IRR Range for Chapel Hill Coffins Company's New Plant

C

Time line: (In millions)

012345 Years

-511222

Financial calculator solution: (In millions)

Inputs: CF(0) = -5; CF(1) = 1.0; CF(2) = 1.5; CF(3) = 2.0; N(j) = 3.

Output: IRR% = 18.37%.

To determine the range within which the plant's Internal Rate of Return (IRR) falls, we can use a trial and error approach. The IRR is the discount rate at which the net present value (NPV) of cash flows is equal to zero.

Given the cash flows provided, we can calculate the NPV at different discount rates and observe where it crosses zero.

Let's start with option A: 17 - 18% IRR. We will use a financial calculator or Excel to perform the calculations.

At a discount rate of 17%, the NPV of the cash flows is calculated as follows:

Year 0: -$5 million Year 1: $1 million / (1 + 17%)^1 Year 2: $1.5 million / (1 + 17%)^2 Year 3: $2 million / (1 + 17%)^3 Year 4: $2 million / (1 + 17%)^4 Year 5: $2 million / (1 + 17%)^5

Calculating the NPV by discounting each cash flow and summing them up, we get:

NPV = -$5 million + $1 million / (1 + 17%)^1 + $1.5 million / (1 + 17%)^2 + $2 million / (1 + 17%)^3 + $2 million / (1 + 17%)^4 + $2 million / (1 + 17%)^5

Evaluating the above expression, we find that the NPV at a discount rate of 17% is negative.

Next, let's calculate the NPV at a discount rate of 18%:

NPV = -$5 million + $1 million / (1 + 18%)^1 + $1.5 million / (1 + 18%)^2 + $2 million / (1 + 18%)^3 + $2 million / (1 + 18%)^4 + $2 million / (1 + 18%)^5

Evaluating the above expression, we find that the NPV at a discount rate of 18% is positive.

Since the NPV changes from negative to positive between 17% and 18%, we can conclude that the IRR is within the range of 17-18%.

Therefore, the correct answer is A. 17 - 18%.