FNCE10002 L1-4

Lectures 1-4 formulas and notes

Future value of a single cash flow

FV_n = PV₀(1+r)ⁿ

Present value of a single cash flow

PV₀ = FV_n / (1+r)ⁿ

Future values of multiple cash flows with a cash flow at Time 0

Present values of multiple cash flows

What is a perpetuity?

An equal, periodic cash flow which recurs forever

Present value of a perpetuity

When does the first cash flow occur for a perpetuity?

At the end of time 1

What is a deferred perpetuity?

A series of equal, periodic cash flows that recur forever but with the first cash flow occurring at a later point in the future

Present value of a deferred perpetuity

What is an annuity?

A series of equal, periodic cash flows occurring over n periods

What is special about an ordinary annuity?

They occur at the end of each period, with the first cash flow occurring at the end of the first period

Present value of an annuity

Future value of an annuity

What is an annuity due?

A series of cash flows where the cash flows occur at the beginning of each period

Present value of an annuity due

What is a growing perpetuity?

A series of periodic cash flows occurring at the end of each period which grow at a constant rate forever

Present value of a growing perpetuity

What does the relationship need to be between r and g?

Can the growth rate be positive or negative?

What is a growing ordinary annuity?

A series of periodic cash flows occurring at the end of each period and lasting for n periods where the cash flows grow at a constant rate

Present value of a growing annuity

Future value of a growing annuity

Characteristics of a standard fixed-rate mortgage

• Equal periodic loan payments typically made on a monthly basis

• Each payment = the interest payment + principal repayment

Present value of the amount borrowed today

Cost of a periodic payment

What is a loan amortisation schedule?

• Shows the total payments on a loan

• Separates this amount into the interest paid, the principal balance repaid and the principal balance outstanding

Interest paid

Previous period’s principal x interest rate per period

Principal repaid

Loan payment - interest paid

Principal balance remaining

Previous period’s principal - principal repaid

What are debt securities?

• Securities where the issuer borrows funds from investors

• There is a contractual obligation to make regular interest payments to these investors

• Funds borrowed must be repaid when the contract matures in the future

Examples of debt securities

• Treasury bills

• Bank bills

• Zero coupon bonds

Differences between treasury/bank bills and zero coupon bonds

Return earned

(Face value - price paid) / price paid

What are some characteristics of zero coupon bonds?

• Mature well into the future

• No other payments made to investors as they receive a lump sum amount in the future

What is the relationship between prices and market yields?

What do valuing coupon paying debt securities require calculating?

• The present value of the face value at maturity

• The promised periodic coupon payments which are stated as a percentage of the face value

What are the two most common types of equity securities?

• Preference shares

• Ordinary shares

How are equity securities different to debt securities?

There are no obligations for payments to be made to shareholders

For equity securities, who receives dividends first? Preference shareholders or ordinary shares?

Preference shareholders

Effective annual interest rate

What is the relationship between r_e and r?

• If interest is calculated once a year (m = 1), r_e = r

• In all other cases, r_e > r

Effective interest rate with continuous compounding

Present value of a single cash flow where the stated annual interest rate r is compounded m times a year

Future value of a single cash flow where the stated annual interest rate r is compounded m times a year

Present value of an ordinary annual annuity over n years

Future value of an ordinary annual annuity over n years