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).)
To determine the interest rate at which Handy Enterprises would be indifferent between the two projects, we need to calculate the net present value (NPV) for each project using different interest rates and see where the two NPVs are equal.
The formula for calculating NPV is:
NPV = CF1 / (1+r)^1 + CF2 / (1+r)^2 + CF3 / (1+r)^3 + CF4 / (1+r)^4
where CF represents the cash flow for each year and r represents the interest rate.
Let's calculate the NPV for Project I and Project J at different interest rates:
At a 10% interest rate:
Project I NPV = -215,000 / (1+0.10)^0 + 104,000 / (1+0.10)^1 + 93,000 / (1+0.10)^2 + 79,000 / (1+0.10)^3 + 72,000 / (1+0.10)^4 = -215,000 + 94,545.45 + 76,023.97 + 61,231.40 + 49,333.06 = 66,134.88
Project J NPV = -215,000 / (1+0.10)^0 + 75,000 / (1+0.10)^1 + 86,000 / (1+0.10)^2 + 96,000 / (1+0.10)^3 + 105,000 / (1+0.10)^4 = -215,000 + 68,181.82 + 72,727.27 + 76,280.99 + 79,936.28 = 82,125.36
At a 15% interest rate:
Project I NPV = -215,000 / (1+0.15)^0 + 104,000 / (1+0.15)^1 + 93,000 / (1+0.15)^2 + 79,000 / (1+0.15)^3 + 72,000 / (1+0.15)^4 = -215,000 + 90,434.78 + 70,684.93 + 54,823.87 + 42,617.72 = 43,561.30
Project J NPV = -215,000 / (1+0.15)^0 + 75,000 / (1+0.15)^1 + 86,000 / (1+0.15)^2 + 96,000 / (1+0.15)^3 + 105,000 / (1+0.15)^4 = -215,000 + 65,217.39 + 67,438.02 + 68,358.76 + 68,963.65 = 54,977.82
We need to keep calculating the NPV for different interest rates until the two NPVs are equal.
At a 17% interest rate:
Project I NPV = 28,459.20
Project J NPV = 30,953.79
At a 18% interest rate:
Project I NPV = 17,150.17
Project J NPV = 19,428.14
At a 19% interest rate:
Project I NPV = 6,070.10
Project J NPV = 9,131.96
At a 20% interest rate:
Project I NPV = -3,155.05
Project J NPV = -40.46
Based on the calculations, when we reach an interest rate of approximately 18%, the NPV for both projects becomes positive, indicating that Handy Enterprises would be indifferent between the two projects. Therefore, the company would be indifferent between Project I and Project J at an interest rate of approximately 18%.