ECON180SPRING2023Project1

pdf

School

University of Victoria *

*We aren’t endorsed by this school

Course

180

Subject

Economics

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by MateLapwing4062

1 ECON 180 SPRING 2023: PROJECT 1 DUE JANUARY 31, 2023 by 11:59 PM VICTORIA, B.C. TIME Honor Code : I guarantee that this submission is entirely my own work . I have cited any outside sources in APA or IEEE style. (You must accept this code to receive a mark.) Name or Signature for Honor Code : __Rolla Elsayed________________________ Last 3 digits of student number : __815_______ Please enter your answers in the spaces and tables provided. Your submission must be in either PDF or Microsoft 365 (Word, etc.) format, so Brightspace can read it properly. Question Marks 1 a-e 75 each Q1 (Average) 75 2 Q2 (Total) 75 3 a-e 75 each Q3 (Average) 75 Q1 to Q3 (Q1+Q2+Q3)/3 75 4 a 5 b 5 c 5 Q3 (Total) 15 Subtotal (Q1 + Q2 + Q3)/3 + Q4 90 Communication 10 Total 100 I’ve provided an Excel spreadsheet with this project, but you don’t have to use it. None of the questions require that you submit it, but you may find it very useful to have the information you gather tabulated and ready for use by projects 2 through 6. Note that the spreadsheet has three tabs: one for Salary, one for Housing, and one for Mortgage information.

2 Grading Each part of questions 1 and 2 will be assigned one of the following marks, in accordance with UVic’s grading scale . • 0: Blank or entirely irrelevant. • 25: An attempt was made, but the result is not in line with what was asked for. • 45: You tried, but there were major issues with understanding the material. • 55: Minimally acceptable work. Significant conceptual or calculation issues. • 65: Adequate work. Minor conceptual or calculation issues. • 75: Good work and full engagement with the course. For more information, see UVic’s Undergraduate Grading Guidelines . Table of Contents ECON 180 SPRING 2023: PROJECT 1 ........................................................................................ 1 Grading .......................................................................................................................................... 2 Introduction: Mandeep’s Seeking a Solution ................................................................................... 3 Basic Information and Assumptions ................................................................................................ 4 Question 1 (Regular): Data Gathering (No associated lecture) ......................................................... 5 a. Income .............................................................................................................................................................. 6 b. Housing near Victoria ....................................................................................................................................... 8 c. Housing in Montreal ....................................................................................................................................... 10 d. Housing in Regina ........................................................................................................................................... 12 e. Mortgage Rates .............................................................................................................................................. 14 Question 2 (Regular): Benefit-Cost Analysis (Lecture 2) ................................................................. 17 Question 3: Housing Costs (Present Value, Annuities, Interest) ...................................................... 19 a. From APRs to Interest Rates (Lecture 6) ........................................................................................................ 19 b. Housing costs in Montreal (Lectures 6,7) ....................................................................................................... 21 c. Housing costs in Regina (Lectures 6,7) ........................................................................................................... 22 d. Housing costs in Victoria (Lectures 6,7) ......................................................................................................... 24 e. A bonus and a yearly raise (Lectures 6,8) ....................................................................................................... 26 Question 4: (Challenge) Salary (Gradients, What’s missing?) ......................................................... 27 a. (5 marks) From a geometric gradient to an arithmetic gradient. (Lecture 8) ................................................ 27 b. (5 marks) A more realistic payment scheme (Lectures 6,7,8) ........................................................................ 28 c. (5 marks) What’s missing? .............................................................................................................................. 30

3 Introduction: Mandeep ’s Seeking a Solution Mandeep (nonbinary, they/them) is completing a bachelor’s degree in your engineering specialty at UVic. They expect to graduate exactly three years from now. Immediately after graduation, they will begin to work as an engineer , but they’re open to the possibility of getting a Master’s degree and/or a PhD. Mandeep has three options on where to work: Victoria, Regina and Montreal. If they end up in Victoria, they will build a garden suite for their parents and move into the main house on the same property. If they choose to work in Montreal, they will rent an apartment or condo. If they end up in Regina, they will buy a home and take out a mortgage to pay for it. Mandeep is firm in the belief that they will work as an engineer for exactly 40 years before retiring. Throughout the four projects in this course, you will examine the benefits and drawbacks of working and living in each city . We’ll start with the basics, and then add more layers to the problem as the relevant topics are covered in class.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

