Question

1. A firm is considering the development of several new products. The products under consideration are listed below; the products in each project group are mutually exclusive. The firm has an MARR of 10% per year and a capital investment budget limitation on development costs of $1,500,000. The life of all products is assumed to be ten years. Use the PW method to determine which combination of products that should be selected. Show complete and proper solutions.

Group	Products	Development Costs, $	Annual Net Cash Inflow, $
A	1	500,000	90,000
	2	650,000	110,000
	3	700,000	115,000
B	4	600,000	105,000
	5	675,000	112,000
C	6	800,000	150,000
	7	1,000,000	175,000

Answer 1

PW of each product is computed as follows.

PW, Product 1 ($) = - 500,000 + 90,000 x P/A(10%, 10) = - 500,000 + 90,000 x 6.1446 = - 500,000 + 553,014 = 53,014

PW, Product 2 ($) = -650,000 + 110,000 x P/A(10%, 10) = -650,000 + 110,000 x 6.1446 = -650,000 + 675,906 = 25,906

PW, Product 3 ($) = -700,000 + 115,000 x P/A(10%, 10) = -700,000 + 115,000 x 6.1446 = -700,000 + 706,629 = 6,629

PW, Product 4 ($) = -600,000 + 105,000 x P/A(10%, 10) = -600,000 + 105,000 x 6.1446 = -600,000 + 645,183 = 45,183

PW, Product 5 ($) = -675,000 + 112,000 x P/A(10%, 10) = -675,000 + 112,000 x 6.1446 = -675,000 + 688,195 = 13,195

PW, Product 6 ($) = -800,000 + 150,000 x P/A(10%, 10) = -800,000 + 150,000 x 6.1446 = -800,000 + 921,690 = 121,690

PW, Product 7 ($) = -1,000,000 + 175,000 x P/A(10%, 10) = -1,000,000 + 175,000 x 6.1446 = -1,000,000 + 1,075,305

= 75,305

Therefore the product can be ordered in descending order of PW:

6 > 7 > 1 > 4 > 2 > 5 > 3.

If products 6 and 7 are selected, total outlay (= 1,000,000 + 800,000 = 1,800,000) exceeds the budget of $1,500,000. Therefore, products 6 and 1 are selected since their total outlay (= 1,000,000 + 500,000 = 1,500,000) equals the budget of $1,500,000, they have the highest PW.