Asked by Ankush Aggarwal on Jul 04, 2024
Verified
(Ignore income taxes in this problem.) Golab Roofing is considering the purchase of a crane that would cost $69,846, would have a useful life of 6 years, and would have no salvage value.The use of the crane would result in labor savings of $21,000 per year.The internal rate of return on the investment in the crane is closest to:
A) 18%
B) 20%
C) 19%
D) 17%
Useful Life
The estimated duration of time that an asset is expected to remain productive or useful for its intended purpose.
Labor Savings
The reduction in the amount of labor (and consequently, labor costs) necessary to perform a particular task or produce a certain amount of goods or services.
Internal Rate
Typically referring to the internal rate of return (IRR), which is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero.
- Learn the fundamentals and arithmetic of the Internal Rate of Return (IRR), and its application in scrutinizing investment possibilities.
- Grasp the contribution of cash inflows and cash outflows in assessing the viability of a project.
Verified Answer
ME
Menna ElsaoudyJul 09, 2024
Final Answer :
B
Explanation :
To find the internal rate of return, we need to calculate the net present value (NPV) of the cash inflows and outflows from the investment.
The initial outflow is the cost of the crane, which is $69,846. The cash inflows are the labor savings of $21,000 per year for 6 years. Using a discount rate of 20%, the NPV is calculated as:
NPV = -$69,846 + $21,000/(1 + 0.20)^1 + $21,000/(1 + 0.20)^2 + ... + $21,000/(1 + 0.20)^6
NPV = -$69,846 + $17,500 + $14,583 + ... + $6,135
NPV = -$69,846 + $48,495
NPV = -$21,351
We then try a different discount rate, such as 19%, and calculate the NPV again. We continue to adjust the discount rate until we find the rate at which the NPV equals zero, which is the internal rate of return.
At a discount rate of 18%, the NPV is:
NPV = -$69,846 + $21,000/(1 + 0.18)^1 + $21,000/(1 + 0.18)^2 + ... + $21,000/(1 + 0.18)^6
NPV = -$69,846 + $17,797 + $14,955 + ... + $6,051
NPV = -$69,846 + $50,950
NPV = -$18,896
At a discount rate of 19%, the NPV is:
NPV = -$69,846 + $21,000/(1 + 0.19)^1 + $21,000/(1 + 0.19)^2 + ... + $21,000/(1 + 0.19)^6
NPV = -$69,846 + $17,621 + $14,754 + ... + $6,005
NPV = -$69,846 + $50,330
NPV = -$19,516
At a discount rate of 20%, the NPV is:
NPV = -$69,846 + $21,000/(1 + 0.20)^1 + $21,000/(1 + 0.20)^2 + ... + $21,000/(1 + 0.20)^6
NPV = -$69,846 + $17,500 + $14,583 + ... + $6,135
NPV = -$69,846 + $48,495
NPV = -$21,351
At a discount rate of 21%, the NPV is:
NPV = -$69,846 + $21,000/(1 + 0.21)^1 + $21,000/(1 + 0.21)^2 + ... + $21,000/(1 + 0.21)^6
NPV = -$69,846 + $17,391 + $14,541 + ... + $5,878
NPV = -$69,846 + $47,272
NPV = -$22,574
From these calculations, we can see that the internal rate of return is between 19% and 20%. The closest choice is B) 20%. Therefore, purchasing the crane would be a good investment at a discount rate of 20% or lower.
The initial outflow is the cost of the crane, which is $69,846. The cash inflows are the labor savings of $21,000 per year for 6 years. Using a discount rate of 20%, the NPV is calculated as:
NPV = -$69,846 + $21,000/(1 + 0.20)^1 + $21,000/(1 + 0.20)^2 + ... + $21,000/(1 + 0.20)^6
NPV = -$69,846 + $17,500 + $14,583 + ... + $6,135
NPV = -$69,846 + $48,495
NPV = -$21,351
We then try a different discount rate, such as 19%, and calculate the NPV again. We continue to adjust the discount rate until we find the rate at which the NPV equals zero, which is the internal rate of return.
At a discount rate of 18%, the NPV is:
NPV = -$69,846 + $21,000/(1 + 0.18)^1 + $21,000/(1 + 0.18)^2 + ... + $21,000/(1 + 0.18)^6
NPV = -$69,846 + $17,797 + $14,955 + ... + $6,051
NPV = -$69,846 + $50,950
NPV = -$18,896
At a discount rate of 19%, the NPV is:
NPV = -$69,846 + $21,000/(1 + 0.19)^1 + $21,000/(1 + 0.19)^2 + ... + $21,000/(1 + 0.19)^6
NPV = -$69,846 + $17,621 + $14,754 + ... + $6,005
NPV = -$69,846 + $50,330
NPV = -$19,516
At a discount rate of 20%, the NPV is:
NPV = -$69,846 + $21,000/(1 + 0.20)^1 + $21,000/(1 + 0.20)^2 + ... + $21,000/(1 + 0.20)^6
NPV = -$69,846 + $17,500 + $14,583 + ... + $6,135
NPV = -$69,846 + $48,495
NPV = -$21,351
At a discount rate of 21%, the NPV is:
NPV = -$69,846 + $21,000/(1 + 0.21)^1 + $21,000/(1 + 0.21)^2 + ... + $21,000/(1 + 0.21)^6
NPV = -$69,846 + $17,391 + $14,541 + ... + $5,878
NPV = -$69,846 + $47,272
NPV = -$22,574
From these calculations, we can see that the internal rate of return is between 19% and 20%. The closest choice is B) 20%. Therefore, purchasing the crane would be a good investment at a discount rate of 20% or lower.
Explanation :
Factor of the internal rate of return = Investment required ÷ Annual net cash inflow
= $69,846 ÷ $21,000 = 3.326
This factor is the present value of an annuity for 6 periods at 20% per period.
= $69,846 ÷ $21,000 = 3.326
This factor is the present value of an annuity for 6 periods at 20% per period.
Learning Objectives
- Learn the fundamentals and arithmetic of the Internal Rate of Return (IRR), and its application in scrutinizing investment possibilities.
- Grasp the contribution of cash inflows and cash outflows in assessing the viability of a project.