1. Chapter 11 Introduction to Finance and Review of Financial Mathematics
11.2 The Time Value of Money
11.3 Simple Interest
11.4 Compound Interest
11.5 Annuities
11.6 Comparison rates

2. Introduction to Finance
Finance is the study of how financial markets work and how companies make decisions in order to maximise shareholder wealth. The three main decisions that companies face are:
The investment decision
The finance decision
The dividend decision

3. The Investment Decision
The question of how funds should be used in productive activities. The objective is to generate future cash flows or to provide a return for investors.

4. The Finance Decision
The decision of how to finance investment projects with capital. The most common types of finance are selling shares (equity) or bonds (debt).

5. The Dividend Decision
The decision of what to do with a businesses profit. Firms can either pay out the profit to shareholders in the form of dividends, or inject the profit back into the business to generate more profit in the future.

6. Assets
An asset is anything that can be owned or controlled that has positive economic value.
Tangible assets are those that are actual items like machinery or a factory, something that is physical and measurable.
Intangible assets cannot be seen, touched or measured. Examples are patents, copyrights, an ability or a skill.

7. Intellectual Property
Intellectual property refers to thought creations or ideas which are assigned ownership to their creators and given legal rights over ownership.

8. The Time Value of Money
A dollar today is worth more than a dollar tomorrow. A dollar today can be invested at an interest rate so that in the future that dollar will be worth one dollar plus some interest. See full explanation and example pg

9. Simple Interest
When an initial amount (the principle) is invested under simple interest, interest is paid only on the principle, so the amount of interest paid each period does not vary.
Future value under simple interest:
FV = PV(1+rT)
Where:
FV = future value
PV = present value
r = interest rate in the market
T = the number of periods
See example pg. 407

10. Present Value with Simple Interest
The value of a future cash flow in today’s terms.
Given the future value of an investment and the simple interest rate we can discount a cash flow back to its present value.
PV = FV__
(1 + rT)
Where:
FV = future value
PV = present value
r = interest rate in the market
T = the number of periods
See example pg. 408

11. Compound Interest
Compound interest differs from simple interest because interest is paid both on the original investment and on the previous interest earned.
The amount of interest each period will grow larger and larger as time goes on.

12. Future value with Compound Interest
FV = PV (1 + r)n
Where:
PV = Present value or principal
r = Compound interest rate per period
n = Number of compound periods
FV = Accumulated sum or future value
See example pg. 386

13. Present Value With Compound Interest
PV = FV
(1+r)n
See example pg. 387

14. The Effective Interest Rate
Used to express interest rates with differing compound periods as equivalent rates with annual compounding.
Effective interest rate: e = ( 1 + r /m)m – 1
e = effective interest rate
m = number of periods
r = nominal annual interest rate
See example pg. 390

15. Annuities PV = a [ 1 – (1 + r) –n ] r
An annuity is a series of cash flows of equal size made at regular, equal time intervals.
Present value of annuities:
PV = a [ 1 – (1 + r) –n ] r
Where:
a = regular cash flow amount
r = interest rate
n = number of periods
See example pg. 391

16. Future Value of Annuities
FV = a [ (1 + r) n - 1 ] r
See example pg . 392

17. Comparison Rates
Consumers shopping for home loans want to compare different home loans from different banks.
A comparison rate is a standardised rate that helps consumers compare home loans.
Comparison rates take into account:
The amount of the loan
The term of the loan
The repayment frequency
The interest rate
Fees and charges connected with the loan