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Now give this answer completely without skipping even a small step of calculation and try not to give answer in long paragraphs and answer the questions by following these instructions: ?Solution should be in proper format. ?A complete answer starts with the problem's objective OR addition of available data/ information Or the right approach. ?Add all necessary steps/supporting explanations until the answer is complete. ?If there are any formulae, you should mention it. ?Write calculations in a format so it can be easily pasted in chegg equation render tool. ?Do not use Python or any code-based for calculations (Important). ?Double check the solution to accomplish the correct concept, explanation, and calculations before submitting. ✅ The Final Answer should be a simple and clear summary of the solution in lucid language. ✅ The Final Answer Step is to include the crux of the entire solution. ✅ The final answer step contains the result of the solution only in a clear & concise manner. ✅ The Final Answer should be a simple and clear summary of the solution in lucid language. ✅ Final Answer Step is to include the crux of the entire solution. ✅Final answer step contains the result of the solution only in clear & concise manner.The Titanic Shipbuilding Company has a noncancelable contract to build a small cargo vessel. Construction involves a cash outlay of $256,000 at the end of each of the next two years. At the end of the third year, the company will receive payment of $640,000. The company can speed up construction by working an extra shift. In this case, there will be a cash outlay of $560,000 at the end of the first year followed by a cash payment of $640,000 at the end of the second year. Use the IRR rule to show the (approximate) range of opportunity costs of capital at which the company should work the extra shift. Note: Enter your answers as a percent rounded to 2 decimal places. Enter the smallest percent first. |The company should work the extra shift f the cost of capital is between [ Jeana iin

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Now give this answer completely without skipping even a small step of calculation and try not to give answer in long paragraphs and answer the questions by following these instructions: ?Solution should be in proper format. ?A complete answer starts with the problem's objective OR addition of available data/ information Or the right approach. ?Add all necessary steps/supporting explanations until the answer is complete. ?If there are any formulae, you should mention it. ?Write calculations in a format so it can be easily pasted in chegg equation render tool. ?Do not use Python or any code-based for calculations (Important). ?Double check the solution to accomplish the correct concept, explanation, and calculations before submitting. ✅ The Final Answer should be a simple and clear summary of the solution in lucid language. ✅ The Final Answer Step is to include the crux of the entire solution. ✅ The final answer step contains the result of the solution only in a clear & concise manner. ✅ The Final Answer should be a simple and clear summary of the solution in lucid language. ✅ Final Answer Step is to include the crux of the entire solution. ✅Final answer step contains the result of the solution only in clear & concise manner.Uploaded ImageThe Titanic Shipbuilding Company has a noncancelable contract to build a small cargo vessel. Construction involves a cash outlay of $256,000 at the end of each of the next two years. At the end of the third year, the company will receive payment of $640,000. The company can speed up construction by working an extra shift. In this case, there will be a cash outlay of $560,000 at the end of the first year followed by a cash payment of $640,000 at the end of the second year. Use the IRR rule to show the (approximate) range of opportunity costs of capital at which the company should work the extra shift. Note: Enter your answers as a percent rounded to 2 decimal places. Enter the smallest percent first. |The company should work the extra shift f the cost of capital is between [ Jeana iin

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Asked by: JAYANTH POTHALA
Created at: 2025-10-07 07:46:23

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## Objective To determine **the range of opportunity costs of capital** at which the Titanic Shipbuilding Company should work the extra shift, using the IRR rule. --- ## Step 1: List Cash Flows for Both Options ### **Normal Schedule (No Extra Shift):** - Year : - Year 1: -$256,000 - Year 2: -$256,000 - Year 3: +$640,000 ### **Extra Shift Schedule:** - Year : - Year 1: -$560,000 - Year 2: +$640,000 - Year 3: --- ## Step 2: Find Cash Flow Differences Calculate incremental cash flows (Extra Shift minus Normal): | Year | Extra Shift | Normal | Difference (Incremental) | |------|-------------|--------|--------------------------| | | | | | | 1 | -560,000 | -256,000| -304,000 | | 2 | +640,000 | -256,000| +896,000 | | 3 | | +640,000| -640,000 | **Incremental Cash Flow:** - Year 1: -304,000 - Year 2: +896,000 - Year 3: -640,000 --- ## Step 3: Internal Rate of Return (IRR) Formula Set NPV of incremental cash flows to zero: \[ NPV = \frac{-304,000}{(1+r)^1} + \frac{896,000}{(1+r)^2} + \frac{-640,000}{(1+r)^3} = \] --- ## Step 4: Solve for IRR \[ -304,000 + \frac{896,000}{1+r} - \frac{640,000}{(1+r)^2} = \] Let \( x = 1 + r \): \[ -304,000x^2 + 896,000x - 640,000 = \] \[ -304,000x^2 + 896,000x - 640,000 = \] \[ 304,000x^2 - 896,000x + 640,000 = \] --- ## Step 5: Quadratic Formula The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, - \( a = 304,000 \) - \( b = -896,000 \) - \( c = 640,000 \) \[ x = \frac{-(-896,000) \pm \sqrt{(-896,000)^2 - 4 \cdot 304,000 \cdot 640,000}}{2 \cdot 304,000} \] --- ## Step 6: Calculate Discriminant \[ (-896,000)^2 = 802,816,000,000 \] \[ 4 \cdot 304,000 \cdot 640,000 = 778,240,000,000 \] \[ \text{Discriminant} = 802,816,000,000 - 778,240,000,000 = 24,576,000,000 \] --- ## Step 7: Calculate \(x\) Values \[ x = \frac{896,000 \pm \sqrt{24,576,000,000}}{608,000} \] \[ \sqrt{24,576,000,000} = 156,800 \] \[ x_1 = \frac{896,000 + 156,800}{608,000} = \frac{1,052,800}{608,000} = 1.73 \] \[ x_2 = \frac{896,000 - 156,800}{608,000} = \frac{739,200}{608,000} = 1.22 \] --- ## Step 8: Calculate IRR Values Remember, \( x = 1 + r \) \[ r_1 = 1.73 - 1 = .73 = 73\% \] \[ r_2 = 1.22 - 1 = .22 = 22\% \] --- ## Final Answer ### The company **should work the extra shift if the opportunity cost of capital is between**: \[ \boxed{22.00\% \text{ and } 73.00\%} \] --- ### Crux: > The company should work the extra shift **if the cost of capital is between 22.00% and 73.00%**. This is the range in which the incremental IRR of the cash flows makes the extra shift worthwhile.

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