Handy Enterprises has gathered projected cash flows for two projects.
Year Project I Project J
0 –$215,000 –$215,000
1 104,000 75,000
2 93,000 86,000
3 79,000 96,000
4 72,000 105,000
Requirement 1:
At what interest rate would the company be indifferent between the two projects? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
Interest rate: %
To determine the interest rate at which the company would be indifferent between the two projects, we can use the Net Present Value (NPV) formula.
The NPV formula calculates the present value of the cash flows for each year, discounted at the interest rate. The NPV for a project represents the difference between the present value of cash inflows and cash outflows over the project's duration.
For the company to be indifferent between the two projects, the NPV of both projects should be equal. Therefore, we need to find the interest rate that makes the NPV of both projects equal.
Here is how we can calculate the interest rate:
Step 1: Calculate the present value (PV) of cash flows for each project.
To calculate the present value of cash flows, we need to discount each year's cash flow by the interest rate. We can use the following formula:
PV = CF / (1 + i)^n
Where:
- PV is the present value of cash flows
- CF is the cash flow for a given year
- i is the interest rate
- n is the year
Project I Cash Flows:
Year 0: PV = -215,000 / (1 + i)^0
Year 1: PV = 104,000 / (1 + i)^1
Year 2: PV = 93,000 / (1 + i)^2
Year 3: PV = 79,000 / (1 + i)^3
Year 4: PV = 72,000 / (1 + i)^4
Project J Cash Flows:
Year 0: PV = -215,000 / (1 + i)^0
Year 1: PV = 75,000 / (1 + i)^1
Year 2: PV = 86,000 / (1 + i)^2
Year 3: PV = 96,000 / (1 + i)^3
Year 4: PV = 105,000 / (1 + i)^4
Step 2: Calculate the NPV for each project.
The NPV is the sum of the present values of cash flows for each project. We can calculate it by summing up the present values calculated in Step 1.
NPV(Project I) = Sum of PV(Project I)
NPV(Project J) = Sum of PV(Project J)
Step 3: Set the NPVs of both projects equal to each other and solve for the interest rate (i).
NPV(Project I) = NPV(Project J)
Step 4: Solve for the interest rate (i) using numerical methods or trial and error.
You can use spreadsheet software like Microsoft Excel or Google Sheets to input the cash flows, calculate the present values, and find the interest rate that makes the NPV of both projects equal. By adjusting the interest rate until the NPVs of both projects are equal, you can find the interest rate at which the company would be indifferent between the two projects.