Time value of Money

By the end of this class you should …

Understand basic time value of money concepts– Be able to apply concepts to:

» Determine the present value of a future cash flow

» Determine the present value of an annuity

» infer effective interest rates

Time Value of Money - Examples

Would you rather have $100 today or $100 in one year?

Would you rather have $100 today or $120 in one year?

What’s the deal?

Time value of Money- Examples

How much do I need to save for my retirement?

I win the lottery and want to spend it all, but still pay for my kids’ education. How much do I spend?

I win the texas lottery ($1,000,000). Can I exchange the winning ticket for a $1,000,000 home?– What’s the deal?

Time Value of Money

Is this just a make-work program for accountants?

Where, if anywhere, are present values used in accounting? (specially Financial Accounting)

Vocabulary

PV: Present Value FV: Future Value Pmt: Payment n: Number of

“periods” r: Discount rate,

Borrowing rate

Basics of Present Values: single payments, compound interest

FV = PV (1+ r) - for one period FV = PV(1+r)(1+r)

– for two periods FV = PV(1+r)n

– for n periods PV = FV(1+r)-n

Note: the discount rate, r, must be on the same basis as the periods, n. For example, if the periods are years, the rate must be annual. If the periods are quarters, the rate

must be in effective quarterly rate.

More Vocabulary

Stated Rate = Coupon Rate = Nominal Rate

Effective Rate = rate that considers compounding

APR = Annual Percentage Rate = Annualized Effective rate

Real Rate = Nominal rate - inflation Principal = Face Value = Par Value Coupon Payment = Interest Payment

Basics of Present Value: Streams of Payments

Example: An insurance contract (annuity) will pay you $100,000 per year for the next 20 years. How much will the contract cost?

PVannuity = Payment ( PV annuity factor , r = ?, n = ?)

This factor is simply the sum of the series of single payment factors

Annuity in Arrears: first payment at time 1 ( also known as an Ordinary annuity)

Annuity Due: first payment at time 0 – use calculator

Maya --- ROI

September 1, 1997 you buy 100 shares o Maya, Inc., at $50/share. You want to earn 12% compounded annually

What is the minimum price that would achieve this by August 31, 1997?

What is the minimum price that would achieve this by August 31, 1998?

What is the minimum price that would achieve this by August 31, 1999 ?

On August 31, 1999 you sell the shares for $6,000. What annual compound rate of return did you earn?

Maya --- ROI

You want to earn a 12% rate of return compounded annually. How much would you pay for:

1) 100 shares of Maya that you expect to sell for $5,500 in one year?

2) 100 shares of Maya that you expect to sell for $5,500 in two years?

3) 100 shares of Maya that you expect to sell for $5,500 in five years and which pay dividends of $5.00 per share at the end

of each year?

Rite-Aid -- Lease or Buy?

Buy a computer for $15,000 or Lease it for $305 per month for 36

months ( first and last payment due up front), $8,500 purchase option at the end of the three years

Need computer for six years, so you would exercise the option

Hydron’s annual cost of capital is 8.5% compounded monthly

What qualitative factors need to be considered before making a final decision?

Take-Home Point

Time value of money is an important concept and is used ( in conjunction with the principle of objectivity) in many places in the F/S

You should understand the vocabulary of “present values”

You should be able to compute present and future values of single payments and streams of payments

You should understand the decision rules investors and managers use when they apply time of money techniques

Next time

Understanding basic valuation methods and their relationships to the F/S– Apply the methods to Maple Leaf

Gardens.