Two mutually exclusive alternatives are being considered.

Alternative A has an initial cost of $100 and uniform annual benefit of $19.93. The useful life is 10 years, and the IRR is 15%
Alternative B has an initial cost of $50 and uniform annual benefit of $11.93. The useful life is 10 years, and the IRR is 20% The MARR is 8%.

Which of the following equation(s) will solve for the IRR that allows you to make a correct decision based on Rate of Return Analysis?

A) PW = - 50 - 8(P/A, i*, 10)B) PW = - 50 + 8(P/A, i*, 10)C)PW(A) = 100 - 19.93(P/A, i*, 10)PW(B) = 50 - 11.93(P/A, i*, 10)D)PW(A) = 100 - 19.93(P/A, 8%, 10)PW(B) = 50 - 11.93(P/A, 8%, 10)

The correct answer is option B PW = - $50 + 8 (P/A, 0.08, 10)

Explanation:

Recall that

The initial cost for Alternative A is $100 and a uniform annual benefit of $19.93

The initial cost for Alternative B is $50 and a uniform annual benefit of $11.93

The two alternatives has a useful life of 10 years

Now, we will show the rate return analysis given below

                                    Alternative -A     Alternative -B    A-B

The First cost                 $100                   $50                  $50

The annual benefit        $19.93                $11.93               $8.93

The Expected life           10 years           10 years             10 years

Thus the increment rate will be computed as,

PW = -P + A (P/A, i, n) ...This is the equation (1)

now,

P = is the first cost

n= The rime period

A= Annual benefit

I = the interest rate

Thus,

We substitute this values into  the equation 1 stated

Which is,

PW = - $50 + 8 (P/A, 0.08, 10)

Therefore PW = - $50 + 8 (P/A, 0.08, 10) this will solve for the IRR correction based on Rate of Return Analysis.

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