You have been offered the opportunity to invest in a project that will pay $2,405 per year at the end of years one through three and $11,406 per year at the end of years four and five. If the appropriate discount rate is 17.6 percent per year, what is the present value of this cash flow pattern?
Round the answer to two decimal places.
Investment decisions often involve evaluating the future cash flows generated by a project and determining their present value. This process helps investors assess the profitability and feasibility of potential opportunities. In this scenario, we are presented with an investment opportunity that promises specific cash flows over a five-year period. To accurately assess the value of these cash flows in today’s terms, we need to apply a discount rate that accounts for the time value of money.
Understanding the Cash Flow Pattern
The investment opportunity offers a series of cash flows: $2,405 per year at the end of years one through three, and $11,406 per year at the end of years four and five. These cash flows represent the returns or revenues that the project is expected to generate. However, due to the principle of time value of money, a dollar received in the future is worth less than a dollar received today. This is because money can be invested or used for other purposes in the present, and there is an inherent uncertainty associated with receiving future cash flows.
Applying the Discount Rate
The discount rate is a crucial factor in calculating the present value of future cash flows. It accounts for factors such as inflation, risk, and opportunity cost. In this scenario, the appropriate discount rate is provided as 17.6 percent per year. This rate serves as a representation of the return an investor could expect to earn from a comparable investment with similar risk.
Calculation of Present Value
To calculate the present value of the cash flows, we need to apply the discount rate to each individual cash flow and then sum them up. Using the provided cash flow pattern and the discount rate of 17.6 percent, we can apply the formula for calculating the present value of a future cash flow:
PV = CF / (1 + r)^n
Where:
PV is the present value of the cash flow
CF is the cash flow in a specific year
r is the discount rate
n is the number of years into the future
Let’s calculate the present value for each year’s cash flow and then sum them up:
PV(year 1) = $2,405 / (1 + 0.176)^1 PV(year 2) = $2,405 / (1 + 0.176)^2 PV(year 3) = $2,405 / (1 + 0.176)^3 PV(year 4) = $11,406 / (1 + 0.176)^4 PV(year 5) = $11,406 / (1 + 0.176)^5
Sum of PVs = PV(year 1) + PV(year 2) + PV(year 3) + PV(year 4) + PV(year 5)
Calculating the Result
After performing the calculations using the provided discount rate, the sum of the present values of all the cash flows can be determined. Rounding the answer to two decimal places provides the accurate present value of the cash flow pattern under consideration.
Conclusion
In conclusion, evaluating investment opportunities requires a comprehensive understanding of cash flows, the time value of money, and appropriate discount rates. By applying the discount rate of 17.6 percent to the given cash flows, we can determine their present value and make an informed decision about the profitability of the investment. The calculated present value serves as a valuable metric for investors to assess whether the projected future cash flows justify the initial investment.
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