Question

Lukow products is investigating the purchase of a piece of automated equipment that will save $400,000 each year in direct labor and inventory carrying costs. this equipment costs $2,500,000 and is expected to have a 15-year useful life with no salvage value. the company’s required rate of return is 20% on all equipment purchases. management anticipates that this equipment will provide intangible benefits such as greater flexibility and higher-quality output that will result in additional future cash inflows.

Required (show all work process):

1. What is the net present value of the piece of equipment before considering its intangible

benefits?

2. What minimum dollar value per year must be provided by the equipment’s intangible benefits

to justify the $2,500,000 investment?

Answer 1

The NPV of the equipment before considering intangible benefits is negative $201,600. To justify the investment, the equipment's intangible benefits must provide a minimum annual value of $35,090.68.

Step-by-step explanation:

The net present value (NPV) of the piece of equipment can be calculated by determining the present value of the annual cost savings the equipment will provide and then subtracting the initial cost of the equipment. Using the given required rate of return (discount rate) of 20%, we can discount the annual savings of $400,000 over the expected 15-year life of the equipment. To find the minimum dollar value per year provided by the equipment's intangible benefits, we first calculate the NPV and then adjust it to break even.

To calculate NPV:

1. Calculate the present value of the annual savings for each year.
2. Sum the present values to get the total present value of the savings.
3. Subtract the initial cost from the total present value to get the NPV.

For the minimum annual value of intangible benefits:

1. Determine the shortfall (if any) between the original NPV and the initial investment.
2. Divide the shortfall by the present value of an annuity factor for 15 years at 20%, to find the additional yearly cash inflow required.

NPV Calculation:

Yearly savings: $400,000

Present value annuity factor for 15 years at 20%: 5.746

Total present value of savings: $400,000 * 5.746 = $2,298,400

Initial investment: $2,500,000

NPV before intangible benefits: $2,298,400 - $2,500,000 = -$201,600

Minimum Annual Intangible Benefits:

To break even, the equipment needs to provide additional yearly benefits of at least:

Shortfall: $201,600

Minimum extra annual benefits: $201,600 / 5.746 = $35,090.68

Therefore, before considering its intangible benefits, the NPV of the equipment is negative $201,600, and to justify the investment, the equipment's intangible benefits must provide a minimum annual value of $35,090.68.

Answer 2

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.