Math Problem Statement

A retailer is considering whether to open a new shop on a vacant block of land it owns. If the company goes ahead with the project, it will construct a new building at a cost of $2,264,000. It will also incur additional expenses of $256,000. The tax office has ruled that the building can be depreciated straight-line over 10 years, but the additional expenses are immediately tax-deductible. The land was purchased ten years ago at a cost of $1,137,000 and is worth $11,474,000 today. Setting up the new shop will require inventory of $424,000. What is the initial cash flow of the project, if the corporate tax rate is 30%? (make sure you indicate outflow as"-" and inflow are positive numbers. Only show the total value at the start of the project)

Solution

To calculate the initial cash flow of the project, we need to consider several components:

  1. Construction costs: This is the cost of building the new shop, which is an outflow. 2,264,000-2,264,000

  2. Additional expenses: These expenses are immediately tax-deductible, which reduces the tax burden. The net outflow will be the expenses after accounting for the tax benefit.

    • The tax deduction is calculated as 256,000×30%=76,800256,000 \times 30\% = 76,800.
    • The net outflow for the additional expenses is: 256,00076,800=179,200256,000 - 76,800 = 179,200 So the net outflow here is: 179,200-179,200
  3. Inventory costs: Setting up the shop requires inventory of $424,000, which is another outflow. 424,000-424,000

  4. Land value: Since the land is not being sold, its value does not impact the initial cash flow. However, it is worth noting for potential future calculations, but for now, it is irrelevant.

Now we sum up all the relevant initial cash flows:

Initial cash flow=2,264,000179,200424,000=2,867,200\text{Initial cash flow} = -2,264,000 - 179,200 - 424,000 = -2,867,200

Total Initial Cash Flow:

2,867,200\boxed{-2,867,200}

This is the total cash outflow at the start of the project.

Would you like further clarification or details on any part of the solution?

Here are five related questions to consider:

  1. How does the corporate tax rate affect the depreciation calculations in future cash flows?
  2. What would be the impact on cash flows if the company sold the land?
  3. How does straight-line depreciation impact financial statements over the 10-year period?
  4. What role does inventory play in working capital management for the project?
  5. How would different financing options for the building affect the initial cash flow?

Tip: Always consider tax benefits when assessing initial cash flows, as they can significantly reduce outflows.

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Math Problem Analysis

Mathematical Concepts

Corporate Finance
Cash Flow Analysis
Tax Deductions
Depreciation

Formulas

Initial Cash Flow = Construction Costs + Net Additional Expenses + Inventory Costs
Net Additional Expenses = Additional Expenses - (Tax Deduction on Additional Expenses)
Tax Deduction = Additional Expenses × Tax Rate

Theorems

Tax Impact on Cash Flow
Straight-line Depreciation

Suitable Grade Level

Undergraduate (Finance or Business Studies)