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Daily Enterprises is purchasing a $10.55 million machine. It will cost $58,505.00 to transport and install the machine. The machine has a depreciable life of five years using the straight-line depreciation and will have no salvage value. The machine will generate incremental revenues of $4.26 million per year along with incremental costs of $1.40 million per year. Daily’s marginal tax rate is 38.00%.

The cost of capital for the firm is 14.00%.

(answer in dollars..so convert millions to dollars)

The project will run for 5 years. What is the NPV of the project at the current cost of capital?

3 answers

To calculate the NPV (Net Present Value) of the project, we'll follow these steps:

  1. Calculate Initial Investment:

    • Cost of the machine = $10.55 million
    • Transport and installation cost = $58,505.00
    • Total Initial Investment = Cost of the machine + Transport and installation cost \[ \text{Total Initial Investment} = 10,550,000 + 58,505 = 10,608,505 \]

  2. Calculate Annual Depreciation:

    • Depreciable life = 5 years
    • Salvage value = $0
    • Annual Depreciation = Initial Investment / Depreciable Life \[ \text{Annual Depreciation} = \frac{10,608,505}{5} = 2,121,701 \]

  3. Calculate Annual Operating Cash Flow:

    • Incremental Revenues = $4.26 million = $4,260,000
    • Incremental Costs = $1.40 million = $1,400,000
    • Operating Income (EBIT) = Incremental Revenues - Incremental Costs - Depreciation \[ \text{Operating Income (EBIT)} = 4,260,000 - 1,400,000 - 2,121,701 = 738,299 \]
    • Tax (38%) = EBIT * Tax Rate \[ \text{Tax} = 738,299 \times 0.38 = 280,561.62 \]
    • Net Income = EBIT - Tax \[ \text{Net Income} = 738,299 - 280,561.62 = 457,737.38 \]
    • Operating Cash Flow = Net Income + Depreciation \[ \text{Operating Cash Flow} = 457,737.38 + 2,121,701 = 2,579,438.38 \]

  4. Calculate NPV:

    • NPV Formula: \[ \text{NPV} = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - \text{Initial Investment} \] where \( CF_t \) is the cash flow for each year, \( r \) is the cost of capital, and \( n \) is the project duration (5 years).
    • Cost of Capital (r) = 14% = 0.14
    • Annual Cash Flow (CF) = $2,579,438.38 (from above)
    • We will sum the present values of the cash flows for 5 years.
    • Present Value of Cash Flows: \[ \text{PV} = CF \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] \[ \text{PV} = 2,579,438.38 \times \left( \frac{1 - (1 + 0.14)^{-5}}{0.14} \right) \]
    • First, calculate \( (1 + 0.14)^{-5} \): \[ (1 + 0.14)^{-5} \approx 0.5432 \]
    • Now calculate the fraction: \[ \frac{1 - 0.5432}{0.14} \approx 3.246 \]
    • Now, calculate the PV of cash flows: \[ \text{PV} = 2,579,438.38 \times 3.246 \approx 8,379,208.89 \]

  5. Final NPV Calculation: \[ \text{NPV} = PV - \text{Initial Investment} \] \[ \text{NPV} = 8,379,208.89 - 10,608,505 \approx -2,229,296.11 \]

Thus, the NPV of the project at the current cost of capital is approximately -$2,229,296.11.

What value do I enter for F0,C1, C2, C3, C4, C5 and I to solve with a calculator?

To use a financial calculator or Excel to calculate the NPV based on the values provided, you will enter the values as follows:

  1. F0: This is the initial investment (cash outflow), which is a negative value since it is an expense.

    • F0 = -10,608,505

  2. C1, C2, C3, C4, C5: These represent the cash inflows for each of the 5 years.

    • Since the operating cash flow from Year 1 to Year 5 is $2,579,438.38, you will enter this value for each cash flow from Year 1 to Year 5:
    • C1 = 2,579,438.38
    • C2 = 2,579,438.38
    • C3 = 2,579,438.38
    • C4 = 2,579,438.38
    • C5 = 2,579,438.38

  3. I: This is the interest or discount rate (cost of capital) used to discount the future cash flows. You will enter this as a percentage.

    • I = 14% or 0.14

Summary of Inputs:

  • F0 = -10,608,505 (Initial Investment)
  • C1 = 2,579,438.38
  • C2 = 2,579,438.38
  • C3 = 2,579,438.38
  • C4 = 2,579,438.38
  • C5 = 2,579,438.38
  • I = 0.14 (or 14%)

Steps to Calculate NPV:

  1. Enter the values into your financial calculator.
  2. Ensure the initial outflow (F0) is entered as a negative number.
  3. Input the cash inflows (C1 to C5) as positive numbers.
  4. Input the interest rate (I) as a percentage.
  5. Use the NPV function to compute the result.

The calculation will produce an NPV result, which should be consistent with our earlier calculation of approximately -$2,229,296.11.