FIN500, Inc. has the following project. It is a 4 year project and required initial investment of $10 million. Depreciation is straight-line over 4 years. Initial net working capital requirement is $1.5 million and is fully recoverable whenever the project ends. The company estimates to generate $8 million pretax revenues and $3 million pretax operating costs. The tax rate is 34%, and the discount rate is 15%. The market value of the equipment over the life of the project is given in the following table:
Year Market Value ($ millions)
1 $7.2
2 $6.2
3 $5.0
4 $2.5
5 $0.0
How much is the NPV of the project if the company abandons the project after 1 year, 2 years, 3 years, and after 4 years? When should it abandon the project? How much is the value of option to abandon?
To calculate the NPV (Net Present Value) of the project, we need to calculate the present value of cash flows. The cash flows include the initial investment, annual net operating cash flows, and the recovery of net working capital at the end of the project.
1. Calculate the initial investment:
- The initial investment is $10 million.
2. Calculate the annual net operating cash flows:
- To calculate the net operating cash flows, subtract the operating costs from the revenues.
- Year 1: $8 million - $3 million = $5 million
- Year 2: $8 million - $3 million = $5 million
- Year 3: $8 million - $3 million = $5 million
- Year 4: $8 million - $3 million = $5 million
3. Calculate the recovery of net working capital:
- At the end of the project, the company recovers the initial net working capital of $1.5 million.
4. Calculate the present value of cash flows for each abandonment scenario:
- We will discount the cash flows at the given discount rate of 15%.
- Use the formula: PV = Cash Flow / (1 + Discount Rate) ^ Year
For abandonment after 1 year:
- Initial investment: ($10 million) * (1 + 0.15) ^ -1 = $8.6957 million (discount back to year 0)
- Operating cash flow: ($5 million) * (1 + 0.15) ^ -1 = $4.3478 million (discount back to year 0)
- Net working capital recovery: ($1.5 million) * (1 + 0.15) ^ -1 = $1.3043 million (discount back to year 0)
- NPV (1 year): $8.6957 million + $4.3478 million + $1.3043 million = $14.3478 million
For abandonment after 2 years:
- Initial investment: ($10 million) * (1 + 0.15) ^ -2 = $7.5123 million (discount back to year 0)
- Operating cash flows: ($5 million) * (1 + 0.15) ^ -1 + ($5 million) * (1 + 0.15) ^ -2 = $7.7710 million (discount back to year 0)
- Net working capital recovery: ($1.5 million) * (1 + 0.15) ^ -2 = $1.6930 million (discount back to year 0)
- NPV (2 years): $7.5123 million + $7.7710 million + $1.6930 million = $16.9763 million
For abandonment after 3 years:
- Initial investment: ($10 million) * (1 + 0.15) ^ -3 = $6.6870 million (discount back to year 0)
- Operating cash flows: ($5 million) * (1 + 0.15) ^ -1 + ($5 million) * (1 + 0.15) ^ -2 + ($5 million) * (1 + 0.15) ^ -3 = $10.4202 million (discount back to year 0)
- Net working capital recovery: ($1.5 million) * (1 + 0.15) ^ -3 = $2.2041 million (discount back to year 0)
- NPV (3 years): $6.6870 million + $10.4202 million + $2.2041 million = $19.3113 million
For abandonment after 4 years:
- Initial investment: ($10 million) * (1 + 0.15) ^ -4 = $5.9150 million (discount back to year 0)
- Operating cash flows: ($5 million) * (1 + 0.15) ^ -1 + ($5 million) * (1 + 0.15) ^ -2 + ($5 million) * (1 + 0.15) ^ -3 + ($5 million) * (1 + 0.15) ^ -4 = $13.6893 million (discount back to year 0)
- Net working capital recovery: ($1.5 million) * (1 + 0.15) ^ -4 = $2.3615 million (discount back to year 0)
- NPV (4 years): $5.9150 million + $13.6893 million + $2.3615 million = $21.9658 million
To determine when the company should abandon the project, we compare the NPV for each abandonment scenario and choose the highest value, which indicates the most financially beneficial option. In this case, the project should be abandoned after 4 years because it has the highest NPV of $21.9658 million.
The value of the option to abandon the project is the difference between the NPV of the project after 4 years ($21.9658 million) and the highest NPV from earlier abandonment scenarios. Hence, the value of the option to abandon is $21.9658 million - $19.3113 million = $2.6545 million.