Question

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.7 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $518,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.50 per trap and believes that the traps can be sold for $6 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 9%. Use the MACRS depreciation schedule.

Year:	0	1	2	3	4	5	6	Thereafter
Sales (millions of traps)	0	0.4	0.5	0.6	0.6	0.4	0.2	0

a. What is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

b. By how much would NPV increase if the firm depreciated its investment using the 5-year MACRS schedule? (Do not round intermediate calculations. Enter your answer in whole dollars not in millions.)

Answer 1

Using the information given in the question, below is the table created:

• CAPEX is the initial investments of 5.7 million.
• Depreciation is using straight line method of 5.7 million over 6 years, which 0.95 million.
• Gain on Sale of Asset is 518,000 to be received after 6 year on sale of assets.
• Sales are given in units and selling price is 6$ each. Multiplying units and price, we get Sales in Dollars.
• Similarly, cost of production is 1.5 $ each, multiplying it with units, we get Cost of Goods sold.
• The working capital requirements are 10% of next year's sales, hence, next year's sales are multiplied with 10% to get current year's Working capital

Next we need to calculate Cashflows.

In this case Cashflows = (Sales - COGS - Depreciation) * (1 - Tax Rate) + Depreciation - CAPEX - Change in Working Capital

For example, Year 0 cashflow is - (5.7+0.24) = -.5.94 (negative sign means outflow)

Year 1 cashflow is (2.4 - 0.6 - 0.95) * (1 - 35%) + 0.95 - 0 - (0.3 - 0.24) = 1.44

Below is the Cashflow table:

In the last year, we are getting 518,000 on sale of asset which is a Gain, hence, it will taxed at 35% rate and after tax gain is added to that year's cashflow.

Next, we calculate Present Value of Cashflows. The required rate of return given is 9%, using same for calculation in formula CF_n / (1 + R)ⁿ.

Below are the Present Value of Cashflows:

Adding all the Cashflows, including the negative cashflow at year 0 with sign intact, we will get the Net Present Value of the project.

The NPV = 1.89 million dollars

If we use MACRS 5-Year schedule for Depreciation, then percentages for Depreciation would as give below:

Where 20% means, Depreciation expense in Year 1 would 20% of 5.7 million investment which 1.14 milion dollars.

Similarly Depreciation schedule was created.

Below is the NPV analysis after replacing straightline depreciation with MACRS 5 year depreciation schedule.

The NPV with MACRS Depreciation is 1.98 million dollars which means NPV increases with MACRS Depreciation schedule.

The NPV in this case is higher than Straightline method NPV by (1.98 - 1.89) = 0.09 million or 90,000 dollars.