Individual project, Part A, DUMINICA Andrada

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Economics

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Jun 19, 2024

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Individual project Part A. For this project, I used excel to compute my data. In this report, I will describe my calculations and give examples of calculations based on the sector I chose, sector 14- Mercier-Hochelaga Maisonneuve, with an overall score of -53.5. Time period Firstly, we have to to convert everything into the same time. In this problem period, it is stated that monthly compounding and payments are used. To change the time period of our data, we have to multiply the time frame, 25 years, by 12, so we know on how many months the payments will be delivered. Then, we must convert the growth rate (g) and the mortgage rate (i) into a monthly data, so we will divide each by twelve. I computed this at the top left corner of my excel sheet (monthly interest rate and monthly g). The interest rate and the growth rate became respectively, 0.42% and 0.167%. g = 0.02 12 = 0.167 % i = 0.05 12 =0.242% Down payments Secondly, we have to calculate the down payments of each appartement. We know that the down payment is 5% for a single-family home or for a condo, and 10% for a 3-unit multiplex. To calculate it, we just multiply the cost of the house (named 2020 in the excel sheet) by 0.05 (if single family or condo) or by 0.1 (if a 3-unit multiplex). We can the find the amount of money that will be left to pay after the down payment. To do so, we subtract the downpayment from the initial cost of the house. Rent Thirdly, the problem states that “all costs are to be calculated to present value” (Individual project- Part A, ENGR201 JJ 23F). With this information, we could understand that we had to bring every expense to the present value. To do so, we have to resort to different techniques for the value of the house and the potential income of the rent. Before going into the detailed calculations for the rent, it is important to note that for each type of housing, the rent calculations will differ. For the single family home, the problem tells us that

we can convert the basement into a 1-bedroom apartment. So we will look at the price of a 1- bedroom apartment for each section and use it for the calculations. For the condos, no rental income can be generated, so the calculations all equal to zero. For the 3-unit multiplex we have to rely on some assumptions. Firstly, we assume that a 3-unite multiplex consists of three bedrooms. If we were to rent part of our multiplex, we could choose to rent a 1 bedroom or a two bedroom, since we would sleep in at least one bedroom. For the project, I chose to rent 2 bedrooms and use only one, because as a student, I would appreciate the extra money coming from the rent and wouldn’t need much extra space. I would be at school all day and wouldn’t invite friends or family to sleep at my house very often. This means that the pros of renting 2 bedrooms (the money), are greater than the one of renting only one (extra space). The problem fails to provide all apartments cost for each sectors and requests us to “use the average cost of all bordering sectors” to compute the missing data. I used the average formula from excel to compute this, using only the real data when doing averages. These computations can be found at the right of my excel document, in the rent prices box. The green lines are given values, and the blue lines are computed. You can notice that sector 18-Pointe Est de l’Ile has no rental income for neither it’s single- family homes, it’s condos or it’s 3-unit multiplex. This is because it is circled by sectors who don’t have apartment cost data. Because of this, the average could not be computed. For the rent, we know that the “basement of a single-family home can be converted into a 1- bedroom apartment” (Individual project- Part A, ENGR201 JJ 23F). This means that we can have income from the single-family homes, which will be a monthly annuity. Depending on the sector, rent fluctuates in price. To find the present value of these rents over a 25-year period, considering the growth rate of 2%, we have to compute the growth-adjusted interest, or i°. To

do so, we must use the formula: ((1=i)/(1=g))-1; The i in this formula is the effective interest rate, since it considers compounding. To compute it, we have to use the formula: (1+ r/m)^m-1, where m is the number of compounding periods and r, the nominal interest rate. R is 5%, because it is the interest rate without considering any fees or compounding interest. M is 12, because there are 12 compounding periods in the year (compounding is once a month). On the excel sheet, the calculation has been made at the top of the sheet, annual effective i . As the title of the calculation lets us know, this effective interest rate is annual. To convert it back to months, we simply divide it by twelve. i e = ¿ -1 = (1+( 0.242% 12 ¿¿¿ 12 - 1= 5.116% i e monthly = i e 12 = 5.116% 12 = 0.426% We then plug this interest rate into the i° formula. On my excel sheet, i° is computed at the top left corner and has a value of 0.26%. i° = 1 + i 1 + g − 1 = 1 + 0.426 % 1 + 0.167 % − 1 = 0.26% Then we can use the geometric gradient to present worth conversion factor (P/A,g,i,N) , whose formula is: (((1+i°)^N-1/ i°(1+ i°)^N)(1/(1+g)); i° being 0.26%, g being 0.167% and n being 300 (months). Once the factor is computed, we have to multiply it by each of the different annuities (rent) to find the present value of the rent of each sector. ( P A ,g,i, N ) = ( ( 1 + i ° ) N − 1 i ° ( 1 + i ° ) N ) ( 1 1 + g ) = ( ( 1 + 0.26% ) 300 − 1 0.26% ( 1 + 0.26% ) 300 ) ( 1 1 + 0.167% ) = 208.0 To compute the present value of the rent, we multiply the annuity with the geometric gradient to present worth factor. This will turn the annuity over 300 months to a present value. PV rent = A ∗ ( P A ,g,i ,N ) = 4293.0 ∗ ( 208.0 ) = 892877.51 $ House

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