Question

Finance question

"An automaker is considering installing a three-dimensional (3-D) computerized car-styling system at a cost of $292,000 (including hardware and software). With the 3-D computer modeling system, designers will have the ability to view their design from many angles and to fully account for the space required for the engine and passengers. The digital information used to create the computer model can be revised in consultation with engineers, and the data can be used to run milling machines that make physical models quickly and precisely. The automaker expects to decrease the turnaround time for designing a new automobile model (from configuration to final design) by 15%. The expected savings in dollars is $215,000 per year. The training and operations and maintenance cost for the new system is expected to be $61,000 per year. The system has a five-year useful life and can be depreciated according to the five-year MACRS class. The system will have an estimated salvage value of $7,500. The automaker's marginal tax rate is 39.2%. Compute the rate of return of the project. Enter your answer as a percentage between 0 and 100."

Answer 1

Let us first write all the variables:-

• Initial Cost- $292000
• Savings-$215000
• Training Cost-$61000
• Cashflow=Savings-Training cost=215000-61000=$154000
• Depricaiation-Calculated as per 5 year MACRS class by 200% declining Balance method
• Salvage Value-$7500
• Tax rate=39.20%

1. Now the Yearly Cash Flow is $154000

2.The Depriciation is as follows:

Year 1-58400, Year 2-93440, Year 3-56064, Year 4-33638, Year 5-33638

So the Book Value of Asset after 5 Years=292000-Sum of Depriciation=292000-275180=16820

3. Now, Since Tax rate is given there will be a tax savings on the Depriciation. The Depriciation Tax savings= Depriciation*(1-0.392).

So the Depriciation Tax Savings(DTS) is as follows:- Year 1=35507.20, Year2=56811.52, Year 3=34086.91, Year 4=20451.90, Year 5=20451.90.

4. The Salvage Value is $7500.

IMP Note:- We have ignored the Capital Gain Tax Savings, Since nothing is mentioned in the question.

Now to calculate IRR we have to apply Trial & Error on the following formula:-

Outflow = PV of Inflow

292000=PV of(Cash flow per Year+DTS per year)+PV of Salvege Value

Please Solve the equation per year and get the answer, you can use Interpolation, and take a higher rate of return for trial