4 Basic Information and Assumptions • Note: Like programmers, project planners count from 0. • It is currently Month 0, Year 0. • Mandeep will be a student until the end of Year 2 (Month 35) • To keep things simple, assume Mandeep has no income and no housing costs while studying 1 . • Mandeep will work as an engineer for exactly 40 years (480 months). • Mandeep will start working as an engineer in Year 3 (Month 36). • For this project, assume that Mandeep’s MARR is 6.45% per year (the current prime lending rate in Canada 2 at the time of writing this project). • While it’s important to calculate the final values asked for in each question, I’m not very interested in the numerical results, which will vary by student: I want to see that you understand how to use discount factors such as (P/A,i,N), (P/F,i,N), etc. • → When asked to show your work, please write your answer using this functional notation – e.g. $300 x (P/A,6%,45). There’s no need to show all your arithmetic – I encourage you to use a math program or Excel to do it for you. It’s fine to write $300x(P/A,6%,45) on one line, and $300 x 16.4558 on the next. (I used Excel to determine that (P/A,6%,45) was about 16.4558.) • While you’re not given marks for it, it may be useful to start each question by sketching a cash flow diagram (or two) to help you picture the situations you’re studying. • While it’s fine to use ‘brute force’ (finding the present value, etc. of each cash flow, one time period at a time) to check your solution, this will not receive full marks. Part of what I’m testing is your ability to use the discount factors. 1 This is an unrealistic assumption, but I’m making it to reduce the work you need to do. In a normal term, I usually ask students to consider tuition costs, food, etc. This is an out-of-major course taking place during a time of global crisis and great uncertainty, and combined with the unusually late posting time I feel a more streamlined project is appropriate. 2 Source: https://www.bankofcanada.ca/rates/daily-digest/ , accessed on January 16, 2023.

5 Question 1 (Regular): Data Gathering (No associated lecture) For this project, we need information on Mandeep ’s housing costs , salary and mortgage rates (if buying a house in Regina). For these parameters, we will need baseline , minimum and maximum values. Most calculations will use the baseline values, but part of the course – the portion on sensitivity analysis - will focus on what to do if your numbers aren’t exactly right, or can vary from what you expect. That’s why we need the minimum and maximum values. We’ll be ‘sitting’ on these for a while, since they won’t co §me into play until Project 4. Baseline Value : If I asked you for only one value, this is the value you would choose. It’s the value you’ll use in your main calculations. Minimum Value : What’s the lowest the value could reasonably go? Maybe you expect Mandeep ’s income to be $100,000 a year, but there’s a good chance it could be as low as $50,000 a year. Maximum Value : What’s the highest the value could reasonably go? Maybe houses of the type Mandeep wants in Regina go for about $500,000, but if Mandeep ’s very unlucky they may end up paying up to $750,000. In brief: the baseline value is what you expect the value to be. The minimum and maximum are the lowest and highest values in the range within which the value can fall. For example, I expect a 473 mL energy drink to cost about $3.50. That’s the baseline. If I’m lucky, I can get it on sale for as low as $1.50, but that’s the minimum price. I’ve also rarely seen them being sold for as much as $4.50. That’s the maximum.

6 a. Income What specialty will Mandeep pursue? (e.g. Software Engineering, Mechanical Engineering) • Mandeep ’s Specialty : Biomedical Engineering City Value Type Yearly Salary 3 ($) Victoria Minimum 29,000 Baseline 46,760 Maximum 77,000 Montreal Minimum 32,000 Baseline 53,124 Maximum 88,000 Regina Minimum 39,000 Baseline 57,055 Maximum 84,000 To find yearly salaries, two useful sites are https://www.glassdoor.ca/index.htm and https://www.payscale.com . Their home pages are not particularly useful, but using Google to search for (e.g.) ‘mechanical engineer salary Victoria ’ will take you to the correct sub -pages within the first page of hits. These sites give you the average yearly salary, which you can use as your baseline, as well as the minimum and maximum values. Don’t worry about raises, bonuses, taxes, etc. We’ll deal with those in later projects. Sources used to find salary (cite in IEEE or APA format): [1] Salary: Biomedical Technician in Regina, SK. (2021). Retrieved January 28, 2023, from Glassdoor.ca website: https://www.glassdoor.ca/Salaries/regina-biomedical-technician- salary-SRCH_IL.0,6_IM985_KO7,28.htm?clickSource=searchBtn 3 How much does an average engineer in your specialty earn, per year, in Victoria? Regina? Montreal? Halifax?

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

7 Explain the reasoning behind your choices below. This will only count toward your project-wide communication mark, so you can skip it and still get a very high mark on the project. Please try to keep your explanation to half a page or less. There’s no minimum length – if you can explain your reasoning in one word, great! Why did you choose these particular values for the minimum, baseline & maximum salaries in Regina? Glassdoor provided me with these values. The website clarified the average, maximum, and minimum salaries. Additionally, I am confident that Glassdoor gives accurate estimates since their questionnaire is detailed.

