Math Problem Statement

Blue Sugar is evaluating Project X, a 2-year project that would involve buying equipment for $150,000 that would be depreciated to $0 over 2 years using straight-line depreciation. Capital spending would be $0 in year 1 and the equipment would be sold for an after-tax cash flow of $38,000 in year 2. Relevant revenues are expected to be $77,000 in year 1 and $111,000 in year 2. Relevant variable costs for the project are expected to be $34,000 in year 1 and $18,000 in year 2. Finally, the firm has no fixed costs in year 1 and one fixed cost in year 2 of the project. Yesterday, Blue Sugar signed a deal with Square Advertising to develop an advertising campaign. The terms of the deal require Blue Sugar to pay $47,000 in 2 years if Project X is pursued or $34,000 in 2 years if Project X is not pursued. The tax rate is 50 percent and the cost of capital for Project X is 6.02 percent. What is the net present value of Project X?

Input instructions: Round your answer to the nearest dollar.

Solution

To calculate the Net Present Value (NPV) of Project X, we will follow these steps:

Step 1: Calculate the annual cash flows (CF)

Year 1

  1. Revenues: $77,000
  2. Variable Costs: $34,000
  3. Fixed Costs: $0
  4. Depreciation: 150,0002=75,000\frac{150,000}{2} = 75,000
  5. EBIT (Earnings Before Interest and Taxes): EBIT=Revenues−Variable Costs−Fixed Costs−Depreciation=77,000−34,000−75,000=−32,000\text{EBIT} = \text{Revenues} - \text{Variable Costs} - \text{Fixed Costs} - \text{Depreciation} = 77,000 - 34,000 - 75,000 = -32,000
  6. Taxes (50%): −32,000×50%=−16,000-32,000 \times 50\% = -16,000
  7. Net Income: −32,000−(−16,000)=−16,000-32,000 - (-16,000) = -16,000
  8. Operating Cash Flow (OCF):
    OCF=Net Income+Depreciation=−16,000+75,000=59,000\text{OCF} = \text{Net Income} + \text{Depreciation} = -16,000 + 75,000 = 59,000

Year 1 Cash Flow: $59,000

Year 2

  1. Revenues: $111,000
  2. Variable Costs: $18,000
  3. Fixed Costs: $47,000
  4. Depreciation: 75,00075,000
  5. EBIT: EBIT=111,000−18,000−47,000−75,000=−29,000\text{EBIT} = 111,000 - 18,000 - 47,000 - 75,000 = -29,000
  6. Taxes (50%): −29,000×50%=−14,500-29,000 \times 50\% = -14,500
  7. Net Income: −29,000−(−14,500)=−14,500-29,000 - (-14,500) = -14,500
  8. Operating Cash Flow (OCF): OCF=−14,500+75,000=60,500\text{OCF} = -14,500 + 75,000 = 60,500
  9. Equipment Salvage Value: 38,00038,000
  10. Total Year 2 Cash Flow: Year 2 CF=60,500+38,000=98,500\text{Year 2 CF} = 60,500 + 38,000 = 98,500

Year 2 Cash Flow: $98,500

Step 2: Calculate Present Value of Cash Flows

The cost of capital is 6.02%. Discount the cash flows to the present value (PV):

  1. Year 1 PV: PV=Year 1 CF(1+r)1=59,000(1+0.0602)1=55,654\text{PV} = \frac{\text{Year 1 CF}}{(1 + r)^1} = \frac{59,000}{(1 + 0.0602)^1} = 55,654
  2. Year 2 PV: PV=Year 2 CF(1+r)2=98,500(1+0.0602)2=87,716\text{PV} = \frac{\text{Year 2 CF}}{(1 + r)^2} = \frac{98,500}{(1 + 0.0602)^2} = 87,716

Step 3: Calculate Initial Investment

The initial investment is $150,000.

Step 4: Calculate NPV

NPV=(PV of Year 1 CF)+(PV of Year 2 CF)−Initial Investment\text{NPV} = (\text{PV of Year 1 CF}) + (\text{PV of Year 2 CF}) - \text{Initial Investment} NPV=55,654+87,716−150,000=−6,630\text{NPV} = 55,654 + 87,716 - 150,000 = -6,630

Final Answer:

The NPV of Project X is $-6,630.

Would you like detailed explanations on any specific aspect of this calculation?

Related Questions:

  1. How is straight-line depreciation applied in NPV calculations?
  2. Why are taxes factored into the EBIT calculation?
  3. How does salvage value influence Year 2 cash flows?
  4. What impact does the cost of capital have on NPV outcomes?
  5. How would changing the tax rate affect the project’s profitability?

Tip:

When calculating NPV, always separate cash flows by type (operating, investing, financing) for a clearer picture of the project’s financial health.

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Math Problem Analysis

Mathematical Concepts

Financial Analysis
Net Present Value (NPV)
Depreciation
Cash Flow Analysis

Formulas

EBIT = Revenues - Variable Costs - Fixed Costs - Depreciation
Taxes = EBIT × Tax Rate
Operating Cash Flow (OCF) = Net Income + Depreciation
Present Value (PV) = Cash Flow / (1 + r)^n
NPV = PV of Year 1 CF + PV of Year 2 CF - Initial Investment

Theorems

Time Value of Money
Straight-Line Depreciation
Tax Impact on Cash Flow

Suitable Grade Level

College-Level (Finance, Accounting)

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