We are evaluating a project that costs $724,000, has an eight-year life, and has

Question

We are evaluating a project that costs $724,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 75,000 units per year. Price per unit is $39, variable cost per unit is $23, and fixed costs are $850,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project. Calculate the accounting break-even point. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure? Calculate the change in NPV if there is a 500-unit decrease in projected sales. What is the sensitivity of OCF to changes in the variable cost figure? Calculate the change in OCF if there is a $1 decrease in estimated variable costs

Explanation / Answer

1)
Depreciation
D=724,000/8=$90,500
the accounting break-even point is
Q=(FC+D)/(P-VC)
Q=(850,000+90,500)/(39-23)=58,781.25

Q=58,781 units

2)

a)Base OCF and NPV

OCF=(sales-costs)(1-T)+D*T

OCF =(75,000*39-23*75000-850,000)(1-0.35)+0.35*90,500

OCF=259,175

There is no salvage value and no change in NWC

PVIFA15%,8years=[1-(1+0.15)-8]/0.15=4.4873

NPV=-724,000+259,175*PVIFA15%,8years

NPV=$439,001.55

3)To calculate the sensitivity to quantity sold, repeat the above calculations for adierent value of Q, say, Q=76,000

OCF =(76,000*39-23*76000-850,000)(1-0.35)+0.35*90,500

OCF=269,575

NPV=-724,000+269,575*PVIFA15%,8years

NPV=485,669.69

Thus, the change in NPV per unit change in Q is

Sensitivity =(485,669.69-439,001.55)/(76,000-75,000)

Sensitivity =$46.668

4)A 500unit decrease in Q decreases NPV by

change in NPV=500*46.668=$23,334

5)To compute the sensitivity of OCF to change in VC, repeat the above calculationsfor OCF (base case only) for a dierent value of VC, say, VC=22.

OCF=(75,000*39-22*75000-850,000)(1-0.35)+0.35*90,500=$307,925

Thus, the change in OCF per unit change in VC is

Sensitivity=(259175-307,925)/(23-22)=-48,750

That is, OCF decreases by $48,750 for every dollar increase in VC

6)For a $1 decrease in VC, OCF increases by

Change in OCF =1*48,750=$48,750

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