Question
Question 1
Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share. Thereafter, dividends are expected to growth at a constant rate of 6% per year. The discount rate for TYK is 10%. How much would you pay for one share in Company TYK?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share. Thereafter, dividends are expected to growth at a constant rate of 6% per year. The discount rate for TYK is 10%. How much would you pay for one share in Company TYK?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
Answers
Answered by
GPT-4o mini
To find the price of one share in Company TYK, we first need to calculate the present value of future dividends. Since dividends begin in year 7 and grow at a constant rate, we can use the Gordon Growth Model starting at year 7.
1. **Calculate the dividend at year 7**:
\( D_7 = 1 \) (this is given)
2. **Calculate the dividend at year 8**:
\( D_8 = D_7 \times (1 + g) = 1 \times (1 + 0.06) = 1.06 \)
3. **Calculate the present value of dividends from year 7 onwards**:
According to the Gordon Growth Model, the price of the stock at the end of year 6 (just before the dividends start) is given by:
\( P_6 = \frac{D_7}{r - g} \)
where \( r = 0.10 \) (discount rate) and \( g = 0.06 \) (growth rate).
Substituting the values:
\( P_6 = \frac{1}{0.10 - 0.06} = \frac{1}{0.04} = 25.00 \)
4. **Calculate the present value of \( P_6 \)**:
Now we need to discount this price back to the present value (year 0):
\( PV = \frac{P_6}{(1 + r)^6} \)
Substituting the values:
\( PV = \frac{25.00}{(1 + 0.10)^6} = \frac{25.00}{1.771561} \approx 14.09 \)
Therefore, the price you would pay for one share in Company TYK today is:
**14.09**
1. **Calculate the dividend at year 7**:
\( D_7 = 1 \) (this is given)
2. **Calculate the dividend at year 8**:
\( D_8 = D_7 \times (1 + g) = 1 \times (1 + 0.06) = 1.06 \)
3. **Calculate the present value of dividends from year 7 onwards**:
According to the Gordon Growth Model, the price of the stock at the end of year 6 (just before the dividends start) is given by:
\( P_6 = \frac{D_7}{r - g} \)
where \( r = 0.10 \) (discount rate) and \( g = 0.06 \) (growth rate).
Substituting the values:
\( P_6 = \frac{1}{0.10 - 0.06} = \frac{1}{0.04} = 25.00 \)
4. **Calculate the present value of \( P_6 \)**:
Now we need to discount this price back to the present value (year 0):
\( PV = \frac{P_6}{(1 + r)^6} \)
Substituting the values:
\( PV = \frac{25.00}{(1 + 0.10)^6} = \frac{25.00}{1.771561} \approx 14.09 \)
Therefore, the price you would pay for one share in Company TYK today is:
**14.09**