Final answer:
The present value of the investment with given cash flows and a discount rate of 5 percent per year is $65,935.
Step-by-step explanation:
The present value of an investment can be calculated by discounting the future cash flows using an appropriate discount rate. In this case, the cash flows are $27,720 at the end of year 1, $2,270 at the end of year 2, $25,250 at the end of year 3, $12,420 at the end of year 4, and $3,780 at the end of year 5. The appropriate discount rate is 5 percent per year.
To calculate the present value of each cash flow, we divide the cash flow by (1 + discount rate) raised to the power of the number of years. Then, we sum up all the present values to get the final answer.
For example, the present value of the cash flow of $27,720 at the end of year 1 would be $27,720 / (1 + 0.05)¹ = $26,400. The present value of the cash flow of $2,270 at the end of year 2 would be $2,270 / (1 + 0.05)² = $2,140. The present value of the cash flow of $25,250 at the end of year 3 would be $25,250 / (1 + 0.05)³ = $22,620. The present value of the cash flow of $12,420 at the end of year 4 would be $12,420 / (1 + 0.05)⁴ = $10,884. The present value of the cash flow of $3,780 at the end of year 5 would be $3,780 / (1 + 0.05)⁵ = $2,891.
The sum of all the present values is $26,400 + $2,140 + $22,620 + $10,884 + $2,891 = $65,935. Therefore, the present value of the investment is $65,935.