Question

Note: If not otherwise stated, assume that:

• Firms make annual dividend payments

• Stock prices are the present value of all future dividends and don’t include dividends that were just paid.

Whitewater Adventures has just paid a dividend of $4.00. An analyst forecasts annual dividend growth of 9% for the next five years at t=1, 2,…, 5, after which dividends will decrease by 1% per year indefinitely (at t=6, 7, …, ∞). The required return is 8% (EAR). What is the current value per share according to the analyst?

Select one:

$81.00

$66.64

$72.92

$71.29

$61.14

$64.00

$100.0

$0.0, since dividends are declining to zero

NOTE: Please show all the work, without using excel, unless necessary. (step by step with equations) Thanks!

Answer 1

It is option B
the dividends for year 1 to 5 is below
Year 1=4*(1+9%)=4.36
Year 2=4*(1+9%)^2=4.75
Year 3=4*(1+9%)^3=5.18
Year 4=4*(1+9%)^4=5.65
Year 5=4*(1+9%)^5=6.15
The present value of year 1 to 5 discounte dusing 8% is below
=(4.36/1.08^1)+(4.75/1.08^2)+(5.18/1.08^3)+(5.65/1.08^4)+(6.15/1.08^5)=20.56
For year 6 =6.15*(1-1%)=6.09
year 7=6.15*(1-1%)^2=6.03
it goes on ,,,,,,
the present value of it
year 6=6.09/1.08^6=3.84
yer 7=6.03/1.08^7=3.52
this is a sum of infinte to GP and formuale for it is = first term/(1-difference)
a,ar,ar^2.....
sum=a/(1-r)
here a=3.84 and r=3.52/3.84=0.916667
sum=3.84/(1-0.916667)=46.075
the total is 20.56+46.07=66.64