COMM 300: Time value of money

From BluWiki

Compounding

Moving money forward

Simple interest

NOT the normal way we compute interest. Interest is earned on PRINCIPAL only.

Compound interest

Interst is earned on principal AND interest already earned.

Discounting

Discounting money backward

Cash flow diagrams

Downward facing arrows represent a cash outflow, upward facing arrows reperesent upward facing arrows.

Future value of a single sum

FVn = PV (1+k)^n

(1+k)^n = FVIF(k%,n)

Present value of a future sum

PV = FV / (1+k)^n

Types of cash flows

Annuities

Annuity: series of equal payments, equally spaced, occuring every period.

Ordinary annuity

Payments occur in end of period

Annuity due

Payments occur in beginning of period

NOTE: He gave the formulas to calculate the future values of annuities - get it off the internet

Perpetuity

An infinite series of equal payments, equally spaced, occurring every period

• PV= Periodic Payment / k (note, this is the NOMINAL (I think? Opportunity cost AND inflation) rate of interest in little numbers)
• (note: the PV create exactly the periodic payment in interest every year...)

Interest rates

• Real rate of interest: does not include inflation, only represents opportuntiy cost.
• Nominal rate of interest: includes inflation and opportunity cost.
• Effective rate: what the nominal rate would be if you compounded only once / period
• Effective annual rate (EAR): what the effective rate would be if compounded annually
• Annual perecnetage rate (APR): A legal implementation of the EAR.

Check out how to calculate effective annual rates (wrote it down on the back of assignment 4)

Rule of 72

Takes 72/k years to double money. Therefore it takes 7.2 years to double your money at 10% interest.

Bonds

• Promissory notes requiring fixed interest payments and prinicpal repayment at maturity
• "level annuity with a tial"
• Issued by coprorations, governments, & municipalities.

Terminology

• Par or face value
  • Value of repayment
• Maturity date
  • Date bond matures
• Coupon rate (eg 10%)
• Coupon payment
  • coupon rate * face value of bond

Indenture

• what you can and cannot do with the bond

• Restrictive covenants
  • what you / the company can & cannot do
• Trustee
  • those who represent the bond holders.

Bond pricing

• See notes for bond pricing

Bond yieds

• Look this up too IMPORTANT

Semiannual compounding

Double payments, half coupon rate & half yield rate.

Common stock

• Market price
• Book value
• Liquidation value
• Relative valuation
  • P/E ratio
  • Market/Book ratio
• Dividend growth model

Dividend growth model

• Assumptions:
  • Dividends are expected to continue ad infinitum (for ever)
  • Growth rate, g, is known & constant
  • Required rate of return, k sub s, is greater than g.

Using a financial calculator

• Notes:
  • Make sure (by pressing Orange, C ALL) that you are at 1 P_YR (one payment / year)
  • Make sure (by pressing Orange, BEG/END) that you are in END mode
  • Make sure you're at 4 decimal places by placing Orange, DISP, 4.
  • Use +/- key to change sign of numbers