Astra Co. is considering introducing a bonus system based on economic value added (EVA) and has short-listed two bonus formulas. The first one would simply compute the bonus as a percentage of EVA, such that Bonus = x percent of EVA = x% × EVA The second bonus formula will make the bonus dependent also on the improvement in EVA from one year to another so that Bonus = y percent of EVA + z percent of DEVA = y% × EVA + z% × DEVA (2)

a. Suppose that the firm anticipates that its EVA will be $16 million this year, $20 million next year, and $24 million the year after. If the bonus formula (1) is chosen, x would be equal to 2 percent. If the bonus formula (2) is preferred, y would be equal to 1 percent and z to 7.5 percent. What would be the three years' cumulative bonus for each of the two formulas?

b. Suppose now that the expected EVA will be -$24 million this year, -$20 million next year, and -$16 million the year after. With the same value of x, y, and z as in the previous question, what would be the three years' cumulative bonus for each of the two formulas?

c. Which formula would you advise Astra to use?