Question

You got asked to analyze a 5-year project for your firm. The project produces an annual revenue of $28,000, but requires an annual labor and materials cost of $6,000. To initiate the project your firm must invest $18,000. The salvage value of the project is $0 at the end of the 5-year useful life. Use straight line depreciation and a 40% income tax rate to compute the after-tax cash flows (15 points) and the IRR for the ATCF of this project

Answer 1

Answer:

The interest rate is i = 53.82%

Explanation:

Initail cost = 18.000

Salvage value = 0

Life = 5 years

Annual revenue = 28000

Annual cost = 6000

Net revenue = 28000 - 6000 = 22000

Tax rate = 40%

Depreciation per year = (Purchase value - Salvage value ) / life = 18000 / 5 = 3600

Taxable income = Net cash flow - Depreciation = 22000 - 3600 = 18400

Tax = Tax rate * Taxable income = 0.4 * 18400 = 7360

ATCF = Taxable income - Tax + Depreciation = 18400 - 7360 + 3600 = 10960

Let IRR be i%, then,

-18000 + 10960 * (P/A, i%, 5) = 0

(P/A, i%, 5) = 18000 / 10960 = 1.642336

Using trail and error method

When i = 50% , value of (P/A, i%, 5) = 1.736626

When i = 51% , value of (P/A, i%, 5) = 1.711012

When i = 53% , value of (P/A, i%, 5) = 1.661749

When i = 54% , value of (P/A, i%, 5) = 1.638054

Using interpolation

i = 53% + (1.661749 - 1.642336) / (1.661749 - 1.638054) *(54% - 53%)

i = 53% + 0.819%

i = 53.82%