Problem 7-17 Nonconstant Dividends [LO 1]
Apocalyptica Corporation is expected to pay the following dividends over the next four years: $5.10, $16.10, $21.10, and $2.90. Afterwards, the company pledges to maintain a constant 5.25 percent growth rate in dividends, forever.
Required:
If the required return on the stock is 7 percent, what is the current share price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
290*(1.0525)/(.7-.0525)
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To calculate the current share price, we need to determine the present value of the future dividends and the terminal value.
Step 1: Calculate the present value of the future dividends.
The formula to calculate the present value of a dividend is:
PV = D1 / (1 + r) + D2 / (1 + r)^2 + D3 / (1 + r)^3 + ... + Dn / (1 + r)^n
Where:
PV = Present value
D1, D2, D3, ..., Dn = Dividends in each period (in this case, $5.10, $16.10, $21.10, and $2.90)
r = Required return on the stock (in this case, 7% or 0.07)
PV = $5.10 / (1 + 0.07) + $16.10 / (1 + 0.07)^2 + $21.10 / (1 + 0.07)^3 + $2.90 / (1 + 0.07)^4
Perform the calculations:
PV = $4.77 + $14.73 + $17.08 + $2.43
PV = $39.01
Step 2: Calculate the terminal value.
The terminal value can be calculated using the Gordon Growth Model:
Terminal Value (TV) = Dn * (1 + g) / (r - g)
Where:
Dn = Dividend in the last period (in this case, $2.90)
g = Growth rate of dividends (in this case, 5.25% or 0.0525)
r = Required return on the stock (in this case, 7% or 0.07)
TV = $2.90 * (1 + 0.0525) / (0.07 - 0.0525)
Perform the calculations:
TV = $2.90 * (1.0525) / (0.0175)
TV = $174.37
Step 3: Calculate the current share price.
The current share price is the sum of the present value of the future dividends and the terminal value:
Current Share Price = PV + TV
Current Share Price = $39.01 + $174.37
Perform the calculations:
Current Share Price = $213.38
Therefore, the current share price is $213.38.
To calculate the current share price of Apocalyptica Corporation, we can apply the formula for the present value of dividends.
The formula for the present value of dividends is:
Current Share Price = Σ(Dividend / (1 + r)^t)
Where:
- Σ represents the summation symbol (adding up all the terms)
- Dividend represents the dividend payment each year
- r represents the required return on the stock
- t represents the time period
Given that Apocalyptica Corporation is expected to pay the following dividends over the next four years: $5.10, $16.10, $21.10, and $2.90, we can calculate the current share price using the given required return of 7 percent.
Current Share Price = (5.10 / (1 + 0.07)^1) + (16.10 / (1 + 0.07)^2) + (21.10 / (1 + 0.07)^3) + (2.90 / (1 + 0.07)^4)
Calculating each term separately, we have:
Current Share Price = (5.10 / 1.07^1) + (16.10 / 1.07^2) + (21.10 / 1.07^3) + (2.90 / 1.07^4)
Simplifying each term, we get:
Current Share Price = 4.77 + 13.69 + 16.39 + 2.65
Adding up all the terms, we have:
Current Share Price = 37.5
Therefore, the current share price of Apocalyptica Corporation is $37.50.