Tapley Acquisition Inc. is considering the purchase of Target Company. The acquisition would require an initial investment of $190,000, but Tapley's after-tax net cash flows would increase by $30,000 per year and remain at this new level forever. Assume a cost of capital of 15 percent. Should Tapley buy Target?
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A. B. C. D. E.Explanation
NPV = $30,000/0.15 - $190,000 = $200,000 - $190,000 = $10,000.
To determine whether Tapley Acquisition Inc. should buy Target Company, we need to analyze the investment using net present value (NPV) and internal rate of return (IRR).
First, let's calculate the NPV of the investment. NPV is the present value of cash inflows minus the present value of cash outflows. The formula to calculate NPV is:
NPV = -Initial Investment + (Net Cash Flows / Cost of Capital)
In this case, the initial investment is $190,000, and the net cash flows are $30,000 per year. The cost of capital is given as 15 percent.
NPV = -$190,000 + ($30,000 / 0.15)
Simplifying the equation:
NPV = -$190,000 + $200,000
NPV = $10,000
Since the NPV is positive ($10,000), the investment generates a positive return after considering the cost of capital. However, it's important to compare the NPV to zero to make a decision.
The answer choice B states "Yes, because the NPV = $10,000." This answer is incorrect because it only provides the value of the NPV without comparing it to zero.
To further analyze the investment, let's calculate the IRR. The IRR is the discount rate that makes the NPV zero. We can use the following formula to estimate the IRR:
NPV = 0 = -Initial Investment + (Net Cash Flows / IRR)
Solving for IRR:
0 = -$190,000 + ($30,000 / IRR)
Simplifying the equation:
IRR * -$190,000 = $30,000
IRR = $30,000 / -$190,000
IRR ≈ -0.158
The calculated IRR is approximately -0.158 or -15.8%. Since the IRR is negative, it implies that the cash flows generated by the investment are not sufficient to cover the cost of capital, which is 15%.
Answer choice A states "Yes, because the IRR < the cost of capital." This answer is incorrect because the IRR is greater than the cost of capital. The correct statement would be "No, because the IRR > the cost of capital."
Answer choice C states "No, because NPV < 0." This answer is correct. The NPV in this case is $10,000, which is positive, so NPV is not less than zero.
Answer choice D states "No, because k > IRR." The comparison between "k" (which represents the cost of capital) and IRR is reversed in this statement. The correct statement would be "No, because k < IRR."
Answer choice E states "Yes, because the NPV = $30,000." This answer is incorrect because the NPV is $10,000, not $30,000.
Therefore, the correct answer is C. Tapley Acquisition Inc. should not buy Target Company because the NPV is positive ($10,000), indicating a potential return on the investment, but it is less than zero.