Question

Your company is investing in a 3D printer for $10,000 that you will use for 5 years. The annual expected revenue generated from sale of products made by this printer is $5,310 and annual expenses for the printer are $3,000. The expected salvage value at the end of 5 years is $2,000. Your company’s minimum attractive rate of return is 12%. Based on internal rate of return analysis, required by your company, is this investment economically acceptable? Why or why not?

1. Cash flow diagram of your problem

2. Specify the model/equation used [e.g. P=F(1+i)-N ]

3. Specify the values of each parameter [e.g. i=0.05 or 5% ]

4. Show your work for how you calculate your numerical results.

5. Report dollar value with cents (e.g. $253.12),

6. Answer the question of the problem with a complete sentence that includes your numerical justification.

Answer 1

The worksheet with the computations is enclosed - wth explanation after the worksheet:

As we can see that the IRR for this investment works out to 9.99% however the company minimum required return is at 12%; since this investment does not cross the minimum return hurdle rate, it will not be acceptable to the company.

The cash flows have been arrived as below:

• Initial investment is the cost of purchase of 3 D printer at current time - Year 0
• The net annual cash flows are expected revenues minus annual expenses
• At the end of Year 5, the printer is expected to have a salvage value of $2000, and the same has been considered in Year 5 cash flows

IRR is simply the discount rate which equates the NPV of the cash flows to zero. NPV will be :

NPV = - Initial Cash flows + Year 1 Cash Flows / (1+r) + Year 2 Cash Flows / (1+r)² + .... + Year 5 Cash Flows / (1+r)⁵

NPV = -10000 + 2310/(1+r) + 2310/(1+r)² + 2310 / (1+r)³ + 2310/(1+r)⁴ + (2310 + 2000)/(1+r)⁵

For IRR, we equate the NPV to zero, i.e.:

2310/(1+r) + 2310/(1+r)² + 2310 / (1+r)³ + 2310/(1+r)⁴ + 4310/(1+r)⁵ = 10000

We will have to calculate value of r by trial and error:

• We start with r = 12% since that is the minimum hurdle set
• At r = 12%, we will have LHS of equation as : 2310/(1+12%) + 2310/(1+12%)² + 2310 / (1+12%)³ + 2310/(1+12%)⁴ + 4310/(1+12%)⁵ = 9461.89
• Now we try with r = 10%, and we have LHS :  2310/(1+10%) + 2310/(1+10%)² + 2310 / (1+10%)³ + 2310/(1+10%)⁴ + 4310/(1+10%)⁵ = - 1.44
• Since it is marginally less than 0, we can try 9.99% and we get LHS value to be 1.36. Hence the IRR is between 9.99% and 10% and we round it to 9.99% at two decimals.

Thus we see that this investment will not be acceptable to the company since its return is less than the minimum required by the company