Quantitative Methods in Real Estate and Construction Management Quiz

23 Questions

Suppose that the net present value (NPV) of an investment is negative. Then the internal rate of return (IRR) of this investment must be_____

lower than the discount rate

Your investment pays you annual cash flows of 200 000 for the next 10 years. Year 10, your investment also pays you 850 000 (in addition to the 200 000). As usual all payments occur at the end of each year. How much must you pay for the investment today, if you want the IRR to be 15.0 %?

$1 214 100

Your dear colleague wants to celebrate your 10th friendship anniversary by extending your old Excel 5-year cash flow tool to 10 years. What a nice gift! With your new tool you want to make an investment analysis of following real estate case: A property can be purchased for 35 000 000 today (USD). As usual, you enjoy doing risk analysis by computing the expected IRR of your real estate investment case by projecting five different scenarios. You choose to compute the exit value at year 10 for all five scenarios based on the following assumptions:

• NOI year 11: based on you NOI projection for year 11 for each of the five scenarios. • Terminal capitalization rate (aka exit cap rate) = 6 % for all five scenarios.

Your five scenarios: Severe recession: NOI will be 1 800 000 the first year, and then decrease 5.5 percent per year until year 11. The probability for this scenario is 10 percent.

Moderate recession: NOI will be 1 800 000 the first year, and then decrease 2.0 percent per year until year 11. The probability for this scenario is 20 percent.

Baseline forecast: NOI will be level 1 800 000 the first year, and then increase by 1.5 percent per year until year 11. The probability for this scenario is 35 percent.

Moderate expansion: NOI will be 1 800 000 the first year, and then increase by 3.0 percent per year until year 11. The probability for this scenario is 30 percent.

Strong boom expansion: NOI will be 1 800 000 the first year, and then increase 4.5 percent per year until year 11. The probability for this scenario is 5 percent. The expected IRR is closest to______

4.61 %

MCQ 3 continued. If the required rate of return (the discount rate) is 7.5 % for each of the five scenarios in MCQ 3, then the expected NPV is closest to_________.

minus 6 154 563

The following diagram shows two different supply curves, S1 and S2, and one demand curve D, for an apartment market. Supply curve S1 has been estimated by you and the supply curve S2 has been estimated by your colleague. Now suppose that the demand for housing starts to increase because households’ incomes increase strongly. Which alternative is correct?

Since the supply curve S1 is more inelastic than the supply curve S2, the price will increase more if the supply curve 1 is the correct supply curve compared to if supply curve S2 were correct.

According to the quantity theory of money, if the money supply is $22 trillion and velocity is 1.165, then nominal GDP is closest to

$25.630 trillion

MCQs number 7 to 9 are based on the following text Use following data: Excel file exam_data_oct_2022.xlsx, sheet HPI. The data was downloaded from the. The country that has the highest (maximum) median quarterly return is_______

Slovenia with median return of 3.38 %

You want to show international house investors how much 100 (units of a currency) invested in different housing markets 1975:Q1 was worth 2022:Q2. You therefore show a diagram of how nominal house prices for France, Japan, Sweden, and the US have evolved starting from 100. Which of the following charts shows the correct evolution of the house prices?

Chart A

MCQs number 10 to 12 are based on the following text Using chi-square test, you want to study the market for exclusive hotels in Tokyo. You have asked 400 hotel guests in each of three luxury hotels (Five Seasons, Seven Senses, and Zhangri-La) on whether they experienced the hotel visits as luxury. The distribution of answers is shown in the Table MCQ 10 to 12 below. Table MCQ 10 to 12 Five Seasons Seven Senses Zhangri-La Yes Luxury! 344 356 338 Not luxury! 56 44 62 10) Referring to the table MCQ 10-12 above, what is the null hypothesis of the chi-square test?

There are no differences among the three hotels in the proportion of guests who experienced the hotel visits as luxury

Referring to the table MCQ10-12 above, the value of the chi-square test statistic is closest to______

3.5967

Referring to the table MCQ 10-12 above, the conclusion for the Chi-square test above, with 5 percent significance level, would be that ______

The p-value must be higher than 5 %, implying that the null hypothesis will not be rejected

The adjusted R square for this model is closest to _________

0.697

The standard error of the regression is closest to _________

0.273

The 90% confidence interval for β5 (WATERFRONT variable) is closest to__________.

(0.0301, 0.1817)

Which of the following interpretations of the coefficient of TRADITIONAL is most correct?

