n considering a capacity expansion at a battery company, we have two alternatives:

$1.$ The first alternative is expected to cost $$1,000,000$ and has an expected profit of

$$500,000$ per year over the next three years.

$2.$ The second alternative is expected to cost $$800,000$ and has an expected profit of

$$450,000$ per year over the next three years.

Currently, the interest rate is $10\%,$ and at that rate, the present value of $$1$ in the

following three years is: $0\mathrm{.}909,0\mathrm{.}826,$ and $0\mathrm{.}751,$ respectively. Which alternative

should we select, and what is the expected value of the expansion.