Project Selection and Value Sacrifice

B

NPV(S) = $243.43; IRR(S) = 23.38%.

NPV(L) = $535.13; IRR(L) = 20.00%.

Value sacrificed: $535.13 - $243.43 = $291.70.

To determine the value sacrificed when selecting the project with the higher Internal Rate of Return (IRR), we need to calculate the Net Present Value (NPV) for each project and compare the results.

Net Present Value (NPV) is calculated by discounting the cash flows of a project to the present value using the company's cost of capital. The NPV represents the value added or subtracted by the project compared to the cost of capital.

Let's calculate the NPV for both projects:

Project S: Year 0: -1,000 Year 1: 500 Year 2: 500 Year 3: 500

Project L: Year 0: 0 Year 1: 123 Year 2: 456 Year 3: 789

To calculate the NPV, we discount each cash flow using the cost of capital of 10%:

Project S: NPV = -1,000 / (1 + 0.10)^0 + 500 / (1 + 0.10)^1 + 500 / (1 + 0.10)^2 + 500 / (1 + 0.10)^3

Project L: NPV = 0 / (1 + 0.10)^0 + 123 / (1 + 0.10)^1 + 456 / (1 + 0.10)^2 + 789 / (1 + 0.10)^3

Calculating the NPV for each project:

Project S: NPV = -1,000 + 500 / 1.1 + 500 / 1.1^2 + 500 / 1.1^3 NPV ≈ -1,000 + 454.55 + 413.22 + 375.66 NPV ≈ 243.43

Project L: NPV = 0 + 123 / 1.1 + 456 / 1.1^2 + 789 / 1.1^3 NPV ≈ 0 + 111.82 + 372.75 + 590.05 NPV ≈ 1,074.62

Now, we can compare the NPVs of both projects. Since we are interested in the value sacrificed when selecting the project with the higher IRR (Project L), we calculate the difference between the NPVs:

Value Sacrificed = NPV(Project L) - NPV(Project S) Value Sacrificed ≈ 1,074.62 - 243.43 Value Sacrificed ≈ 831.19

Therefore, the value sacrificed if the company selects the project with the higher IRR (Project L) is approximately $831.19.

None of the provided answer options match the calculated value, so there might be an error in the question or answer choices.