A traditional house in on average about 15.5 % less expensive than non-traditional houses

Using the above model, predict the prices of a house with 2500 square feet that is not close to the university. Use the natural predictor (not the corrected predictor). The predicted price is closest to

$207 479

Using the above model, predict the prices of a house with 2500 square feet that is close to the university. Use the natural predictor (not the corrected predictor). The predicted price is closest to

$282 742

When you performed the regression analysis above, you did not correct for problem with heteroscedasticity. Suppose that you have a problem with heteroscedasticity in the above model. Therefore, you estimate the model using the White heteroscedasticity-consistent estimator. (You do not need to do it to answer this question!) Which of the following statements is true? The White’s heteroscedasticity-consistent estimator prevent us from computing incorrect values____

for test statistics or incorrect interval estimates in the presence of heteroskedasticity

Use following data: Excel file exam_data_oct_2022.xlsx, sheet usmacro. The dependent variable (the y-variable) u (or U) is the U.S. unemployment rate. The variable g (or G) denotes the x-variable which is the U.S. GDP growth rate. The variable inf is not used in this question. See the data definitions in the sheet usmacro_data_def. Estimate an ARDL(p, q) model where p = 3 and q = 3. The estimated coefficient of the variable Gt-3 is closest to_________

0.063539

Is the coefficient of the NETWORTH variable significant at 1% level?

What is the estimated probability of a borrower choosing an adjustable-rate mortgage if FIXRATE = 14, MARGIN = 3, and NETWORTH = 4? The probability is closest to___

0.4780

Using Model 2, what is the marginal effect of MARGIN on the probability of choosing an adjustable rate mortgage if FIXRATE = 11.5 and MARGIN = 2.5?

‒0.0202

Using Model 1, what is the marginal effect of NETWORTH on the probability of choosing an adjustable rate mortgage if FIXRATE = 11.5, MARGIN = 2.5 and NETWORTH = 3

0.0142

Study Notes

Investment Analysis

If the net present value (NPV) of an investment is negative, the internal rate of return (IRR) of this investment must be less than the discount rate.

Cash Flow Analysis

An investment pays annual cash flows of 200,000 for the next 10 years, with an additional 850,000 in the 10th year.
The present value of the investment must be calculated to determine the required investment cost at 15% IRR.

Real Estate Investment

A property can be purchased for 35,000,000 USD today.
Five scenarios are projected to compute the expected IRR:
- Severe recession: NOI decreases by 5.5% per year.
- Moderate recession: NOI decreases by 2% per year.
- Baseline forecast: NOI increases by 1.5% per year.
- Moderate expansion: NOI increases by 3% per year.
- Strong boom expansion: NOI increases by 4.5% per year.
The expected IRR is calculated based on the probabilities of each scenario.

Expected NPV

The expected NPV is calculated based on the five scenarios and the discount rate of 7.5%.

Supply and Demand

The supply curve S1 and S2, and the demand curve D, show the apartment market.
If the demand for housing increases due to household income growth, the quantity supplied will increase.

Quantity Theory of Money

The quantity theory of money states that if the money supply is 22 trillion and velocity is 1.165, then nominal GDP is closest to 25.5 trillion.

Housing Market

The country with the highest median quarterly return is to be determined.
A diagram shows the evolution of nominal house prices for France, Japan, Sweden, and the US from 1975:Q1 to 2022:Q2.

Chi-Square Test

A chi-square test is used to study the market for exclusive hotels in Tokyo.
The null hypothesis is that the proportion of hotel guests who experienced the hotel visits as luxury is the same across the three hotels.
The chi-square test statistic is calculated based on the observed frequencies.
The conclusion of the chi-square test is that the null hypothesis can be rejected or not rejected.

Regression Analysis

The adjusted R-squared for the model is to be calculated.
The standard error of the regression is to be calculated.
The 90% confidence interval for β5 (WATERFRONT variable) is to be calculated.
The coefficient of TRADITIONAL is interpreted.
The predicted prices of a house are calculated based on the model.
The problem of heteroscedasticity is addressed using the White heteroscedasticity-consistent estimator.

Time Series Analysis

An ARDL(p, q) model is estimated with p = 3 and q = 3.
The estimated coefficient of the variable Gt-3 is calculated.
The coefficient of the NETWORTH variable is tested for significance at the 1% level.

Probability Analysis

The estimated probability of a borrower choosing an adjustable-rate mortgage is calculated based on the model.
The marginal effect of MARGIN on the probability of choosing an adjustable-rate mortgage is calculated.
The marginal effect of NETWORTH on the probability of choosing an adjustable-rate mortgage is calculated.

Test your knowledge of quantitative methods as they apply to real estate and construction management. Explore the various ways quantitative methods contribute to decision-making in these industries and learn about their primary benefits.

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