B. Problem Statement You are the owner of a mushroom farm and are planning to ex

Question

B. Problem Statement You are the owner of a mushroom farm and are planning to expand your operation to meet the growing demand for mushrooms While you've done the necessary due diligence and are satisfied with the projected values of key project parameters (e.g., annual revenues and operating costs), you are not fully confident that your world will unfold exactly as projected Because of your lingering uncertainty, you've mandated a former classmate of yours to perform project. . m a one-way sensitivity analysis of your o The current "best guesses for project parameters are listed below: I. Initial cost (P)= $450,000 2. Salvage value (SV) = $45,265 3. Annual operating revenues (AOR)= $300,000 4. Annual operating costs (AOC)= $180,000 5. Economic life (N) 5 years 6. MARR= 10% 7. Inflation Rate= 0% One-way Sensitivity Table Net Present Worth (NP Parameters | -15% |-10%| -5% | Reference l +5% | +10% | +15% Scenario AOR AOC SV MARR

Explanation / Answer

1

Let x be the AOC

Breakeven NPV=0

Hence, 0=-450000+(300000-x)/1.1+(300000-x)/1.1^2+(300000-x)/1.1^3+(300000-x)/1.1^4+(300000-x)/1.^5+45265/1.1^5

0=-450000+300000/0.1*(1-1/1.1^5)-x/0.1*(1-1/1.1^5)+45265/1.1^5

Solving for x, we get 188705.4

Hence, Breakeven ANnual Operating cost (to the nearest 100)=188700

2

Let x be the Salvage Value

Breakeven NPV=0

Hence, 0=-450000+(300000-180000)/1.1+(300000-180000)/1.1^2+(300000-180000)/1.1^3+(300000-180000)/1.1^4+(300000-180000)/1.^5+x/1.1^5

0=-450000+120000/0.1*(1-1/1.1^5)+x/1.1^5

Solving for x, we get -7882.5

Hence, Breakeven Salvage Value (to the nearest 100)=-7900

3

Let n be the breakeven duration

Breakeven NPV=0

Hence, 0=-450000+(300000-180000)/1.1+(300000-180000)/1.1^2+(300000-180000)/1.1^3+(300000-180000)/1.1^4+...(300000-180000)/1.^n+45265/1.1^n

=-450000+120000/0.1*(1-1/1.1^n)+45265/1.1^n

Hence, n=4.52

So breakeven duration of the project is 4.52 years

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