In the consumer goods industry, Unimagic, Inc. has proven itself to be an innovative leader in product development. Unimagic is planning a new plant to make a consumer packaged good called Unibubble, which will allow microwaveable foods to have the same appearance, texture, and taste of those prepared in a conventional oven. The latest proposal is as follows. A plant with the capacity to produce 10 million units of Unibubble a year is to be constructed at a cost of $17 million. Sales of this amount will produce revenues of $15 million a year for 10 years. Direct manufacturing costs are expected to be $9 million a year. Unimagic pay corporate tax at 46 percent. The plant would be depreciated on a straight-line basis over 10 years with zero salvage value at the end of the period.

The financial director has data that indicates that the investment offers an internal rate of return of about 20 percent. Since Unimagics required rate of return for a project of this type is 12 percent, the financial director is strongly in favor of the proposal. The production manager agrees that the project is viable, but he would like to see the company build an even larger plant. He points out that there are significant economies of scale in the costs of building a larger plant. Within the capacity range of 7 to 13 million units per year, each additional one million units of capacity costs only $0.80 million, as against the average cost of $1.70 million per million units for the proposed plant. (costs 17 million and produces 10 million) The operating costs would remain at $0.90 per unit.

The marketing manager likes the production managers idea. The demand for Unibubble is very elastic and he is sure that he can sell an extra 1 million units with only a very modest decrease in price from $1.50 to $1.45. Conversely, if the plant capacity and output were to be reduced by 1 million units, the selling price would rise to $1.55. On the basis of this data, what size plant should Unimagic build?

Find NPV = -initial cost + [inflow from units sold production costs of size of plant (.90 for x units) depreciation * (1-tax rate) + depreciation]*PVIFA

(produced $9M)

NPV = -I + [(inflow outflow depreciation)(1-T) + depreciation]*PVIFA

NPV = -$16,200,000 + [($13,950,000 $8,100,000 - $1,620,000)(1-.46) + $1,620,000] *PVIFA

NPV = -$16,200,000 + [($4,230,000)(.54) + $1,620,000] *PVIFA

NPV = -$16,200,000 + [2,284,200 + $1,620,000] *PVIFA

NPV = -$16,200,000 + $3,904,200*PVIFA

NPV = -$12,295,800*PVIFA

(produced $10M)

NPV = -I + [(inflow outflow depreciation)(1-T) + depreciation] *PVIFA

NPV = -$17,000,000 + [($15,000,000 $9,000,000 - $1,700,000)(1-.46)+$1,700,000] *PVIFA

NPV = -$17,000,000 + [($4,300,000)(.54)+$1,700,000] *PVIFA

NPV = -$17,000,000 + [2,322,000+$1,700,000] *PVIFA

NPV = -$17,000,000 + $4,022,000*PVIFA

NPV = -$12,978,000*PVIFA

(produced $11M)

NPV = -I + [(inflow outflow depreciation)(1-T) + depreciation] *PVIFA

NPV = -$17,800,000 + [($15,950,000 $9,900,000 - $1,780,000)(1-.46) + $1,780,000] *PVIFA

NPV = -$17,800,000 + [($4,270,000)(.54) + $1,780,000] *PVIFA

NPV = -$17,800,000 + [2,305,800 + $1,780,000] *PVIFA

NPV = -$17,800,000 + $2,483,800*PVIFA

NPV = -$15,316,200*PVIFA

I don't know how to calculate PVIFA. Please help.