8 b. Housing near Victoria 4 Mandeep’s parents own a house in Saanich. This house has a large backyard. They would like their child to con tinue to live with them, so they’re making the following offer: If, after graduation, Mandeep stays in Victoria for work, they can have their parents’ house, as long as they build a garden suite in the backyard, for the parents. The deal is that Mandeep would have to pay for the garden suite, but it would be built for the parents, and then the parents would vacate their house and leave it to Mandeep. For more information (including a ballpark estimate of cost) on garden suites in Saanich, see the following articles: Derosa, Katie. (2020, September 18). Saanich gives green light to garden suites after years of consultation. https://www.timescolonist.com/local-news/saanich-gives-green-light-to-garden- suites-after-years-of-consultation-4684095 District of Saanich. (2022). Garden suites. https://www.saanich.ca/EN/main/local- government/development-applications/garden-suites.html Juras, S. (2020, February 10). How much to build a garden suite in City of Victoria or Saanich? [Video File]. https://youtu.be/D_VuAb3uPgU City Value Type Garden Suite Construction Cost in Saanich ($) Victoria (Saanich) Minimum $160,000 Baseline $180,000 Maximum $210,000 (For now, we’re ignoring taxes. This is on purpose. A later project, due after we’ve covered taxes in class, may add property taxes as a recurring expense if Mandeep chooses to work in Victoria – or in Regina, where we assume Mandeep will buy a home if they settle there.) 4 The scenario in this question, and much of the phrasing, is by Dr. E. Gugl. The rest of the assignment questions are by C. Willmore.

9 Explain the reasoning behind your choices below. This will only count toward your project-wide communication mark, so you can skip it and still get a very high mark on the project. Please try to keep your explanation to half a page or less. There’s no minimum length – if you can explain your reasoning in one word, great! Why did you choose these particular values for the minimum, baseline & maximum garden suite construction costs in Saanich? The sites provided gave an average baseline cost of $180,000, and the video clarified that the cost will be around $200,000 plus or minus per garden suite. The maximum value is higher than the highest estimate given to allow for any additional costs and give a margin of error.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

10 c. Housing in Montreal What kind of housing will Mandeep rent while working as an engineer? (2-bedroom condo? 3- bedroom?) • Type of housing (Montreal) : ______1-bedroom apartment_____________ City Value Type Monthly Rent ($) Montreal Minimum $1030 Baseline $1359 Maximum $1600 A convenient place to find the figures needed above is the Rent Board web site. They have tabulated minimum, average and maximum rental values by type of housing in each city: • Montreal: https://www.rentboard.ca/montreal-qc This is only a suggestion. You may use other sources if you wish. Sources used to find rent (cite in IEEE or APA format): [1] Montreal, Quebec Apartments For Rent. (2019). Retrieved January 29, 2023, from RentBoard website: https://www.rentboard.ca/montreal-qc?beds=1

11 Explain the reasoning behind your choices below. This will only count toward your project-wide communication mark, so you can skip it and still get a very high mark on the project. Please try to keep your explanation to half a page or less. There’s no minimum length – if you can explain your reasoning in one word, great! Why did you choose these particular values for the housing type and minimum, baseline & maximum rents in Montreal? I selected values for housing type and minimum, baseline, and maximum rents in Montreal by researching the highest and lowest prices in a suitable region around downtown Montreal and using the prices on the extremes. I then found the average price of renting and used that as the baseline .

12 d. Housing in Regina If they choose to live in Regina, Mandeep will buy a housing unit that they will live in until the end of their working life. Due to the way in which house price data is reported in public sources, it may be easier to treat the minimum, maximum and baseline prices as different types of housing that Mandeep may choose – for example, they may expect to buy a mid-price condo, but may end up with a cheap bungalow or expensive two-storey home. You are free, however, to choose the Same housing type for the minimum, baseline and maximum. Type of Regina housing used for minimum price: 3-bedroom house Type of Regina housing used for baseline price: 3.bedroom house Type of Regina housing used for maximum price: 4-bedroom house City Value Type Home Purchase Price ($) Regina Minimum $89,900 Baseline $619,900 Maximum $1,350,000 If you are using a different type of housing for the min/baseline/max, there are good standard sources with this information available: • Royal LePage’s Home Prices and Forecasts: https://www.royallepage.ca/en/realestate/info-and-advice/market-reports-and- surveys/regional-market-updates/ Their National House Price Composite for Q1 2022 is especially useful: • https://marketing.rlpnetwork.com/Communications/Royal_LePage_National_House_Pri ce_Composite_in_the_First_Quarter_2022.pdf

