Logan, Inc.is considering the purchase of a warehouse directly across the street from its manufacturing plant.Logan currently warehouses its inventory in a public warehouse across town.Rent on the warehouse and delivering and picking up inventory cost Logan $48,000 per year.The building will cost Logan $450,000.Logan will depreciate the building for 20 years.At the end of 20 years, the building will have a $125,000 salvage value.Logan's required rate of return is 10%.Using the interest tables, the building's net present value is
A)($41,347).
B)($22,772).
C)$427,228.
D)$960,000.

Question

Quizplus · Accepted Answer

To calculate the net present value, we need to calculate the present value of the cost savings and the present value of the salvage value.

The cost savings is the annual rent and delivery costs that Logan will no longer have to pay. Using the present value of an annuity table, we can calculate that the present value of the cost savings over 20 years is:

PV = $48,000 x (1 - 1/1.1^20)/0.1
PV = $469,144

The salvage value is the amount that Logan can sell the building for after 20 years. We can calculate the present value of the salvage value using the present value factor for a single sum:

PV = $125,000 / 1.1^20
PV = $18,372

The net present value is the present value of the cost savings minus the cost of the building plus the present value of the salvage value:

NPV = $469,144 - $450,000 + $18,372
NPV = $37,516

But, we also need to adjust for the fact that Logan will depreciate the building for 20 years. Using the declining balance method, the total depreciation over 20 years is:

Depreciation = $450,000 x (1 - 0.1)^20 x 2
Depreciation = $32,922

So, the adjusted net present value is:

Adjusted NPV = $37,516 - $32,922
Adjusted NPV = $4,594

Since the adjusted net present value is positive, Logan should purchase the building. The best choice is (B).