The Time Value of Money

Question 1

The total amount due at the end of the investment is called the ____ _____.

Answer 1

The total amount due at the end of the investment is called the Future Value.

Question 2

In the one period case, the formula for FV can be
written as:

FV = __ ×(1 + __)

Answer 2

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.

Question 3

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.

Answer 3

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.

Question 4

In the one-period case, the formula for PV can be
written as:

PV = __ ÷ (1 + _)

Answer 4

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.

Question 5

Net Present Value (NPV) of an investment is the present value of the ______ cash flows, less the ____ of the investment.

NPV = −_____ + ____

Answer 5

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

Question 6

The general formula for the future value of an investment over many periods can be written as:

FV = __ ×(1 + _)^__

Answer 6

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.

Question 7

Present Value < Cost

→ Purchase?

Answer 7

Present Value < Cost

→ Do Not Purchase

Question 8

Compounding an investment m times a year for T years provides for future value of wealth:

FV = ___ ×(1 + ___)^__*__

Answer 8

Compounding an investment m times a year for T years provides for future value of wealth:

FV = C0 ×(1 + r/m)^m*T

Question 9

The Effective Annual Interest Rate (EAR) is the annual rate that would give us the ___ __-of investment wealth after X years.

Answer 9

The Effective Annual Interest Rate (EAR) is the annual rate that would give us the same end-of investment wealth after X years.

Question 10

The general formula for the future value of an investment compounded continuously over many periods can be written as:

FV = C0 × __^*

Answer 10

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.

Question 11

Perpetuity

– A ____ stream of cash flows that lasts ___.

Answer 11

Perpetuity
– A constant stream of cash flows that lasts forever.

PV = C ÷ r

Question 12

Growing perpetuity
– A stream of cash flows that ___ at a _____ rate
forever.

Answer 12

Growing perpetuity
– A stream of cash flows that grows at a constant rate
forever.

PV = C ÷ (r - g)

Question 13

Annuity
– A stream of constant cash flows that lasts for a ____
number of periods.

Answer 13

Annuity
– A stream of constant cash flows that lasts for a fixed
number of periods.

PV = (C ÷ r) ( 1 - 1/(1+r)^T)

Question 14

Growing annuity
– A stream of cash flows that grows at a ____ rate for a
____ number of periods.

Answer 14

Growing annuity
– A stream of cash flows that grows at a constant rate for a
fixed number of periods.

Question 15

An annuity is valued as the _____ between two
perpetuities:
– one perpetuity that starts at time ___
– less a perpetuity that starts at time __ + __

Answer 15

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)

Question 16

Canadian Mortgages: Canadian banks quote the annual interest based on
compounding ____ annually, although interest is
calculated (compounded) every _____.

Answer 16

Canadian Mortgages: Canadian banks quote the annual interest based on
compounding semi annually, although interest is
calculated (compounded) every month.

Question 17

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.

Answer 17

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.

Question 18

Annuity formulas assume that the first payment is made at the end of the ____ period.

Answer 18

Annuity formulas assume that the first payment is made at the end of the first period.

Question 19

Annuity due or annuity in advance is an annuity where the payment is made at the ______ of the period.

Answer 19

Annuity due or annuity in advance is an annuity where the payment is made at the beginning of the period.

Question 20

Conceptually, a firm should be worth the ____ value of the firm’s future ___ cash flows.

Answer 20

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.

Question 21

Interest rates are commonly expressed on an ____ basis, but semi-annual, quarterly, monthly, and even continuously compounded interest rate arrangements exist.

Answer 21

Interest rates are commonly expressed on an annual basis, but semi-annual, quarterly, monthly, and even continuously compounded interest rate arrangements exist.