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

13 If you are using the Same type of housing for all three prices, then you will probably have to search real estate listings at sites such as the following: • Realtor.ca: https://www.realtor.ca/sk/regina/real-estate • Homes Regina: https://www.homesregina.ca/property- search/results/?city=Regina&state=SK • Royal LePage’s Regina listings: https://www.royallepage.ca/en/sk/regina/properties/ The above sources are just a suggestion. You are free to use your own. Sources used to find rent (cite in IEEE or APA format): [1] 1848 Montreal Street, Regina, SK, S4P 1L1 - house for sale | Listing ID SK917705 | Royal LePage. (2019). Retrieved January 29, 2023, from Royal LePage website: https://www.royallepage.ca/en/property/saskatchewan/regina/1848-montreal- street/19079975/mlssk917705/ [2] 1833 Eagles Road, Regina, SK, S4X 4C8 - house for sale | Listing ID SK917639 | Royal LePage. (2020). Retrieved January 29, 2023, from Royal LePage website: https://www.royallepage.ca/en/property/saskatchewan/regina/1833-eagles- road/19076901/mlssk917639/ [3] 4134 Fieldstone Way, Regina, SK, S4V 3H7 - house for sale | Listing ID SK917582 | Royal LePage. (2022). Retrieved January 29, 2023, from Royal LePage website: https://www.royallepage.ca/en/property/saskatchewan/regina/4134-fieldstone- way/19069255/mlssk917582/

14 Explain the reasoning behind your choices below. This will only count toward your project-wide communication mark, so you can skip it and still get a very high mark on the project. Please try to keep your explanation to half a page or less. There’s no minimum length – if you can explain your reasoning in one word, great! Why did you choose these particular values and housing types for the minimum, baseline & maximum housing costs in Regina? I determined the minimum purchase by finding the most affordable house suitable for a family. Similarly, I found the maximum rent by searching for the most expensive house that would fit that criteria. To determine the baseline rent, I took one of the houses that were priced moderately.

15 e. Mortgage Rates Pick a Canadian bank, visit its web page, and find minimum, baseline and maximum values for the APR (the advertised rate) it charges on fixed rate mortgages. (Almost any rate quoted for a fixed mortgage will be an APR, as the term is used in our course 5 .) Note that a 1-year fixed mortgage does not mean the entire loan must be paid back in one year – a typical mortgage term is 25 years, and the ‘1 - year fixed’ means that the bank won’t change the rate charged for at least 1 year. That means you could choose a 1-year fixed rate for your minimum, a 5-year for your baseline and a 10-year for your maximum. We will be using a 25-year amortization period (just in case this matters for your rates – basically, we assume mortgage payments go on for 25 years). Bank Chosen: ___CIBC___________________________ Value Type Mortgage Type Fixed Rate APR (%) Minimum 1 year 6.34% Baseline 5 years 6.49% Maximum 10 years 7.49% A few bank mortgage sites to get you started. Feel free to choose another bank : • CIBC: https://www.cibc.com/en/interest-rates/mortgage-rates.html • Royal Bank: https://www.rbcroyalbank.com/mortgages/mortgage-rates.html • TD: https://www.td.com/ca/en/personal-banking/products/mortgages/mortgage-rates/ 5 If a bank advertises a ‘Special Rate’ and ‘APR’ for the Same mortgage, use the APR. If a bank only lists a ‘posted rate,’ use that as the APR.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

16 Why did you choose these particular values for the mortgage rates? (There’s no ‘wrong’ answer here, but I hope that putting this question here may encourage you to think about what mortgage would be preferred by Mandeep.) I selected these values because CIBC offers a wide range of options for fixed rates over time. Additionally, I believe that Mandeep would likely prefer a 10-year mortgage term due to the lower risk it poses, as they will be less affected by market fluctuations, even though the interest rate may be higher.

