Question
EME is a manufacturer of toy construction equipment. If it pays out all of its earnings as dividends, it will have earnings of 0.3 million per quarter in perpetuity. Suppose that the discount rate, expressed as an effective annual rate (EAR), is 16%. TEME pays dividends quarterly.
What is the value of TEME if it continues to pay out all of its earnings as dividends? Assume that the next dividend is paid one quarter from now.
*Make sure to input the answer without any currency symbols, commas, and remove M as Million value.
e.g. 6,000,000 = 6M, so the answer should be written as 6
What is the value of TEME if it continues to pay out all of its earnings as dividends? Assume that the next dividend is paid one quarter from now.
*Make sure to input the answer without any currency symbols, commas, and remove M as Million value.
e.g. 6,000,000 = 6M, so the answer should be written as 6
Answers
GPT-4o mini
To determine the value of TEME, we can use the formula for the present value of a perpetuity:
\[
PV = \frac{D}{r}
\]
where \( D \) is the dividend per period and \( r \) is the discount rate per period.
1. **Finding the quarterly dividend**:
The earnings are \( 0.3 \) million per quarter, which translates to dividends of:
\[
D = 0.3
\]
2. **Finding the discount rate per quarter**:
The effective annual rate (EAR) is \( 16\% \). We need to convert this to a quarterly rate. The relationship between the EAR and the effective quarterly rate is given by:
\[
(1 + r_{annual}) = (1 + r_{quarterly})^4
\]
Letting \( r_{annual} = 0.16 \):
\[
1.16 = (1 + r_{quarterly})^4
\]
Now, we can solve for \( r_{quarterly} \):
\[
1 + r_{quarterly} = 1.16^{1/4}
\]
Calculating this:
\[
1.16^{1/4} \approx 1.0373
\]
Therefore:
\[
r_{quarterly} \approx 0.0373 \text{ or } 3.73\%
\]
3. **Calculating the present value**:
Now we can substitute \( D \) and \( r \) into the perpetuity formula:
\[
PV = \frac{0.3}{0.0373} \approx 8.0255
\]
Thus, the value of TEME is approximately 8.0255.
Since the answer needs to be in a specific format (without currency symbols and M for million), we'll round it to 8.
Final answer:
\[
\boxed{8}
\]
\[
PV = \frac{D}{r}
\]
where \( D \) is the dividend per period and \( r \) is the discount rate per period.
1. **Finding the quarterly dividend**:
The earnings are \( 0.3 \) million per quarter, which translates to dividends of:
\[
D = 0.3
\]
2. **Finding the discount rate per quarter**:
The effective annual rate (EAR) is \( 16\% \). We need to convert this to a quarterly rate. The relationship between the EAR and the effective quarterly rate is given by:
\[
(1 + r_{annual}) = (1 + r_{quarterly})^4
\]
Letting \( r_{annual} = 0.16 \):
\[
1.16 = (1 + r_{quarterly})^4
\]
Now, we can solve for \( r_{quarterly} \):
\[
1 + r_{quarterly} = 1.16^{1/4}
\]
Calculating this:
\[
1.16^{1/4} \approx 1.0373
\]
Therefore:
\[
r_{quarterly} \approx 0.0373 \text{ or } 3.73\%
\]
3. **Calculating the present value**:
Now we can substitute \( D \) and \( r \) into the perpetuity formula:
\[
PV = \frac{0.3}{0.0373} \approx 8.0255
\]
Thus, the value of TEME is approximately 8.0255.
Since the answer needs to be in a specific format (without currency symbols and M for million), we'll round it to 8.
Final answer:
\[
\boxed{8}
\]