Determine which of two investment projects a manager should choose if the discount rate of the firm is 20%. The first project promises a profit of $100,000 in each of the next four years, while the second project promises a profit of $75,000 in each of the next six years.
No its a.100(.8)+100(.8^2)+100(.8^3)+100(.8^4)=236K then b. 75(.8)+75(.8^2)+75(.8^3)+75(.8^4)+75(.8^5)+75(.8^6)=222k little bitttt
a. 100(.8)+100(.8^2)+100(.8^3)+100(.8^4)=236K
b. 75(.8)+75(.8^2)+75(.8^3)+75(.8^4)+75(.8^5)+75(.8^6)=221K
To determine which investment project the manager should choose, we will evaluate the present value of cash flows for each project based on the discount rate of 20%.
For the first project, which promises a profit of $100,000 in each of the next four years, we will calculate the present value of each cash flow.
PV1 = $100,000 / (1 + 0.20)^1 = $100,000 / 1.20 = $83,333.33
PV2 = $100,000 / (1 + 0.20)^2 = $100,000 / 1.44 = $69,444.44
PV3 = $100,000 / (1 + 0.20)^3 = $100,000 / 1.728 = $57,870.37
PV4 = $100,000 / (1 + 0.20)^4 = $100,000 / 2.07456 = $48,188.41
For the second project, which promises a profit of $75,000 in each of the next six years, we will calculate the present value of each cash flow.
PV1 = $75,000 / (1 + 0.20)^1 = $75,000 / 1.20 = $62,500
PV2 = $75,000 / (1 + 0.20)^2 = $75,000 / 1.44 = $52,083.33
PV3 = $75,000 / (1 + 0.20)^3 = $75,000 / 1.728 = $43,402.78
PV4 = $75,000 / (1 + 0.20)^4 = $75,000 / 2.07456 = $36,196.53
PV5 = $75,000 / (1 + 0.20)^5 = $75,000 / 2.489472 = $30,091.52
PV6 = $75,000 / (1 + 0.20)^6 = $75,000 / 2.9873664 = $25,094.60
To determine which project has a higher present value, we sum up the present values for each project.
Project 1: $83,333.33 + $69,444.44 + $57,870.37 + $48,188.41 = $258,836.55
Project 2: $62,500 + $52,083.33 + $43,402.78 + $36,196.53 + $30,091.52 + $25,094.60 = $249,368.76
Comparing the two values, we find that Project 1 has a higher present value of $258,836.55 compared to Project 2's present value of $249,368.76. Therefore, the manager should choose Project 1.
To determine which investment project a manager should choose, we need to calculate the present value of the cash flows for each project and compare them. The present value is a calculation that accounts for the time value of money, or the fact that a dollar received in the future is worth less than a dollar today.
Let's calculate the present value of each project using the discount rate of 20%.
For the first project, we will receive $100,000 in each of the next four years. We can calculate the present value of each year's cash flow using the formula:
Present Value = Cash Flow / (1 + Discount Rate)^n
Where:
Cash Flow = $100,000
Discount Rate = 20%
n = number of years (1, 2, 3, 4)
Calculating the present value for each year of the first project:
Year 1:
Present Value = $100,000 / (1 + 0.20)^1 = $83,333.33
Year 2:
Present Value = $100,000 / (1 + 0.20)^2 = $69,444.44
Year 3:
Present Value = $100,000 / (1 + 0.20)^3 = $57,870.37
Year 4:
Present Value = $100,000 / (1 + 0.20)^4 = $48,225.31
Now, let's calculate the present value of each year's cash flow for the second project, where we will receive $75,000 in each of the next six years:
Year 1:
Present Value = $75,000 / (1 + 0.20)^1 = $62,500
Year 2:
Present Value = $75,000 / (1 + 0.20)^2 = $52,083.33
Year 3:
Present Value = $75,000 / (1 + 0.20)^3 = $43,402.78
Year 4:
Present Value = $75,000 / (1 + 0.20)^4 = $36,169.32
Year 5:
Present Value = $75,000 / (1 + 0.20)^5 = $30,141.10
Year 6:
Present Value = $75,000 / (1 + 0.20)^6 = $25,117.58
Now, sum up the present values for each project:
For the first project:
PV1 = $83,333.33 + $69,444.44 + $57,870.37 + $48,225.31 = $258,873.45
For the second project:
PV2 = $62,500 + $52,083.33 + $43,402.78 + $36,169.32 + $30,141.10 + $25,117.58 = $249,414.11
Comparing the present values, we can see that the present value of the cash flows of the first project is higher than that of the second project. Therefore, based on the discounted cash flow analysis, the manager should choose the first project, which promises a profit of $100,000 in each of the next four years.