The Cimeron Cimmamon Co. is undertaking a program to reduce operating costs. The

Question

The Cimeron Cimmamon Co. is undertaking a program to reduce operating costs. The vice president in charge of operations has established a goal of saving an equivalent total present amount of $90,000 in the next 4 years through reduced finished-product losses. Me estimates that the company will be able to save $40,000 the first year, but cost reductions will become more difficult each year. If the reductions are expected to follow a uniformly decreasing gradient, what must the reductions be in years 2, 3, and 4 in order for the company to meet its established goal? The company's interest rate is 15% per year.

Explanation / Answer

Let the uniform reduction each year be $x

Present Value = 40000 * 0.8696 + 0.7561(40000 - x)+0.6575(40000 - 2x)+0.5718(40000 - 3x) = 34782.61 + 1.9854*40000 - 3.7864x

34782.61 + 1.9854*40000 - 3.7864x = 90000

3.7864x = 34782.61 + 79416.53 - 90000 = 24199.13

x = 24199.13/3.7864 = $6391.00

Thus, reduction each year should be $6,391

Year Savings Discount Factor = 1.15^-year 1 40000 0.869565 2 40000-x 0.756144 3 40000-2x 0.657516 4 40000-3x 0.571753

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