The consequence variable used in the House-Hunting example was Net Annual Cost, but as we mentioned, houses are also purchased as investments, suggesting that it might be useful to include equity and appreciation 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 6.25% 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 5.2. 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 5.11.Run a two-way sensitivity analysis on p1 and q1 from Figure 5.11,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 measure.

Table 5.2

Figure 5.11

Senstivity Graph Net Annual Cost with Variation of Tax Rate (B5) $44,000 $40,000 36,000 Barnard Charlotte $32.000 S28,000 Astoria 27% 31% 33% 35% 37% Tax Rate (B5) 25% 29% 39% 41% 43% 45% 1.0 0.8 0.6 Savings Account 0.4 0.2 Low-Risk Stock High-Risk Stock 02 04 06 0.8