16. Which of these three stock would you rather own if you rate of discount is 5%?
a. stock that currently earns $2 per share whose earnings are growing 3% each year.
b. stock that currently earns $1 per chare whose earnings are growing 4% each year.
c. sock that currently earns $5 per share whose earnings are growing 2% each year.
To determine which stock you would rather own based on a discount rate of 5%, we need to calculate the present value of the future earnings for each stock. The present value allows us to compare the future earnings of different stocks in today's dollars.
The formula for calculating the present value of future earnings is:
PV = CF / (1 + r)^n
Where:
- PV is the Present Value
- CF is the Cash Flow or Earnings per share
- r is the discount rate
- n is the number of years
Now, let's calculate the present value for each stock:
a. Stock A:
- Cash Flow (CF) = $2 per share
- Discount Rate (r) = 5%
- Growth rate (g) = 3%
- Number of years (n) = 1
PV = $2 / (1 + 5%)^1
PV = $2 / (1.05)^1
PV = $1.90
b. Stock B:
- Cash Flow (CF) = $1 per share
- Discount Rate (r) = 5%
- Growth rate (g) = 4%
- Number of years (n) = 1
PV = $1 / (1 + 5%)^1
PV = $1 / (1.05)^1
PV = $0.95
c. Stock C:
- Cash Flow (CF) = $5 per share
- Discount Rate (r) = 5%
- Growth rate (g) = 2%
- Number of years (n) = 1
PV = $5 / (1 + 5%)^1
PV = $5 / (1.05)^1
PV = $4.76
Based on the calculations, the present value of the future earnings for each stock are as follows:
a. Stock A: $1.90
b. Stock B: $0.95
c. Stock C: $4.76
Therefore, if the discount rate is 5%, you would rather own Stock C, which has the highest present value of future earnings.