King's Department Store is contemplating the purchase of a new machine at a cost of $35,419. The machine will provide $4,700 per year in cash flow for twelve years. King's has a cost of capital of 10 percent. Calculate your final answer using the formula or financial calculator methods.
a. What is the internal rate of return?
Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.
b. Should the project be undertaken?
Yes
No
Answer (2)
Calculate the Internal Rate of Return (IRR) using the formula: 0 = − 35419 + ∑ t = 1 12 ( 1 + I RR ) t 4700 .
Find that the IRR is approximately 8.0%.
Compare the IRR to the cost of capital (10%).
Since IRR (8.0%) < cost of capital (10%), the project should not be undertaken. N o
Explanation
Problem Analysis Let's analyze the problem. We are given the initial cost of a machine, the annual cash flows it generates, and the project's lifespan. We are also given the company's cost of capital. The goal is to calculate the internal rate of return (IRR) and determine whether the project should be undertaken.
Understanding IRR The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of the project equal to zero. In other words, it's the rate at which the present value of the future cash flows equals the initial investment. We can use the following formula to represent this:
0 = − I ni t ia l I n v es t m e n t + ∑ t = 1 n ( 1 + I RR ) t C a s h Fl o w t
Setting up the Equation In our case, the initial investment is $35 , 419 , the annual cash flow is $4 , 700 , and the project life is 12 years. So, the equation becomes:
0 = − 35419 + ∑ t = 1 12 ( 1 + I RR ) t 4700
Calculating IRR Solving this equation for IRR typically requires numerical methods or a financial calculator. Using a numerical method, the IRR is found to be approximately 8.0%.
Decision Making Now, we need to compare the calculated IRR with the cost of capital, which is 10%. If the IRR is greater than the cost of capital, the project should be undertaken because it means the project's rate of return is higher than the company's required rate of return. If the IRR is less than the cost of capital, the project should not be undertaken.
In this case, the IRR (8.0%) is less than the cost of capital (10%).
Conclusion Therefore, the project should not be undertaken.
Examples
Imagine you're deciding whether to invest in a small business. You need to put in an initial investment, and you expect to receive annual profits for a certain number of years. Calculating the IRR helps you determine the actual rate of return on your investment, allowing you to compare it with other investment opportunities or your required rate of return. If the IRR is high enough, the investment is worth pursuing; otherwise, you might want to consider other options. This concept is crucial in making informed financial decisions, whether it's for personal investments or large-scale corporate projects.
The internal rate of return (IRR) for the machine is approximately 8.0%, which is less than the cost of capital of 10%. Therefore, the project should not be undertaken. The final answer is: No.
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