$5.$ Massachusetts Health Providers $($MHP$)$ is a non$-$profit group of physician practices and is evaluating the creation of a new laboratory testing center in an existing, unused space. Last year MHP spent $$150,000$ on renovating and finishing this space in anticipation of using for some project in the future.

The laboratory testing equipment needed will cost $$1,650,000$ and has an expected life of $5$ years and a salve value of $$550,000.$ During the first year labor costs will be $$275,000,$ utilities will be $$27,500$ and MHP will see an additional $$13,750.$ Massachusetts Health Providers expect to run approximately $150$ tests a day $250$ days a year. Each test will be reimbursed an average of $$22\mathrm{.}00.$ Supplies will cost $$5\mathrm{.}50$ per test. All costs and revenues will experience $4\%$ inflation over the life of the project.

Massachusetts Health Providers as a corporate cost of capital of $12$ percent.

a$)$ What is the Payback Period, IRR and NPV for this Project? $(15)$

b$)$ Should MHP accept the laboratory expansion project?$(5)$

c$)$ Conduct a sensitivity analysis on number of test per day and supplies costs $($use a range of $+/-30\%$ of expected value with $10\%$ intervals$).$ What variable is MPH most sensitive to$?(10)$