Topic 3: Discounted Cash Flow Valuation

Question 1

Future Value with multiple cashflows

Answer 1

Check examples on Notes

Question 2

Present Value with multiple cashflows

Answer 2

Check examples on Notes

Question 3

Annuities

Answer 3

A contract between you and an insurance company that requires the insurer to make payments to you, either immediately or in the future. In other words it is as level stream of cash flows for a fixed period.

Question 4

Present value of annuity (formula)

Answer 4

PV = (C/r) * (1-(1/(1+r)^t) )

Where:
PV = Present Value
C = Cashflow
r = discount rate
T = length of the Annuity

Check question examples on notes

Question 5

Ordinary Annuity

Answer 5

A finite series of equal payments made at the end of each period.

Question 6

Annuity due

Answer 6

An annuity whose first payments is to be made immediately rather than at the end of the period.

In other words its a finite series of equal payments made at the beginning of each period.

Check examples for calculating Annuity due on notes.

Question 7

Growing Annuity

Answer 7

Refers to a series of regular payments that increase in amount with each payment.

A series of growing payments made at the end of each period over a fixed amount of time.

Question 8

Present value of a growing annuity (formula)

Answer 8

PV = (C / (r - g)) * (1 - ((1 + g)^T / (1 + r)^T))

Where:
PV = present value
C = Cashflow
g = growth rate
r = discount rate
T = length of the annuity

Question 9

Perpetuity

Answer 9

An infinite series of equal payments made at the end of each period. (An annuity with no end)

Question 10

Present value of perpetuity (formula)

Answer 10

PV = C/r

Where:
PV = present value
C = cash flow
r = discount rate

Question 11

Ordinary Perpetuity

Answer 11

Perpetuity with payments at the end of each period.

Question 12

Perpetuity Due

Answer 12

Perpetuity with payments at the beginning of the period.

Question 13

Growing Perpetuity

Answer 13

An endless series of payments that increase in amount with each payment.

Question 14

Present value of a growing perpetuity formula

Answer 14

PV = C / (r - g)

Where:
PV = present value
C = cash flow
r = discount rate
g = growth rate

Check examples on notes

Question 15

Nominal Interest rate

Answer 15

The interest rate expressed in terms of the interest payments made each period.

Also known as the stated or quoted interest rate.

Look out for: the period over which the rate is quoted, if it is not specified it generally means it is an annual rate. Also look out for the period over which it is compounded.

Note: Check examples on notes

Question 16

Effective Annual percentage rate (EAR)

Answer 16

The interest rate expressed as if it were compounded once per year.

Question 17

Effective annual percentage rate (EAR) formula

Answer 17

EAR = ([1 + (quoted rate / m)]^m) - 1

Where:
m = number of times interest is compounded during the year
quoted rate = period of which rate is quoted

Question 18

EAR formula for compounding continuously

Answer 18

EAR = (e^q) - 1

Where:
e = euler’s number (2.71828 or e on calculator)
q = quoted rate

Question 19

Annual Percentage Rate (APR)

Answer 19

The harmonised interest rate that expresses the total cost of borrowing or investing as a percentage interest rate.

A measure of the interest rate plus the additional fees charged with the loan. Both are expressed as a percentage. A loan’s interest rate and APR are two of the most important measures of the price you pay for borrowing money.