Thirsty Cactus Corp. just paid a dividend of $1.25 per share. The dividends are expected to grow at 28 percent for the next eight years and then level off to a 6 percent growth rate indefinitely. If the required return is 13 percent, what is the price of the stock today? (Do not include the dollar sign ($). Round your answer to 2 decimal places. (e.g., 32.16))
1) N=8 / I%=28 / PV=1.25 therefore FV = 9.008
2) 9.008 x 1.06 = 9.54848
3) 9.54848 / (.13-.06) = 136.41
4) N=8 / I%=13 / FV= 136.41 therefore PV = 51.31
5) PV of Growing Annuity (From t=0 to infinity) = 18.25
6) 51.31 + 18.25 = 69.56
I wanted to know how you calculated for present value of the growing annuity.
how did you calculate the present value of growing annuity?
To find the price of the stock today, we need to calculate the present value of all the future dividends.
First, let's calculate the present value of the dividends for the first eight years since they are growing at 28 percent.
1. Calculate the discounted value of the dividends for the first eight years using the formula for the present value of a growing perpetuity:
PV = D * (1 - (1 + g)^(-n)) / (r - g)
where PV is the present value of the dividends, D is the dividend payment, g is the growth rate, r is the required return, n is the number of years.
In this case:
D = $1.25 (dividend payment)
g = 28% = 0.28 (growth rate)
r = 13% = 0.13 (required return)
n = 8 (number of years)
PV = $1.25 * (1 - (1 + 0.28)^(-8)) / (0.13 - 0.28)
2. Calculate the present value of the dividends after the eighth year, when the growth rate levels off at 6 percent.
For the dividends after the eighth year, they are growing at a constant rate. We can use the formula for the present value of a growing perpetuity to calculate this:
PV = D / (r - g)
In this case:
D = $1.25 * (1 + 0.28)^8 (dividend payment in the eighth year)
g = 6% = 0.06 (growth rate after the eighth year)
r = 13% = 0.13 (required return)
PV = [$1.25 * (1 + 0.28)^8] / (0.13 - 0.06)
3. Finally, calculate the total present value of all dividends by adding the present value of the dividends for the first eight years with the present value of the dividends after the eighth year.
Total PV = PV (first eight years) + PV (after eighth year)
Round the final answer to two decimal places.
Now let's perform the calculations:
PV (first eight years) = $1.25 * (1 - (1 + 0.28)^(-8)) / (0.13 - 0.28)
PV (after eighth year) = [$1.25 * (1 + 0.28)^8] / (0.13 - 0.06)
Total PV = PV (first eight years) + PV (after eighth year)
The final answer will be the price of the stock today.
Christina, Erika, Rusty, Delaney, Samy -- several similar questions from the same person -- without any attempt at posting what you don't understand -- is a big turnoff for Jiskha tutors. We expect students to make an effort be and be explicit about what they don't understand.
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