Your firm is contemplating the purchase of a new $869,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $84,600 at the end of that time. You will be able to reduce working capital by $117,500 (this is a one-time reduction). The tax rate is 32 percent and your required return on the project is 23 percent and your pretax cost savings are $291,450 per year. What is the NPV of this project? What is the NPV if the pretax cost savings are $404,750 per year? At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?
To calculate the Net Present Value (NPV) of the project, we need to discount the cash flows to their present value using the required return rate of 23%. The formula for calculating NPV is:
NPV = -Initial Investment + PV(Cash Flows)
Now let's break down the cash flows:
1. Initial Investment:
The initial investment is the cost of the computer-based order entry system. Given as $869,500.
2. Cash Flows:
The cash flows include the annual cost savings and the salvage value at the end of the project's life.
a. Annual Cash Savings:
Given as $291,450 or $404,750, depending on the scenario. This amount represents the pre-tax cost savings per year.
b. Salvage Value:
Given as $84,600, which is the estimated value of the computer-based order entry system at the end of its useful life.
3. Working Capital:
The working capital reduction of $117,500 is a one-time reduction that is not considered in the calculation of NPV.
4. Tax Rate:
The tax rate is 32 percent, applied to the cash savings.
Now, let's calculate the NPV for each scenario:
Scenario 1: Pretax cost savings of $291,450 per year
NPV = -$869,500 + [PV($291,450) + PV($84,600)]
To calculate present value (PV) of cash flows, we use the following formula:
PV = Cash Flow / (1 + Return Rate)^n
where n represents the number of years.
PV($291,450) = $291,450 / (1 + 0.23)^1
PV($84,600) = $84,600 / (1 + 0.23)^5
Calculate the values and substitute them into the NPV equation to find the NPV for scenario 1.
Scenario 2: Pretax cost savings of $404,750 per year
Calculate the NPV using the same formula and steps as in scenario 1, but with the new cash flow value of $404,750 for the annual cost savings.
Break-even Point: Determine the level of pretax cost savings where the NPV is zero.
Set up the equation NPV = 0 and solve for the cash flow value.
After calculating the NPV for each scenario and determining the break-even point, you will have the answers to the questions posed.