Question
In: Finance
Sarah would like to purchase a condo in Vancouver. She currently rents an apartment for $4,500...
Sarah would like to purchase a condo in Vancouver. She currently rents an apartment for $4,500 per month. The condo she is looking at costs $1,600,000. She intends to put $300,000 down. The condo has monthly condo fees of $300/month, property taxes of $200/month and repairs of $100/month. She can obtain a 30-year mortgage for 3% per year compounded monthly.
There are the following closing costs at purchase:
Land transfer tax $20,000
Legal fees $1,500
There are the following closing costs when selling:
Real estate commission of 3% of selling price
Legal fees $2,000
(a) What is the principal outstanding for the loan after 10 years? (Calculate the value at year 10 of the remaining 20 years of mortgage payments)
(b) Compute the cost (NPV) under buying and renting over the next 10 years assuming the unit is sold in 10 years for $1,800,000 and rent stays constant. Is it better to rent or buy? Upon sale, you will need to pay off the outstanding loan balance (see part a).
Solutions
Expert Solution
Using equated monthly installement formula
EMI= [P x R x (1+R)^N]/[(1+R)^N-1]
a)Hence, Monthly EMI=$5,481 and principal at the end of 10th year=$9,88,258
| Calculation of schedule for loan | |||||
| Year | Principal | Interest | Total Payment | Balance | Loan Paid To Date |
| Principal | Interest | (A + B) | |||
| 2020 | $18,004 | $25,843 | $43,847 | $12,81,996 | 1.38% |
| 2021 | $27,689 | $38,081 | $65,770 | $12,54,307 | 3.51% |
| 2022 | $28,531 | $37,239 | $65,770 | $12,25,776 | 5.71% |
| 2023 | $29,399 | $36,371 | $65,770 | $11,96,377 | 7.97% |
| 2024 | $30,293 | $35,477 | $65,770 | $11,66,084 | 10.30% |
| 2025 | $31,215 | $34,556 | $65,770 | $11,34,869 | 12.70% |
| 2026 | $32,164 | $33,606 | $65,770 | $11,02,705 | 15.18% |
| 2027 | $33,142 | $32,628 | $65,770 | $10,69,563 | 17.73% |
| 2028 | $34,150 | $31,620 | $65,770 | $10,35,413 | 20.35% |
| 2029 | $35,189 | $30,581 | $65,770 | $10,00,223 | 23.06% |
| 2030 | $36,259 | $29,511 | $65,770 | $9,63,964 | 25.85% |
|
Jan |
$2,980 | $2,501 | $5,481 | $9,97,243 | 23.29% |
| Feb | $2,988 | $2,493 | $5,481 | $9,94,255 | 23.52% |
| Mar | $2,995 | $2,486 | $5,481 | $9,91,260 | 23.75% |
| Apr | $3,003 | $2,478 | $5,481 | $9,88,258 | 23.98% |
| May | $3,010 | $2,471 | $5,481 | $9,85,247 | 24.21% |
b) Calculation of cash outflows under buy option
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Ouflows under buy option | 300000 | Monthly ouflow of $600 for all months for condo fees, property tax and repairs+5481 as monthly EMI's | |||||||||
| Land transfer tax | 20000 | ||||||||||
| Legal fees | 1500 | ||||||||||
| Selling price | -1800000 | ||||||||||
| Legal fees | 2000 | ||||||||||
| Real estate commission(3%) | 54000 | ||||||||||
| Oustanding loan | 988258 |
Present cash value of cash outflows is $-390,164.38
| Calculation of cash outflows under rent option | |||||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Monthly outflow of $5100 each month for 10 years | |||||||||||
| Present value of cash outflows is $-529,178.40 |
Buying option is more profitable since it has a better NPV of $(390164.38) over rent option which has NPV of $(529178.40)
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