The consequence variable used in the House$-$Hunting example was Net Annual Cost, but as we mentioned, houses are also purchased as invest$-$ ments, suggesting that it might be useful to include equity and apprecia$-$ tion in the consequence measure.$$a$)$ In this problem, we will consider the consequence measure Appreciation $$ Equity $$ Net Annual Cost. Sanjay and Sarah will gain equity in each property by paying down the loan. Averaging over the first five years, they will gain $$6,131$ in Astoria, $$8,522$ in Barnard, and $$7,071$ in Charlotte. To model appreciation, add a row to your spreadsheet model labeled Appreciation Percentage and enter $6\mathrm{.}25\%$ for Astoria. Then, use cell referencing; we will assume the same appreciation percentage across all three properties. Doing so should result in Appreciation $+$ Equity $$ Net Annual Cost equaling $$5,582$ for Astoria, $$17,576$ for Barnard, and $$10,771$ for Charlotte. Run a one$-$way sensitivity analysis on the spreadsheet model using this new consequence measure and Table $5\mathrm{.}2.$ Add Appreciation Percentage to the sensitivity analysis with lower bound $2\%$ and upper bound $10\%.$ Discuss the sensitivity graph of Appreciation Percentage. How important is Appreciation Percentage? Do any of the lines in the sensitivity graphs cross? For which variables do the sensitivity graphs cross and at what value?$$b$)$ Create a decision tree for the House$-$Hunting example by adding a chance node for Appreciation Percentage to the tree in Figure $5\mathrm{.}11.$ Run a two$-$way sensitivity analysis on p$1$ and q$1$ from Figure $5\mathrm{.}11,$ but using the consequence measure Appreciation $+$ Equity $$ Net Annual Cost. How has this changed the results when using Net Annual Cost as the consequence measure?$$c$)$ We have looked at two different consequence measures for the House$-$ Hunting example. Discuss the pros and cons of each measur