Question

Dog Up! Franks is looking at a new sausage system with an installed cost of $505,000. This cost will be depreciated straight-line to zero over the project's five-year life, at the end of which the sausage system can be scrapped for $75,000. The sausage system will save the firm $185,000 per year in pretax operating costs, and the system requires an initial investment in net working capital of $34,000. If the tax rate is 30 percent and the discount rate is 8 percent, what is the NPV of this project? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) NPV References eBook & Resources Learning Objective 10-01 How to determine the relevant cash flows for a proposed projeet Worksheet ction , 10.6 Some Special Cases of Discounted Cash Flow Analysis Difficulty: Basic

Answer 1

First, we will calculate the annual depreciation of the new equipment. It will be:

Annual depreciation = $505,000 / 5

Annual depreciation = $101,000

Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus)the taxes on the sale of the equipment, so:

Aftertax salvage value = MV + (BV − MV)t_c

Very often, the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:

Aftertax salvage value = MV + (0 − MV)t_c

Aftertax salvage value = MV(1 −t_c)

We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is:

Aftertax salvage value = $75,000(1 − .30)

Aftertax salvage value = $52,500

Using the tax shield approach, we find the OCF for the project is:

OCF = $185,000(1 − .30) + .30($101,000)

OCF = $159,800

Now we can find the project NPV. Notice we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.

NPV = −$505,000 − 34,000 + $159,800(PVIFA_8%,5) + [($52,500 + 34,000)/1.08⁵]

NPV = $157,905.51