17 Question 2 (Regular): Benefit-Cost Analysis (Lecture 2) Assume the following: • For this question, ignore the time value of money (present values, etc.) , and don’t worry about realistic considerations like inflation, taxes, raises, being paid twice a month, etc. We’ll bring those in during later projects. • Mandeep will work as an engineer for exactly 40 years. Their yearly salary and monthly rent (if they live in Victoria or Montreal) will never change. • The benefits of living in a city are equal to the total salary Mandeep earns, as an engineer, after graduating. If you earn $100,000 a year for 40 years, then the total benefits are $4,000,000. • The costs of living in a city are equal to the total housing costs. For Montreal, this is 40 x 12 = 480 rent payments. • For Regina, instead of rent payments, housing costs are a single payment equal to the cost of the house (we’re ignoring mortgages for now). • For Victoria (well, Saanich), housing costs are equal to the cost of the garden suite. • The relevant values are the baseline values. Use incremental benefit-cost analysis to determine the preferred city to live and work in. The cities are mutually exclusive, and you may assume you MUST pick one of the cities (even if it turns out they all have negative benefit-cost ratios). • Preferred city: ______ Regina _______________________ Work: The preferred city is just a checksum, and different students may end up with different preferred cities – what you’re being graded on here is your ability to correctly perform a simple incremental benefit-cost analysis . Because of this, you must show your work. No work, no mark. If y ou’re going for a high communication mark, make sure that your calculation is clearly laid out, in such a way that someone else reading it can understand each step without having to ask additional questions. (Think of the format that YOU would like to see in a long-form answer key for this question.)

18 Costs Benefits BCR IB IC IBCR Victoria $180,000.00 $1,870,400 10.4 Regina $619,900.00 $2,282,200 3.7 $411,800 $439,900 $0.9 Montreal $652,320.00 $2,124,960 3.3 -$157,240 $32,420 -$4.9 Victoria: - Cost of living: $180,000.00 (the cost of building the garden suite) - Benefits: 40*$46760 = $1,870,400 Regina: - Cost of living: $619,900.00 (the cost of the house) - Benefits: 40*$57055 = $2,282,200 Montreal: - Cost of living: $1359*480 = $652,320.00 (the cost of rent over 40 years) - Benefits: 40*$53124 = $2,124,960

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

19 Question 3: Housing Costs (Present Value, Annuities, Interest) a. From APRs to Interest Rates (Lecture 6) i. For reference only, please fill out your baseline values from Project 1 In the first two columns of the table below. If you did not submit Project 1, you may use the values from the Project 1 sample value spreadsheet. Once you’ve written down the APRs, use techniques from this course to calculate the corresp onding monthly (per month) interest rate. Remember, you’re going from an APR compounded every six months to a per-month interest rate. To show you know what you’re doing, write down the calculation for your baseline monthly mortgage interest rate. This sample calculation (room to answer on the next page ) is most of what you’ll be marked on in this part of the question. Bank Chosen: ________CIBC______________________ Value Type Mortgage Type Fixed Rate APR (%) Monthly Interest Rate (%) Minimum 1 year 6.34% 0.521% Baseline 5 years 6.49% 0.534% Maximum 10 years 7.49% 0.615% Remember that even though it looks like one, the APR is not an interest rate. At best, it’s an encrypted interest rate, and the decryption key is the compounding rate per year, as discussed in class. To go from an APR compounded semi- annually to a monthly interest rate, first you’ll need to decrypt the APR into a semi-annual (per 6 months) interest rate, then convert the per six months interest rate into the equivalent per month interest rate 6 . 6 This is the Same interest rate , just in terms of a different time scale, just like 60 km/hr and 1 km/minute are the Same speed. Conversion is a bit trickier for interest rates than for speed, because interest (usually) compounds.

20 Sample Calculation: Baseline APR to Baseline Monthly Mortgage Interest Rate . If you’re going for a high communication mark, make sure that your calculation is clearly laid out, in such a way that someone else reading it can understand each step without having to ask additional questions. (Think of the format that YOU would like to see in a long-form answer key for this question.) Step 1: Find convert APR to interest rate i = 𝐴𝑃𝑅 ? , where m is the time period of the compound interest = 6.49% 2 = 3.245% , since fixed mortgage rates are compounded semi-annually by law Step 2: Find 𝑖 ????ℎ?𝑦 (1+ 𝑖 ?𝑒?𝑖−𝑎???𝑎? ) = (1 + 𝑖 ????ℎ?𝑦 ) 6 , this is power 6 since there is two 6 months in a year! (1+ 0.03245) = (1 + 𝑖 ????ℎ?𝑦 ) 6 𝑖 ????ℎ?𝑦 = 0.534%

