The Time Value of Money Flashcards
The total amount due at the end of the investment is called the ____ _____.
The total amount due at the end of the investment is called the Future Value.
In the one period case, the formula for FV can be
written as:
FV = __ ×(1 + __)
In the one period case, the formula for FV can be
written as:
FV = C0 ×(1 + r)
C0 is cash flow at date 0, and
r is the appropriate interest rate.
The amount that a borrower would need to set aside today to be able to meet the promised payment of $10,000 in one year is called the _____ _____ of $10,000.
The amount that a borrower would need to set aside today to be able to meet the promised payment of $10,000 in one year is called the Present Value (PV) of $10,000.
In the one-period case, the formula for PV can be
written as:
PV = __ ÷ (1 + _)
In the one-period case, the formula for PV can be
written as:
PV = C1 ÷ (1 + r)
C1 is cash flow at date 1, and
r is the appropriate interest rate.
Net Present Value (NPV) of an investment is the present value of the ______ cash flows, less the ____ of the investment.
NPV = −_____ + ____
Net Present Value (NPV) of an investment is the present value of the expected cash flows, less the cost of the investment.
NPV = −Cost + PV
The general formula for the future value of an investment over many periods can be written as:
FV = __ ×(1 + _)^__
The general formula for the future value of an investment over many periods can be written as:
FV = C0 ×(1 + r)^T
C0 is cash flow at date 0,
r is the appropriate interest rate per period, and
T is the number of periods the cash is invested.
Present Value < Cost
→ Purchase?
Present Value < Cost
→ Do Not Purchase
Compounding an investment m times a year for T years provides for future value of wealth:
FV = ___ ×(1 + ___)^__*__
Compounding an investment m times a year for T years provides for future value of wealth:
FV = C0 ×(1 + r/m)^m*T
The Effective Annual Interest Rate (EAR) is the annual rate that would give us the ___ __-of investment wealth after X years.
The Effective Annual Interest Rate (EAR) is the annual rate that would give us the same end-of investment wealth after X years.
The general formula for the future value of an investment compounded continuously over many periods can be written as:
FV = C0 × __^*
The general formula for the future value of an investment compounded continuously over many periods can be written as:
FV = C0 × e^r*T
C0 is cash flow at date 0,
r is the stated annual interest rate,
T is the number of periods over which the cash is invested, and
e is a transcendental number approximately equal to 2.718.
e x is a key on your calculator.
Perpetuity
– A ____ stream of cash flows that lasts ___.
Perpetuity
– A constant stream of cash flows that lasts forever.
PV = C ÷ r
Growing perpetuity
– A stream of cash flows that ___ at a _____ rate
forever.
Growing perpetuity
– A stream of cash flows that grows at a constant rate
forever.
PV = C ÷ (r - g)
Annuity
– A stream of constant cash flows that lasts for a ____
number of periods.
Annuity
– A stream of constant cash flows that lasts for a fixed
number of periods.
PV = (C ÷ r) ( 1 - 1/(1+r)^T)
Growing annuity
– A stream of cash flows that grows at a ____ rate for a
____ number of periods.
Growing annuity
– A stream of cash flows that grows at a constant rate for a
fixed number of periods.
An annuity is valued as the _____ between two
perpetuities:
– one perpetuity that starts at time ___
– less a perpetuity that starts at time __ + __
An annuity is valued as the difference between two
perpetuities:
– one perpetuity that starts at time 1
– less a perpetuity that starts at time T + 1
PV = (C ÷ r) ( (C/r) /(1+r)^T)
Canadian Mortgages: Canadian banks quote the annual interest based on
compounding ____ annually, although interest is
calculated (compounded) every _____.
Canadian Mortgages: Canadian banks quote the annual interest based on
compounding semi annually, although interest is
calculated (compounded) every month.
The terms of the mortgage are usually renegotiated
during the period of the _____. For example, the
interest of a 25 year mortgage may be renegotiated
_____ years after the initiation of the mortgage.
The terms of the mortgage are usually renegotiated
during the period of the mortgage. For example, the
interest of a 25 year mortgage may be renegotiated
5 years after the initiation of the mortgage.
Annuity formulas assume that the first payment is made at the end of the ____ period.
Annuity formulas assume that the first payment is made at the end of the first period.
Annuity due or annuity in advance is an annuity where the payment is made at the ______ of the period.
Annuity due or annuity in advance is an annuity where the payment is made at the beginning of the period.
Conceptually, a firm should be worth the ____ value of the firm’s future ___ cash flows.
Conceptually, a firm should be worth the present value of the firm’s future net cash flows.
The tricky part is determining the amount, timing, and riskiness of those cash flows.
Interest rates are commonly expressed on an ____ basis, but semi-annual, quarterly, monthly, and even continuously compounded interest rate arrangements exist.
Interest rates are commonly expressed on an annual basis, but semi-annual, quarterly, monthly, and even continuously compounded interest rate arrangements exist.
