Final answer:
The Net Present Value (NPV) of Lukow Products' equipment before considering intangible benefits is -$492,400. The minimum dollar value per year that must be provided by the equipment's intangible benefits to justify the $2,500,000 investment is approximately $98,105.
Step-by-step explanation:
The Net Present Value (NPV) of an investment is calculated by subtracting the present value of cash outflows from the present value of cash inflows over a period of time. For Lukow Products, the NPV calculation before considering intangible benefits involves discounting the annual savings of $400,000 over the equipment's 15-year life span at the company's required rate of return, which is 20%. Since the equipment has no salvage value, the cost is simply the initial investment of $2,500,000.
To calculate the present value of the annual savings, we use the formula for the present value of an annuity: PV = P × [(1 - (1 + r)⁻ⁿ) / r], where P is the annual cash flow, r is the discount rate, and n is the number of periods. The present value of annual savings of $400,000 at a 20% discount rate over 15 years is:
PV = $400,000 × [(1 - (1 + 0.20)⁻¹⁵) / 0.20] = $400,000 × [1 - (1 + 0.20)⁻¹⁵] / 0.20 = $400,000 × (5.019) = $2,007,600.
Now, subtract the initial cost of the equipment from the present value of savings to get the NPV:
NPV = $2,007,600 - $2,500,000 = -$492,400.
Intangible Benefits Valuation
To justify the investment, Lukow Products needs the equipment's intangible benefits to cover the negative NPV of -$492,400. Since these benefits occur every year over 15 years, we can use the same PV formula to find the minimal annual intangible benefits needed. Let X be the unknown annual intangible benefit value:
PV = X × (5.019) = $492,400
X = $492,400 / 5.019 = $98,105 approximately.
The minimum dollar value per year of the equipment's intangible benefits to justify the investment is around $98,105.