21 b. Housing costs in Montreal (Lectures 6,7) i. For reference only, please fill out your baseline values from Project 1. If you did not submit Project 1, you may use the values from the Project 1 sample value spreadsheet. City Baseline Monthly Rent ($) Montreal $1359 ii. Calculate the present value (Month 0 value) of the rent in Montreal. • Monthly rent remains at its baseline level forever. (We’ll relax this in later projects.) • Mandeep pays rent from Month 36 to Month 515, inclusive. This is a total of 480 months. • Consider converting Mandeep’s MARR ( 6.45% per year) into an equivalent % per month. • Show your work. • When showing your work, you must use correct functional notation such as (P/F,10%,12) for full marks. (Think of how problems are presented in the lecture notes). • Your solution should make use of (P/A,i,N). City Present Value of Rent ($) Montreal $199,148.2821 Calculations: MARR monthly => (1+6.45%) = (1 + 𝑖 ????ℎ?𝑦 ) 12 𝑖 ????ℎ?𝑦 = 0.522% PV calculation: A*(P/A,i,N) = A*(P/A, 𝑖 ????ℎ?𝑦 ,480) Let A be rent. This will give the original value before paying rent by using n=month 35. Find Month 0: (P/F, 𝑖 ????ℎ?𝑦 , 35) Thus, the present value can be calculated by PV = A*(P/A, 𝑖 ????ℎ?𝑦 ,480) *(P/F, 𝑖 ????ℎ?𝑦 , 35) = 1359*(P/A, 0.522%,480)*(P/F,0.522%,35) =$199,148.2821

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

22 c. Housing costs in Regina (Lectures 6,7) i. For reference only, please fill out your baseline house price and mortgage % per month from Project 1. If you did not submit Project 1, you may use the value from the Project 1 sample value spreadsheet. City Baseline House Price ($) Regina $619,900 Baseline Mortgage interest 0.534 % per month ii. Calculate Mandeep’s monthly mortgage payments if they choose to buy a house in Regina. Show your work , and use correct notation (e.g. (P/A,10%,52)). • Assume Mandeep takes out a mortgage for the entire value of the house. That means that the only housing costs you need to consider in Regina are the mortgage payments. (We’ll relax this assumption in later projects.) • Mandeep buys the house in Month 36. The net cash flow related to housing in month 36 is zero, because the money coming in from the bank and the money going out to pay for the house are exactly the same, and cancel out. • Mandeep’s Regina mortgage is for 25 years. Mandeep makes exactly 25 years (3 00 months) of payments, and the first payment is in Month 37. • To calculate mortgage payments, you need to split the house price into an equivalent sequence of monthly payments, using (A/P,i,N). The ‘i’ you use will be the mortgage interest rate , not Mandee p’s MARR, because you want to find the monthly payments the bank thinks are equivalent (worth) the initial cost of the house. • For example: suppose Alex took out a mortgage and bought a house in Month 0 for $10,000. Suppose that the interest rate on the mortgage is 1% per month, and Alex will pay it off over 10 years (120 months), with the first payment due the month after buying the house – month 1. In that case, the amount of each monthly mortgage payment is given by $10,000 x (A/P,1%,120) = $143.47 Mande ep’s monthly mortgage payment ($) $2416.76 per month Calculations: Using P*(A/P,i,N), we can get the monthly mortgage payment, where N is 300 months, P is the price of the house and i is the monthly interest. So, $619,900 *(A/P, 0.534, 300) = $2416.76

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

23 iii. Calculate the present (Month 0) value of the mortgage payments. Show your work. • For this calculation, you will use Mandeep’s MARR of 6.45% per year (or the monthly equivalent). • You can treat the mortgage payments as a sequence of 300 equal payments, starting in month 37. • Your solution should make use of (P/A,i,N). City PV of Mortgage ($) Regina 301,484.42 [Show your work] PV = Ax(P/A,i,N) x (P/F, i,N) = 2416.76 x (P/A,0.522%,300) x (P/F, 0.522%,37) = $365,879.15 x 0.824 =$ 301,484.4196

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

24 d. Housing costs in Victoria (Lectures 6,7) i. For reference only, please fill out your baseline values from Project 1. If you did not submit Project 1, you may use the values from the sample value spreadsheet. City Baseline Garden Suite Construction Cost ($) Victoria $180,000 ii. Calculate the present value (Month 0 value) of the cost of building the garden suite, taking into account the information below. • Mandeep is required to pay for the garden suite immediately upon graduation. • Mandeep will pay for the first $10,000 of the garden suite construction cost in cash, from their savings. This payment will be made immediately upon graduation. • Mandeep will take out a personal loan to pay for the remaining construction cost. • This loan is offered to Mandeep at a fixed interest rate of 8% per year . (This is roughly in line with non-mortgage consumer loan rates 7 in Canada, at the time of writing this project.) • Mandeep will pay the loan over the course of five years. Payments are monthly, for a total of 5x12 = 60 payments. The bank will deposit the funds directly into Mandeep’s account immediately upon graduation. The first payment is due one month after that. • Calculate monthly loan payments in the same way that you calculated mortgage payments in part b (taking into account the 5-year repayment schedule, and the 8% interest rate). There is room for your answers and work on the next page. 7 See “Funds advanced for non - mortgage loans” in Bank of Canada. (2023). Interest rates charged for new and existing lending by chartered banks. https://www.bankofcanada.ca/rates/banking-and-financial-statistics/interest- rates-for-new-and-existing-lending-by-chartered-banks/ (Accessed January 16, 2023)

