Assume the following productivity improvements:

Round

$1$

$-$

$2$

$\%$

Round

$2$

$-$

$5$

$\%$

Round

$3$

$-$

$8$

$\%$

Round

$4$

$-$

$1$

$2$

$\%$

Round

$5$

$-$

$1$

$5$

$\%$

Round

$6$

$-$

$1$

$8$

$\%$

Therefore, in Round

$6$

$$each worker would be

$1$

$.$

$1$

$8$

$$times as effective as the beginning worker, and your workforce complement would fall to

$1$

$/$

$1$

$.$

$1$

$8$

$$or

$8$

$5$

$\%$

$$of its current level.

For a quick evaluation, assume your total labor expenditure from the Annual Report Income Statement will stay flat for the next six years.

How much of a cost savings might you expect in the sixth year? For example, if the total labor costs on the Income Statement says $

$2$

$9$

M

$,$

$$and costs stay the same for six years, then in the last year your costs would fall to $

$2$

$9$

$/$

$1$

$.$

$1$

$8$

$$M

$.$

Apply the same approach to years one through five to get a total savings over time.

Would this justify the necessary expenditures in recruiting and training made over time?

So far

$($

above

$)$

$$we have assumed our workforce and labor contracts are constant. In practice

$($

and moving forward

$)$

$$the market is growing at about

$1$

$4$

$\%$

$,$

$$and your labor contract has a

$5$

$\%$

$$wage escalator. How does this affect the numbers?

At what level, if any, would you recommend that your company invest in recruiting and training? Are there any factors beyond the simple numbers that should be considered?