Math Problem Statement

WTF Ltd is considering replacing its old fully depreciated forklift with a new model. Two months ago, WTF paid LMAO Consulting $12,000 in consulting fees to help them evaluate the various forklifts on offer. Your manager suggests this consulting fee be spread over the life of the project. The cost of the recommended forklift is $41,000. The consultants estimate the old forklift will be able to be sold today for a salvage value of $29,000. In addition, WTF has estimated it will need to increase its holdings of inventory from $14,000 to $33,000 at the start of the project. The company tax rate is 30%. What is the total cash flow at the start of the project (report your answer to the nearest dollar)?

Solution

To calculate the total cash flow at the start of the project, we need to account for the following components:

  1. Cost of the new forklift: This is an outflow of cash for purchasing the forklift, which is given as $41,000.

  2. Salvage value of the old forklift: Since the old forklift can be sold for $29,000, this is an inflow of cash.

  3. Change in inventory holdings: WTF needs to increase its inventory from $14,000 to $33,000, which represents an increase of 33,00014,000=19,00033,000 - 14,000 = 19,000. This increase is an outflow, as it requires additional cash investment.

  4. Consulting fees: The consulting fee of $12,000 has already been paid. Since it is a sunk cost (a cost that has already been incurred and cannot be recovered), it should not be included in the cash flow calculation at the start of the project.

  5. No taxes on salvage value: The old forklift is fully depreciated, meaning that any gain from selling it is taxable. Since the salvage value is $29,000 and the tax rate is 30%, the taxes on the salvage value will be 0.30×29,000=8,7000.30 \times 29,000 = 8,700. Therefore, the net inflow from the sale of the old forklift is 29,0008,700=20,30029,000 - 8,700 = 20,300.

Total Cash Flow Calculation:

The total cash flow at the start of the project will be:

Total Cash Flow=41,000+20,30019,000\text{Total Cash Flow} = -41,000 + 20,300 - 19,000

Total Cash Flow=39,700\text{Total Cash Flow} = -39,700

Thus, the total cash flow at the start of the project is -$39,700.

Key Points:

  • The cost of the new forklift is a cash outflow.
  • The salvage value of the old forklift, after taxes, is a cash inflow.
  • The increase in inventory is a cash outflow.
  • The consulting fee is a sunk cost and should not be included.

Would you like further details on any part of the process?

Here are five related questions for further exploration:

  1. How would the cash flow change if the salvage value of the old forklift were higher?
  2. What would happen if the inventory requirements were less?
  3. How would spreading the consulting fees over the project life affect profitability metrics?
  4. How would the cash flow change if the company could sell the old forklift at a higher price?
  5. How do tax benefits on equipment purchases affect project cash flows?

Tip: Always remember that sunk costs (costs already incurred) should not be included in future cash flow calculations.

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Math Problem Analysis

Mathematical Concepts

Cash Flow Analysis
Depreciation
Taxation
Salvage Value

Formulas

Total Cash Flow = -Cost of New Forklift + (Salvage Value - Tax on Salvage) - Increase in Inventory
Tax on Salvage = Tax Rate * Salvage Value

Theorems

Tax Impact on Cash Flow
Sunk Cost Fallacy

Suitable Grade Level

Undergraduate Level - Finance/Accounting