##### Reference no: EM131410197

**Question 1.**

a. According to the rule of 72, how many times your money will be doubled over a 36- year period if it earns a rate of return of 8% per year? Show your work.

b. Using the rule of 72, estimate the value of an initial investment of $50K at the end of a 36-year period if it earns a rate of return of 8% per year? Show your work.

c. According to the 4% rule, what the size of your investment portfolio needs to be in order for you to withdraw an initial annual amount of $250K? Show your work.

d. Referring to part c, what will be your 4th annual withdrawal amount if the inflation rate during the 3 years since your initial withdrawal averaged 2.5% per year? Show your work.

**Question 2.**

Consider the "buy vs. rent" Excel spreadsheet provided to you in tab A2.

a. According to the assumptions made in that spreadsheet, should the average individual buy or rent? Briefly explain.

b. Using "Goal Seek" alter the "buy vs. rent" Excel spreadsheet so that it shows the minimum rate of price appreciation the homeowner must receive in order to be better off buying than renting. Highlight in yellow the cell that includes this price appreciation rate.

**Question 3.**

Consider the levered DCF model provided to you in tab A3 of the Excel spreadsheet.

a. Calculate the maximum price that an investors with the assumptions made in the model should be willing to pay for that property. Show this maximum price in cell C8.

b. If you expect a general increase in the risk premium for real estate investments over the next 8 years, how would this affect the expected levered return on this property? Briefly Explain.

**Question 4.**

Using the headers in tab A4 of the Excel spreadsheet and the input values included in the green "box":

a. Create a monthly amortization schedule for a fixed rate 15-year mortgage. Make sure that any value that the user (me in this case) changes in the green "box" will be reflected in your amortization schedule. Your monthly payment calculation should be included in cell J5 and should also automatically change with any changes to the values in the green "box".

b. Next to the amortization schedule, create an Excel graph that shows the remaining mortgage balance overtime. Make sure that your graph is labeled appropriately.

c. Include a vlookup function in cell L7 that will reflect the remaining mortgage balance associated with the end of the month entered by the user into cell J7. For example, if the user enters 34 into cell J7, cell L7 will automatically show the remaining mortgage balance after 34 months.

**Question 5.**

Calculate the nominal and real annual rate of housing price appreciation rate for Miami and for Houston for the requested different time periods using the housing price index data and the inflation index data provided to you in tab A5 of the Excel spreadsheet. In total, you need to calculate 16 values that will appear in the 16 yellow cells of that Excel tab.

**Question 6.**

Given your results from the previous problem:

a. What can you say about the magnitude and the volatility of housing price appreciation in the short, medium and long run?

b. Are the results from question 5 consistent with the theory of price appreciation we discussed in the beginning of this course? Briefly explain.

**Attachment:-** EXCEL.xlsx