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

25 Mandeep’s monthly loan payment ($) $3,423.93 per month Find 𝑖 ????ℎ?𝑦 : (1+8%) = (1 + 𝑖 ????ℎ?𝑦 ) 12 𝑖 ????ℎ?𝑦 = 0.643% PV=$180,000-$10,000=$170,000 A = PV(A/P,i,N) = 170,000x(A/P,0.643,60) A = $3,423.93 City PV of Garden Suite Construction Costs (Loan + $10,000 from savings) ($) Victoria $185,984.95 [Show your work] (1+6.45%) = (1 + 𝑖 ????ℎ?𝑦 ) 12 𝑖 ????ℎ?𝑦 = 0.522% PV = A(P/A,I,N) + 10,000 = $3,423.93 x(P/A,0.522%,60) + 10,000 = $175,984.95 +10,000 PV = $185,984.95

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

26 e. A bonus and a yearly raise (Lectures 6,8) i. For reference only, please fill out your baseline salaries from Project 1. If you did not submit Project 1, you may use the values from the Project 1 sample value spreadsheet. City Baseline Yearly Salary ($) Victoria $46760 Montreal $32,000 Regina $57,055 ii. Calculate the present (Year 0) value of Mandeep’s income, given the following assumptions: • To keep things simple, assume that Mandeep gets paid once a year, at the start of the year. • This means you can use ‘years’ as your time scale. • Mandeep’s first salary payment is in year 3 • There are a total of 40 salary payments. • In year 3, in addition to t he year’s salary, Mandeep receives a one -time bonus equal to one fourth of the starting salary. • Mandeep’s salary increases by 3.5% each year, so that their year 4 salary is 1.035 x their Year 3 salary, etc. • Show your work for the Victoria calculation (all other calculations will be the same except for the numbers). Your answer should make use of (P/A,g,i,N). City PV of Mandeep’s Income ($) Victoria $2,017,748.114 Montreal $1,380,837.87 Regina $2,461,988.695 Calculation: - Let A be the first pay and g is the growth rate of 3.5% - The first equivalent payment right before the payments start in year 3 can be calculated using o (P/A,g,i,2), where N=2 before payments - Since Mandeep is going to get a bonus on his starter salary, A/4 will be multiplied to salary of year 3 (first year he receives a salary). o (A/4) x (P/F,i,3) - By adding the salary with growth rate of 40 payments to the bonus of year 3, it gives the present value. i is 6.45% per year (MARR) o PV Salary = A x (P/A,g,i,40) x (P/F,i,2) + (A/4) x (P/F,i,3) o PV Salary = 46760 x (P/A,3.5%,6.45%,40)x(P/F, 6.45%,2)+(46760/4)x(P/F,6.45%,3) o PV Salary = $ 2017748.114

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

27 Question 4: (Challenge) Salary (Gradients, What’s missing?) a. (5 marks) From a geometric gradient to an arithmetic gradient. (Lecture 8) Let’s go back to the situation from question 1.e (where you calculated the present value of Mandeep’s salary). Suppose that Mandeep is in Victoria, but instead of Mandeep’s salary going up by 3.5% each year, it goes up by a constant amount G per year, so Mandeep’s salary in Year 4 is equal to their Year 3 starting salary plus G, etc. Calculate the value of G needed to make the present value of this stream of income equal to the present value of Mandeep’s income that you calculated (for Victoria) in question 1.e. • Apart from replacing a yearly raise of 3.5% with a yearly raise of G dollars, everything else is exactly as in question 1.e. This includes the signing bonus of ¼ of the starting salary. • Show your work. Your answer should make use of (A/G,i,N). Required value of G: $ 3,919.25 [Show your work (only need Victoria values)] Arithmetic gradient Mandeep ’s starting salary is A and it increases by a constant amount G. Convert the arithmetic gradient into an annuity: A+G x (A/G,i,40) Get Year 0 value (P/A,i,40) x (P/F,i,2) Account for the bonus in year 3 (A/4) x (P/F,i,3) Find present salary PV = A+G x (A/G,i,40)* (P/A,i,40) x (P/F,i,2) + (A/4) x (P/F,i,3) Plugging in $2,017,748.114= ($46760+ G x (A/G,6.45%,40)) x (P/A,6.45%,40) x (P/F,6.45%,2) + ($46760) x (P/F,6.45%,3) $2,017,748.114= ($46760+ G x 11.93) x $665,465.19 x 0.882487715 + ($46760) x 0.829016172 So, G = $3,919.25

