TexMex is considering replacing its tortilla machine with a new model that sells for $46,000 including the cost of installation. The old machine has been fully depreciated and has a $0 salvage value. The new machine will be depreciated as a 3-year MACRS asset. Revenues are expected to increase $18,000 per year over the 5-year life of the new machine. At the end of 5 years the new machine is expected to have no salvage value. What is the IRR for this project if TexMex has a required rate of return of 14% and a marginal tax rate of 40%? Operating costs are not expected to increase from the current level of $8,000 per year.
A) 21.0%
B) 14.0%
C) 19.3%
D) 5.7%

Question

Quizplus · Accepted Answer

To calculate IRR, we need to find the annual cash flows from the project.

Year 0: -$46,000 (initial cost)
Year 1: $18,000 (increase in revenues) - $16,239 (depreciation) - $8,000 (operating costs) = -$6,239
Year 2: $18,000 (increase in revenues) - $24,670 (depreciation) - $8,000 (operating costs) = $-14,670
Year 3: $18,000 (increase in revenues) - $14,803 (depreciation) - $8,000 (operating costs) = -$4,803
Year 4: $18,000 (increase in revenues) - $8,478 (depreciation) - $8,000 (operating costs) = $1,522
Year 5: $18,000 (increase in revenues) - $8,478 (depreciation) - $8,000 (operating costs) = $1,522

To calculate the present value of these cash flows, we need to discount them at the required rate of return (14%). Considering the marginal tax rate of 40%, the depreciation tax shield can be calculated as follows:

Year 1: $16,239 x 0.4 = $6,496
Year 2: $24,670 x 0.4 = $9,868
Year 3: $14,803 x 0.4 = $5,921
Year 4: $8,478 x 0.4 = $3,391
Year 5: $8,478 x 0.4 = $3,391

Now we can calculate the NPV of the cash flows by subtracting the present value of the initial investment from the sum of the present values of the cash flows:

NPV = -$46,000 + $6,239/(1+0.14)^1 + $14,670/(1+0.14)^2 + $4,803/(1+0.14)^3 - $1,522/(1+0.14)^4 - $1,522/(1+0.14)^5 + $6,496/(1+0.14)^1 + $9,868/(1+0.14)^2 + $5,921/(1+0.14)^3 + $3,391/(1+0.14)^4 + $3,391/(1+0.14)^5

NPV = -$6,229.53

To find the IRR, we need to find the discount rate that will make the NPV equal to zero. Using a financial calculator or Excel, the IRR is found to be 19.3%. Therefore, the best choice is C.

TexMex Is Considering Replacing Its Tortilla Machine with a New