Relevant Cost Analysis Quality Improvement

An automobile manufacturer plans to spend $1 billion to improve the quality of a new model. The manufacturer expects the quality-improvement program to eliminate the need for recall and reduce the costs for other warranty repairs. The firms experience had been, on average, 1.5 recalls for each new model at a cost of $300 per vehicle per recall. The average cost per recall, if one is needed, is expected to increase by 10 percent for the new model. Costs for other warranty repairs are expected to decrease from $200 to $80 per unit sold. Sales of the new model were expected to be 500,000 units without the quality-improvement program. The company believes that the well-publicized quality-improvement program will increase total sales of 650,000 units.

Please answer the following question

If there is a profit of $5,000 per unit on any incremental sales attributable to the quality-improvement program, is the $1 billion expenditure justified?