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

28 b. (5 marks) A more realistic payment scheme (Lectures 6,7,8) Suppose that Mandeep is in Victoria. The situation is exactly as in question 1.e, except that Mandeep is paid once a month, instead of once a year. Mandeep’s salary still goes up by 3.5% a year, starting with the first salary payment eac h year. In the first year of work, Mandeep’s monthly salary is equal to 1/12 of the baseline yearly salary. In the second year of work, Mandeep’s monthly salary is equal to 1.035 times their Year 1 monthly salary, and so on. The sign-on bonus of ¼ of Mande ep’s starting yearly salary is still paid all at once. Timing notes: Assume that the bonus is paid at the start of month 36, and the first salary payment is at the start of month 37. (The bonus gets Mandeep through the first month, and at the start of the next month, Mandeep gets paid for the work done the previous month. There are a total of 40x12 = 480 salary payments.) Calculate the present value of Mandeep’s income 8 and show your work. You must use (P/A,g,i,N) in your answer. (Hint: You’ll also want to use (P/A,i,N), and you may find a use for both the ‘per year’ and ‘per month’ versions of the MARR.) Present value of Mandeep’s income : $ 1,023,559.08 [Show your work (only need Victoria values)] So, we want to calculate how much will Mandeep’s income be in present time because the income is a future payment that they are receiving. Step 1: Find a single equivalent payment A = 46760 N = 12 (1+6.45%) = (1 + 𝑖 ????ℎ?𝑦 ) 12 𝑖 ????ℎ?𝑦 = 0.522% Ax(P/A, 𝑖 ????ℎ?𝑦 ,12) =A (1+𝑖) 𝑁 −1 [𝑖(1+𝑖) 𝑁 ] = $542,536.05 Step 2: Adjustment to the year Since A x (P/A, 𝑖 ????ℎ?𝑦 ,N) gives for one time period before, we have to adjust the year to one year in the future to be at the start of the year so use (F/P,imonthly,1). Thus, multiply the A x (P/A, 𝑖 ????ℎ?𝑦 ,N) by (F/P,imonthly,1) to account for this adjustment. A x (P/A, 𝑖 ????ℎ?𝑦 ,N) x (F/P,imonthly,1) Step 3: Year 2 and 3 Since they start receiving salary at Year 3, the expression can be adjusted to be A x (P/A, 𝑖 ????ℎ?𝑦 ,N) x (F/P,imonthly,1) x (P/A, 𝑖 ,2) Step 4: Bonus Mandeep gets a A/4 bonus at the start of month 36 so 8 This will NOT be the same as in 1.e, because the time distribution of payments is different. Getting $12,000 now is not the same as getting $1,000 a month, starting today.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

29 A x (P/A, 𝑖 ????ℎ?𝑦 ,N) x (F/P , 𝑖 ????ℎ?𝑦 ,1) x (P/A, 𝑖 ,2) + A/4 (P/A, 𝑖 ,3) Step 5: Plugging in A x (P/A, 𝑖 ????ℎ?𝑦 ,12) x (F/P , 𝑖 ????ℎ?𝑦 ,1) x (P/A, 𝑖 ,2) + A/4 (P/A, 𝑖 ,3) $542,536.05 x 1.00522 x $1.82 + $30,989.16 = $1,023,559.08

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

30 c. (5 marks) What’s missing? Questions 1 and 2 deal with Mandeep’s situation. For teaching purposes, the analysis has been simplified from what would be done in a professional, realistic analysis. Given that you are one of UVic’s finest problem solvers, by now you probably have some thoughts about what’s missing from this analysis. This is your place to share your ideas (and get marks for it). What’s something that you think is missing from our analysis of Mandeep’s situation, but should definitely be added if we were doing it ‘for real’? For full marks, you should attempt an implementation (i.e. try it out, at least in a limited fashion). This question is intended to be fun, not stressful. It’s a sandbox for you to show your stuff to an audience of TAs and be rewarded for it. Please don’t spend hours on it, unless you really want to. Even a simple, 15-minute answer, is enough for at the very least 1 mark out of 5. In real life, I think that we should have calculated his income in school and houses costs, but for the purposes of this project we assumed that Mandeep had none of these. Also, we didn’t take into account any additional taxes.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

ECON180SPRING2023Project1

Related Documents