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Caspian Sea Drinks is considering the production of a diet drink. The expansion of the plant and the purchase of the equipment necessary to produce the diet drink will cost $22.00 million. The plant and equipment will be depreciated over 10 years to a book value of $2.00 million, and sold for that amount in year 10. Net working capital will increase by $1.20 million at the beginning of the project and will be recovered at the end. The new diet drink will produce revenues of $8.64 million per year and cost $2.32 million per year over the 10-year life of the project. Marketing estimates 20.00% of the buyers of the diet drink will be people who will switch from the regular drink. The marginal tax rate is 32.00%. The WACC is 14.00%. Find the NPV (net present value).

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To determine the NPV (Net Present Value) for Caspian Sea Drinks' potential diet drink project, we need to follow several steps to project cash flows, account for taxes, and finally calculate the NPV using the Weighted Average Cost of Capital (WACC).

Step 1: Calculate the initial investment and cash flows:

  1. Initial Investment:

    • Cost of Equipment/Plant: $22.00 million
    • Increase in Net Working Capital: $1.20 million
    • Total Initial Investment: $22.00 million + $1.20 million = $23.20 million

  2. Annual Cash Flows Calculation:

    • Revenues: $8.64 million per year
    • Costs: $2.32 million per year
    • Annual Operating Income (before tax): \[ \text{Operating Income} = \text{Revenues} - \text{Costs} = 8.64 \text{ million} - 2.32 \text{ million} = 6.32 \text{ million} \]
    • Tax: \[ \text{Tax} = \text{Operating Income} \times \text{Tax Rate} = 6.32 \text{ million} \times 0.32 = 2.0224 \text{ million} \]
    • Net Income (after tax): \[ \text{Net Income} = \text{Operating Income} - \text{Tax} = 6.32 \text{ million} - 2.0224 \text{ million} = 4.2976 \text{ million} \]
    • Add back Depreciation:
      • Depreciation per year: \[ \text{Depreciation} = \frac{(22.00 \text{ million} - 2.00 \text{ million})}{10 \text{ years}} = 2.00 \text{ million/year} \]
      • Annual Cash Flow: \[ \text{Annual Cash Flow} = \text{Net Income} + \text{Depreciation} = 4.2976 \text{ million} + 2.00 \text{ million} = 6.2976 \text{ million/year} \]

Step 2: Cash flow at Year 10

In Year 10, we also need to consider the salvage value and recovery of working capital:

  • Salvage Value: $2.00 million (the book value at the end of year 10)
  • Recovery of Working Capital: $1.20 million
  • Total Cash Flow in Year 10: \[ \text{Total Cash Flow Year 10} = 6.2976 \text{ million} + 2.00 \text{ million} + 1.20 \text{ million} = 9.4976 \text{ million} \]

Step 3: Calculate NPV

Now we have:

  • Year 0 Cash Flow: \(-23.20\) million
  • Year 1-9 Cash Flow: \(6.2976\) million each year
  • Year 10 Cash Flow: \(9.4976\) million

NPV Formula:

\[ \text{NPV} = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t} \] Where:

  • \(CF_t\) is cash flow at time \(t\)
  • \(r\) is the discount rate (WACC = 14%)
  • \(n\) is the total number of years (10 years)

NPV Calculation:

  1. Year 0: \[ NPV_0 = -23.20 \text{ million} \]
  2. Years 1-9: \[ NPV_1 = \frac{6.2976}{(1 + 0.14)^1} + \frac{6.2976}{(1 + 0.14)^2} + \dots + \frac{6.2976}{(1 + 0.14)^9} \] Using the formula for the present value of an annuity: \[ NPV_{1-9} = 6.2976 \times \left( \frac{1 - (1 + 0.14)^{-9}}{0.14} \right) \] Calculation: \[ NPV_{1-9} \approx 6.2976 \times 4.7858 = 30.0677 \text{ million} \]
  3. Year 10: \[ NPV_{10} = \frac{9.4976}{(1 + 0.14)^{10}} \approx \frac{9.4976}{3.478} \approx 2.726 \text{ million} \]

Total NPV:

\[ \text{NPV} = NPV_0 + NPV_{1-9} + NPV_{10} \] \[ \text{NPV} = -23.20 + 30.0677 + 2.726 \approx 9.5937 \text{ million} \]

Conclusion:

The NPV for the diet drink project is approximately $9.59 million. Since the NPV is positive, it suggests that the project should be accepted.