum price you should be willing to pay for the stockis
$nothing.
(Round to the nearest cent.)
Answer:
Under DVM, price of the stock isthe present value future dividends
In the given case, there are 2stages of growth: first for 7 years at the rate of 5% (growingannuity) and infinitely at 3% thereafter (growingperpetuity).
Also given, last dividend=$2.50
Part (a):
Given, required rate of return (r )= 8.6%
Present value of first stagedividend= (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 indecimals (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 currentvalue of the stock.
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