$($Please show all work$)$ Setup: Baker Corp. has several new projects that look attractive, but some are riskier than the firm's

past projects. Baker has received a major inflow of cash from a venture capital firm, in exchange for

$25\%$ of the firm's closely held stock. The VC firm has asked Baker managers to "run the numbers" to

examine both the market outlook and the expected returns on each of the projects they are

considering. The cash infusion will not cover all the proposed projects; Baker and its new investors

need to know which projects should be approved.

Based on Baker's earnings history over the past $10$ years across a variety of projects, which have covered

various states of the economy, the venture capital execs want Baker to estimate their overall returns. Given

the following estimates of economy over the next several years, determine Baker's expected rate of return.

$(6pts)$

Note, this type of development firm has much higher than normal returns under normal and boom conditions. The probability

of each state of the economy reflects the current situation, not necessarily historic market conditions for the firm.

Expected return for "average" company project $($based on assumed economic probabilities$)=$