We are evaluating a project that costs $1,675,000, has a six-year life, and has

Question

We are evaluating a project that costs $1,675,000, has a six-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 91,000 units per year. Price per unit is $35.95, variable cost per unit is $21.40, and fixed costs are $775,000 per year. The tax rate is 35 percent, and we require a return of 11 percent on this project.

Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent. Calculate the best-case and worst-case NPV figures. (Do not round intermediate calculations.Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).)

We are evaluating a project that costs $1,675,000, has a six-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 91,000 units per year. Price per unit is $35.95, variable cost per unit is $21.40, and fixed costs are $775,000 per year. The tax rate is 35 percent, and we require a return of 11 percent on this project.

Explanation / Answer

               OCFbase = [(P – v)Q – FC](1 – TC) + Depreciation(TC)

                     OCFbase = [($35.95 – 21.40)(91,000) – $775,000](.65) + .35($1,675,000/6)

                     OCFbase = $454,590.83

               Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is:

               NPVbase = –$1,675,000 + $454,590.83(PVIFA11%,6)

               NPVbase = $248,163.73

               Form an income statement then extract the numbers from income statement for the base case:

               Sales= 91,000× $35.91= $3,271,450.00

               Depreciation= $1,675,000/6 = $279,166.67

               VC= 91,000× $21.40= $1,947,400.00

               FC=$775,000

OCF= $    269,883.33+$ 279,166.67- $ 94,459.17= $454,590.83

With the PVA annuity factor of 6 years NPV becomes

NPV= -1,675,000+ 454,590.83×4.2305= $248,163.73

OCFbest = [(P – v)Q – FC](1 – TC) + Depreciation(TC)

                     OCFbest = [($35.95 – 21.40)(1001,00) – $775,000](.65) + .35($1,675,000/6)

                     OCFbest = $5,40,654

        Sales=91000+9100=1,00,100

         With the PVA annuity factor of 6 years NPV becomes

NPV= -1,675,000+ 5,40,654×4.2305= $612236

So, the change in NPV for every unit change in sales is:

               DNPV/DS = [($248,163.73 – 612236)]/(100100 – 91,000)

               DNPV/DS = +$27.27

OCFworset = [(P – v)Q – FC](1 – TC) + Depreciation(TC)

                     OCFworse = [($35.95 – 21.40)(81900) – $775,000](.65) + .35($1,675,000/6)

                     OCFworse = $368527.58

With the PVA annuity factor of 6 years NPV becomes

NPV= -1,675,000+ 368527.58×4.2305= $115944

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