Financial Management Flashcards
Jim and Betty plan to retire in 10 years. Currently they have saved enough to provide $60,000 retirement income at the end of each year when they retire. They feel that they could live on $100,000 per year income at the end of each year when they retire. They assume that they can earn a 6% real after-tax return on their investments. Upon retirement, they expect to live for 25 years. How much must they save at the end of each year prior to retirement to reach their goal?
Shortfall of $40,000 per year for 25 years, discount rate 6%
Step 1:
- PMT 40,000
- N 25
- I/Y 6
- FV 0
CPT PV = 511,334
Step 2:
- FV 511,334
- N 10
- I/Y 6
- PV 0
- CPT PMT = 38,794
Jane has accumulated $600,000 for her retirement. If Jane obtains 4% real after-tax return annually on her funds, and also starts to withdraw a lump sum amount of $38,407 at the end of each year from her accumulated retirement fund, how long will her savings last?
600,000 ± PV
38,407 PMT
4 I/Y
0 FV
CPT N = 25 years
One dollar invested at the begining of the year at an annual interest rate of $100% and compounded quarterly would equal what amount at year-end?
1 ± PV
4 N
25 I/Y (25% quarterly)
0 PMT
CPT FV = 2.44
or (1+R)^n
= 1.25 ^ 4 = 2.44
The Nature of Real Property - Land
The earth extending to the centre of the planet
Real Property
Any right, interest or benefit in land, which includes mines, minerals, and improvements on, above, or below the surface of the land
Real Estate
The land and buildings on the land (tangibles)
Eminent domain
政府征地权
Governments at every level have the power to take ownership of or “expropriate” an individual’s property for public use upon payment of compensation
expropriate - vt.没收，征用
Easement
n. 地役权
有限使用(电力公司)
- Is a right acquired by one party to use another’s immovable real estate
- Can be established only by contract or by will
Example: Hydro one have the right to enter Ontario property for the purpose of reading the hydro meter affixed to your home
Power of Sale
- The right of the lender to force the sale of a property without judicial proceedings
- The mortgagee is entitled to their mortgage loan
- Any proceeds in addition to that amount belongs to the mortgagor
- If there is a shortfall, the mortgagor is liable for the shortfall
Foreclosure
- Court proceedings are involved
- Mandatory waiting period
- The mortgagee takes over the ownership of the property
- Any profits on the future sale of the property belongs to the mortgagee
- Any loss would be absorbed by the mortgagee
Interest Rate Differential
= Outstanding mortgage balance * Differential rate * Time remaining
Example:
$250,000 on mortgage, 2 years remaining on the term, interest rate of 4.5%
New two-year rate is 3%
- Three months’ interest
= $250,000 *4.5% * (3months/ 12months)
= $11,250 * 0.25
= $2,812.50 - IRD
= $250,000 *(4.5% - 3%) * 2 years remaining
= $250,000 *1.5% *2
= $7,500
Earning an annual after-tax return on an investment of 12%. How many years will it take to double the money?
Assume $1 PV and $2 PV and an annual after-tax return of 12%
1± PV
2 FV
12 I/Y
0 PMT
CPT N = 6.12 years
Mr. and Mrs. want to set up a college fund for their son’s post-secondary education. They estimated tuition cost commencing 18 years from now is $30,000 per year. Assuming that a university degree takes 4 years to complete and that the discount rate and real after-tax return is 7.5% p.a., how much will they have to contribute on an annual basis to the fund in order to achieve their goal. Their contributions will be at year end.
First determine what lump sum is necessary to produce an income of $30,000 per year for 4 years. The money will be needed at the begining of the year.
Step 1:
Begin mode
30,000 PMT
4 N
7.5 I/Y
0 FV
CPT PV = -108,015.77
Step 2:
End mode
108,015.77 FV
18 N
7.5 I/Y
0 PV
CPT PMT = 3,027.57
Interest rates are currently at 4% and the inflation rate is currently at 1.5%. What is the real rate of return?
Real rate of return = (Nominal rate - Inflation rate) / (1 + Inflation rate)
= (4% - 1.5%) / (1 + 1.5%) = 2.46%
Bart earns a 13% annual yield on a bond. The CPI year over year went from 152 to 155. Bart has a marginal tax rate of 40%. What is real after-tax return?
Inflation rate = (Current CPI - Previous CPI) / Previous CPI
= (155 - 152) / 152 = 1.97%
After tax return = 13% x (1-0.4) = 7.8%
Real after-tax return = (7.8% - 1.97%) / (1+1.97%) = 5.7174%
Effective December 15, 2024, federal government mortgage rules
- insured mortgages in Canada can be granted with an amortization period of up tp 30 years
- approved lenders can grant insured mortgages on properties worth up to $1,500,000
- for insured mortgage in Canada, the minimum downpayment required:
5% for the first $500,000
10% for the property value between $500,001 and $1,500,000
Annie wants to obtain a mortgage. She can afford a maximum $2500 mortgage payment per month; payable at the beginning of each month. She is quoted an 8% annual mortgage rate, with semi-annual compoundings and monthly payments at the beginning of each month. What maximum mortgage amount can Annie afford based on the above terms and a 25 year amortization period?
Step 1:
Determine the monthly mortgage rate, for semi-annual compoundnig:
Semi annual mortgage rate = 8% / 2 = 0.04
Monthly mortgage rate = [ (1 + 0.04) ^ 2/12 ] - 1
= 1.04 ^ 0.16667 - 1 = 0.6558%
Step 2:
Calculate present value
2500 ± PMT
300 N (25*12)
0.6558 I/Y
0 FV
CPT PV = 329,717
