Objectives:
· Determining effective “period” rates (other than annual)
· Estimating mortgage payments
· Consideration of all relevant cash flows – including opportunity costs
· Finding the present value of future cash flows (annuities and lump-sum cash flows)
· Net present value (NPV)
Questions:
1. Determine the required monthly payments for the mortgage
2. Determine the “opportunity” costs, on a monthly basis, of using the required funds for closing (i.e., down payment plus all closing costs), rather than leaving those funds invested and earnings the monthly effective rate determined in part (a)
3. Determine the monthly additional payments required to buy versus rent (include the monthly opportunity costs determined in part (b))
4. Determine the principal outstanding on the mortgage after:
a. 2 years
b. 5 years
c. 10 years
5. Determine the “net” future gain or loss after 2, 5, and 10 years under the following scenarios, which Rebecca Young has determined are possible after some “due diligence” regarding future real-estate prices in the Toronto condo market:
a. The condo price remains unchanged
b. The condo price increases annually by an annual rate of 2 percent per year over the next 10 years.
c. The condo price increases annually by an annual rate of 5 percent per year over the next 10 years.
6. As Rebecca Young, what decision would you make? Describe any
qualitative considerations that could factor into your decision.
1
Time Value of Money
2
Time Value of Money
Future value
Amount to which investment will grow after earning interest
Present value
Value today of future cash flow
Key principle
$1 today > $1 tomorrow
3
FV of an initial $100 after
3 years (I = 10%)
FV = ?
0
1
2
3
10%
Finding FVs (moving to the right
on a time line) is called
100
compounding
4
After 1 year
FV1 = PV + INT1
= PV + PV (I)
= PV(1 + I)
= $100(1.10)
= $110.00
5
After 2 years
FV2 = FV1(1+I)
= PV(1 + I)(1+I)
= PV(1+I)2
= $100(1.10)2
= $121.00
In general,
FVN = PV(1 + I)N
6
Future values with annual compounding
7
What’s the PV of $100 due in 3 years if I/YR = 10%?
10%
Finding PVs is the reverse of compounding; it is called
100
0
1
2
3
PV = ?
discounting
8
1.10
Solve FVN = PV(1 + I )N for PV
PV =
FVN
(1+I)N
= FVN
1
1 + I
N
PV
=
$100
1
= $100(0.7513) = $75.13
3
9
What is the PV of this
uneven cash flow stream?
0
100
1
300
2
300
3
10%
-50
4
?
?
?
-?
?= PV
10
What is the PV of this
uneven cash flow stream?
0
100
1
300
2
300
3
10%
-50
4
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