Question

global water treatment, incorporated, is analyzing a proposed investment that would initially require $750,000 of new equipment. this equipment would be depreciated on a straight - line basis to a zero balance over the four - year life of the project. the estimated salvage value is $150,000. the project requires $50,000 initially for net working capital, all of which will be recouped at the end of the project. the projected operating cash flow is $265,000 a year. what is the internal rate of return on this project if the relevant tax rate is 21 percent?

Explanation:

Step1: Calculate annual depreciation

The equipment cost is $750,000 and has a 4 - year life with zero salvage value. Using straight - line depreciation, \(Depreciation=\frac{750000}{4}=187500\)

Step2: Calculate after - tax operating cash flow

The operating cash flow is $265,000. The tax rate is 21%.
\(After - tax\ operating\ cash\ flow=(265000)\times(1 - 0.21)+187500\times0.21\)
\(=265000\times0.79 + 187500\times0.21\)
\(=209350+39375=248725\)

Step3: Calculate initial investment

The initial investment is the cost of equipment plus net working capital, \(I = 750000+150000=900000\)

Step4: Calculate terminal cash flow

The terminal cash flow is the recouped net working capital, \(TCF = 150000\)

Step5: Set up the NPV equation for IRR (NPV = 0)

Let \(r\) be the IRR.
\(NPV=-900000+\sum_{t = 1}^{4}\frac{248725}{(1 + r)^{t}}+\frac{150000}{(1 + r)^{4}}=0\)

We can use a financial calculator or trial - and - error.
Using a financial calculator:
\(CF0=-900000\)
\(CF1 = 248725\), \(F1 = 3\)
\(CF2=248725 + 150000=398725\), \(F2 = 1\)

Solving for \(r\), we find \(r\approx17.64\%\)

Answer:

17.64%