What is the value of a company stock if it grows at a supernormal rate of 18% for the first four years, and then slows down to a constant growth rate of 10%. The company just paid annual dividend of $2.00/share, and the rate of return on common stock (rcs) is 13%.
Possible Solution:
Supernormal Growth:
D0 = $2.00
D1 = 2.00(1+0.18) = $2.36
D2 = 2.36(1+0.18) = $2.78
D3 = 2.78(1+0.18) = $3.28
D4 = 3.28(1+0.18) = $3.87
Constant Growth:
D5 = [3.87(1+0.10)] / [0.13 – 0.10] = 4.257 / 0.03 = $141.90
NPV = 141.90 / [(1+0.13)^4] = 141.90 / 1.630 = $87.03?
The supernormal rate and the constant growth rate require us to calculate the annulised rate. If we assume the stock will be kept for 10 years, then the 6 years at 10% will reduce the annulised (kind of average over 10 years) rate to be 13.14%. Do your own calculations to confirm this.
However, at the end of the question, the round number 13% is already given as the rate of return, so we don't really have to go through annulization.
Dividends are usually paid each quarter, so that the projected annual dividend is $2*4=$8, at a rate of return of 13%. Assuming the stock is not over- or under-valued, and the dividend is not reinvested, the stock is valued at $8/0.13=$61.54.
To calculate the value of a company stock using the supernormal growth model and constant growth model, we need to follow these steps:
1. Calculate the dividends for each year during the supernormal growth phase.
- Start with the most recent dividend, D0, which is given as $2.00/share.
- Apply the supernormal growth rate of 18% to calculate future dividends:
- D1 = D0 * (1 + growth rate) = $2.00 * (1 + 0.18) = $2.36
- D2 = D1 * (1 + growth rate) = $2.36 * (1 + 0.18) = $2.78
- D3 = D2 * (1 + growth rate) = $2.78 * (1 + 0.18) = $3.28
- D4 = D3 * (1 + growth rate) = $3.28 * (1 + 0.18) = $3.87
2. Calculate the constant growth dividend, D5, using the constant growth rate and the rate of return on common stock (rcs).
- Use the formula: D5 = [D4 * (1 + constant growth rate)] / [rcs - constant growth rate]
- Plugging in the given values: D5 = [3.87 * (1 + 0.10)] / [0.13 - 0.10] = 4.257 / 0.03 = $141.90
3. Calculate the present value of the constant growth dividend.
- Use the formula: NPV = D5 / (1 + rcs)^n
- In this case, the constant growth phase starts at year 5, so n = 4 (years).
- Plugging in the values: NPV = 141.90 / (1 + 0.13)^4 = 141.90 / 1.630 = $87.03
Therefore, the value of the company stock, based on the given growth rates and dividend payments, is approximately $87.03.