Types of cash flows:

– Lump sum

– Annuity

– Uneven cash flow

Time Line

Time lines show timing of cash flows (Slide 6)

What is the relationship of time and the value of money?

FVN + PV (1+I)N = 0.

There are 4 variables.

If 3 are known, you can (or the calculator will) solve for the 4th.

Financial calculators solve this equation

FV- Lump sum

Finding FVs (moving to the right on a time line) is called compounding (Fomula: Slide 14)

Four Ways to find FV

- Step-by-step approach using time line (as shown in previous slides).
- Solve the equation with a regular calculator (formula approach).
- Use a financial calculator.
- Use a spreadsheet.

Annuity

Ordinary Annuity vs. Annuity Due

Nominal rate

- Stated in contracts, and quoted by banks and brokers.
- Not used in calculations or shown on time lines
- Periods per year (M) must be given.
- Examples:
- > 8%; Quarterly
- > 8%, Daily interest (365 days)

Periodic rate

- IPER = INOM/M, where M is number of

compounding periods per year. M = 4 for quarterly, 12 for monthly, and 360 or 365 for daily compounding. - Used in calculations, shown on time lines. -

Examples:

-> 8% quarterly: IPER = 8%/4 = 2%.

-> 8% daily (365): IPER = 8%/365 = 0.021918%.

The Impact of compounding: Will the FV of a lump sum be larger or smaller if we compound more often, holding the stated I% constant?

LARGER!

If compounding is more frequent than once a year–for example, semiannually, quarterly, or daily–interest is earned on interest more often.

Formula

Slide 44-45

Effective Annual Rate

- The EAR is the annual rate that causes PV to grow to the same FV as under multi- period compounding.
- The effective annual interest rate is calculated by taking the nominal interest rate and adjusting it for the number of compounding periods the financial product will experience in the given period of time

Comparing Rates

- An investment with monthly payments is different from one with quarterly payments. Must put on EFF% basis to compare rates of return. Use EFF% only for comparisons.
- Banks say “interest paid daily.” Same as compounded daily.

Can the effective rate ever be qeual to the nominal rate?

Yes, but only if annual compounding is used, i.e., if M = 1.

If M > 1, EFF% will always be greater than the nominal rate.

When is each rate used?

- Inom :

Written into contracts, quoted by banks and brokers.

Not used in calculations or shown on time lines. - Iper: Used in calculations, shown on time lines.
- EAR Used to compare returns on investmetns with different payments per year. Used for calculations if and only if dealing with annuities where payments don’t mach interest compounding periods

Amortization

Construct an amortization schedule for a $1,000, 10% annual rate loan with 3 equal payments.

Step 1: Find the required payments

Step 2: Find interest charge for Year 1.

Step 3: Find Repayment of principal Year 1.

Step 4: Find ending balance after Year 1.

Amortization tables:

Amortization tables are widely used–for home mortgages, auto loans, business loans, retirement plans, and more. They are very important!

Financial calculators and spreadsheets are great for setting up amortization tables.