Math Problem Statement

You have just completed a $25,000 feasibility study for a new coffee shop in some retail space you own. You bought the space two years ago for $95,000, and if you sold it today, you would net $114,000 after taxes. Outfitting the space for a coffee shop would require a capital expenditure of $35,000 plus an initial investment of $5,500 in inventory. What is the correct initial cash flow for your analysis of the coffee shop opportunity? Calculate the initial cash flow below: (Select from the options below)

  1. Capital Expenditure (outfit of space)
  2. Capital Expenditure (price of space)
  3. Change in Net Working Capital
  4. Feasibility Study Cost
  5. Opportunity Cost

Solution

To calculate the initial cash flow for the coffee shop opportunity, let's break down each relevant cost and include the components that affect the initial cash flow. Here’s an analysis of each component in the context of capital investment analysis.

1. Capital Expenditure (outfit of space):

  • This is the $35,000 required to outfit the space specifically for the coffee shop. It’s a capital expenditure, so it’s part of the initial cash outlay.

2. Capital Expenditure (price of space):

  • Although you bought the space for $95,000 two years ago, the initial cash flow calculation would consider the opportunity cost of the current value of the space (net of taxes if sold today). Therefore, this item doesn’t contribute directly to the cash flow itself but indirectly affects it as an opportunity cost (covered below).

3. Change in Net Working Capital:

  • The $5,500 investment in inventory represents a change in net working capital (NWC), which must be included in the initial cash flow.

4. Feasibility Study Cost:

  • The $25,000 feasibility study cost is a sunk cost because it has already been incurred. Sunk costs do not affect the decision-making process for new investments, so it should not be included in the initial cash flow calculation.

5. Opportunity Cost:

  • If you decide to open the coffee shop, you are foregoing the opportunity to sell the space for $114,000 today. This opportunity cost of $114,000 is relevant as it represents the potential cash inflow you’re giving up.

Initial Cash Flow Calculation:

Based on the above analysis, the correct initial cash flow should include:

  • Capital Expenditure (outfit of space): $35,000
  • Change in Net Working Capital (inventory): $5,500
  • Opportunity Cost (current space value if sold): $114,000

So, the initial cash flow 35,000+5,500+114,000=154,500\text{= } 35,000 + 5,500 + 114,000 = 154,500.

Thus, the correct initial cash flow for the analysis is $154,500.

Would you like further details on any part of this analysis?


  1. Why is the feasibility study considered a sunk cost and excluded from the initial cash flow?
  2. How does the opportunity cost affect investment decisions in projects?
  3. Why is inventory considered a change in net working capital for initial cash flow?
  4. Could other potential expenses be relevant in similar capital budgeting cases?
  5. How does this initial cash flow impact projected returns or break-even points for the coffee shop?

Tip: Opportunity cost is essential in capital budgeting, as it represents the benefits you give up by choosing one investment over another.

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Math Problem Analysis

Mathematical Concepts

Capital Budgeting
Cash Flow Analysis
Opportunity Cost
Sunk Cost

Formulas

Initial Cash Flow = Capital Expenditure (outfit of space) + Change in Net Working Capital (inventory) + Opportunity Cost (current space value)

Theorems

Opportunity Cost Principle
Sunk Cost Principle

Suitable Grade Level

College/University Level