MMP321 2024 T1 - seminar solutions - Week 4 (Topic 3)

MMP321 – Week 4 (Topic 3) Seminar Solutions 1 Week 4 (Topic 3): Property Debt Finance Question 1: Part a: Using “MMP321 - Zetland data for 2022 A1.xlsx” posted under “Assignment 1” on CloudDeakin, run a regression model using the sale price as the dependent variable and the building area and numbers of bedrooms, bathrooms, and parking spaces as independent variables . Is the model a good fit? Explain. * Hint: First, ‘clean’ the data by removing properties with unrealistic sales prices (e.g. ‘not disclosed’ or $1) or unrealistic characteristics (no bedrooms, no bathrooms, or zero ‘building area’) SOLUTIONS: Regression Model: Sale Price = β 0 + β 1 No .Beds + β 2 No. Baths + β 3 No.Carparks + β 4 Building Area + e Regression Statistics Standard error 248,631.6 R -squared 0.659 No. Observations 181 F-statistic 84.943 P-value 0.000*** Regression Outputs Variable Coefficients t Stat P-value Intercept 247,462.0 3.529 0.001*** No. Beds 525,296.3 12.586 0.000*** No. Baths −208,928.9 -3.600 0.000*** No. Carparks 99,247.8 2.467 0.015** Building Area 207.2 1.075 0.284 ***, **, * indicate statistical significance at the 1%, 5% and 10% levels, respectively.  The model has a standard error of 248,631.6. Remember that the magnitude of the standard error needs to be considered relative of the mean value of the dependent variable. From the descriptive statistics, sale price has a mean of 1,008,974. Therefore, s.e./mean(y) = 248,631.6 / 1,008,974 = 24.64%.  The model has an R -squared ( R 2 ) of 0.659, which means 65.9% of the variation in in sales price is explained by the independent variables, while 34.1% remains unexplained.

2 MMP321 – Topic 3 Seminar Solutions  The F -statistic has a p -value of 0.000, so it is highly significant. This shows that the model is very useful (i.e. the independent variables explain variation in the dependent variable).  Overall, the R 2 and F -statistic show that the model is a good fit and is useful for explaining sale prices. Part b: Using the regression formula developed in Question 1, calculate the projected price of a unit that has:  Three bedrooms  One bathroom  An internal living area of 86m 2  One car parking space SOLUTIONS: Substituting the coefficient fitted in Part a and the dwelling characteristics detailed in Part b into the regression equation, the projected price is: Sale Price = $247,462.0 + $525,296.3×(3) + −$208,928.9×(1) + $99,247.8×(1) + $207.21×(86) Sale Price = $1,731,489 (rounded to nearest dollar) Recall that the error=0 when we’re calculating projected values Part c: Assuming the market rent of the house, based on advertised rents of similar houses on the market, is $1,450/week and the running costs (agent leasing fees, maintenance, council fees, strata levies, etc.) are 7% of the weekly rent. Estimate the house’s value using the capitalised resale value formula from Week 2’s lecture (capitalised resale value = net rental income/capitalisation rate). Compare the price to that in Part b and discuss the reasons for any similarities or differences with emphasis on the choice of cap rate that you use? SOLUTIONS: You answer will vary depending on the capitalisation rate you use. This is the expected return you would want to generate from the house. This is highly subjective and depends on many factors such as the expected rate of return from housing and interest rates (which at the moment are very high). For this exercise, let’s assume 6% being a modest rate of return for property based on historical returns of Australian property: Capitalised resale value = (annual rental income – annual running cost) / capitalisation rate = ( $ 1,450 7 × 365 − $ 1,450 × 7% 7 × 365 ) /6% = $1,171,910

4 MMP321 – Topic 3 Seminar Solutions PMT = $83,265 (there may be rounding differences) If you sum over the 12 payments during the year, this would be: 12 × 83,265 = $999,185 Therefore, the loan with monthly repayments has lower payments overall, as less interest accumulates due to the principal being repaid slightly earlier on average (at the end of each month rather than the end of each year). Part b: You have organised a mortgage on your new property. The bank has agreed to lend you $450,000 for 20 years at an interest rate of 4.5% p.a. compounding monthly. i) Calculate the monthly repayments ii) Assume you are 10 years into the loan (i.e. there are 10 years remaining). How much of the loan is still outstanding? iii) Using the information from ii), how much of the principal has been repaid over the 10 years and how much interest have you paid? SOLUTIONS: Part a) L = $450,000 i = 4.5% = 0.045 n = 20 years m = 12 Thus we have: n / m = 0.045/12 = 0.00375 nm = 20 × 12 = 240 PMT = 450,000 ( 0.00375 1 − ( 1.00375 ) − 240 ) PMT = $2,846.92 (there may be rounding differences) Part b) We now have 10 years remaining on a loan that has monthly repayments of $2,846.92. The interest rate remains the same; the only change is that n = 10. Thus we have: nm = 10 × 12 = 120 OL = PMT ( 1 −( 1 + i m ) − nm i m )

MMP321 – Week 4 (Topic 3) Seminar Solutions 5 OL = 2,846.92 ( 1 −( 1.00375 ) − 120 0.00375 ) OL = $274,697.60 Part c) Principal repaid over 10 years = Original Loan Amount − Outstanding Amount Principal repaid over 10 years = 450,000 − 274,697.60 = $175,302.40 Total Interest Paid = Total repayments − Principal repaid Total repayments made over 10 years = ($2,846.92 × 120) = $341,630.40 Total Interest Paid = $341,630.40 − 175,302.40 = $166,328 Part c: You are investigating borrowing $15 million. You have identified two banks that will lend you the money, both have identical terms and conditions and fees. The only difference are the interest rates. Bank A is offering you 8% p.a. compounding semi-annually. Bank B is offering 7.8% p.a. compounding monthly. Which bank would you choose? SOLUTIONS: In this case we need to calculate the effective annual rate: i e = ( 1 + i m ) m − 1 Bank A: i = 8% = 0.08 and m = 2 (semi-annual) i e = ( 1 + 0.08 2 ) 2 − 1 = ( 1.04 ) 2 − 1 = 0.0816 = 8.16% Bank B: i = 7.8% = 0.078 and m = 12 (monthly) i e = ( 1 + 0.078 12 ) 12 − 1 = ( 1.0065 ) 12 − 1 = 0.0808 = 8.08% Therefore it would be better to go with Bank B, as it has a lower effective annual rate. Part d: Calculate the outstanding loan amount for the following loan:  Years remaining: 5  Nominal interest rate: 9% p.a.  Repayments: $15,500 fortnightly SOLUTIONS:

MMP321 – Week 4 (Topic 3) Seminar Solutions 7 Interest payments = $345,000 × 0.045 = $15,552 ICR = 18,552 15,552 = 1.195