The price of Garden Designs, Inc. is now $ 85. The company pays no dividends. Sean Perth expects the price four years from now to be $ 125 a share. Should Sean buy Garden Designs if he wants a 15 percent rate of return? Explain.
Yes.
End of year 1 >> 85 * 1.15 = 97.75
Year 2 >> 91.74 * 1.15 = 112.41
Complete this chart.
To determine if Sean should buy shares of Garden Designs, we need to calculate the present value of the stock and compare it to the current price. The present value is the value of future cash flows discounted back to the present at a specific rate of return.
In this case, we assume a 15 percent rate of return. The formula for calculating the present value is:
Present Value = Future Value / (1 + Rate of Return)^n
Where:
- Future Value is the expected price four years from now ($125)
- Rate of Return is the desired rate of return (15% or 0.15)
- n is the number of years (4)
Using this formula, we can calculate the present value:
Present Value = $125 / (1 + 0.15)^4
Present Value = $125 / (1.15)^4
Present Value = $125 / 1.74900625
Present Value ≈ $71.45
The calculated present value is approximately $71.45. Since the current price of Garden Designs is $85, the present value is lower than the current price.
Based on this analysis, Sean should not buy shares of Garden Designs at the current price if he wants a 15 percent rate of return. The present value is lower than the current price, indicating that the stock is overvalued. It would be more prudent for Sean to wait for a lower price in order to achieve a 15 percent rate of return.