Copyright © 2003 Pearson Education, Inc. Slide 4-0 Ch 4, Time Value of Money, Learning Goals 1.Concept of time value of money (TVOM). 2.Calculate for a

Copyright © 2003 Pearson Education, Inc. Slide 4-1

Ch 4, Time Value of Money, Learning Goals

1. Concept of time value of money (TVOM).2. Calculate for a single cash flow, ordinary

annuity, annuity due, mixed cash flow & perpetuity:– PV– FV– Rate of return (or growth rate)– Number of periods

3. Calculate payment for an annuity. 4. Calculate effective annual rate.


The Role of Time Value in Finance

• Many financial decisions involve costs & benefits that

occur over several years.

• Cash flows occurring now are worth ______________

than cash flows occurring in the future; we must adjust

for that difference.

• Time value of money (TVOM) allows comparison of

cash flows from different periods.


Time Value of Money

• Example

• Would it be better for a company to invest $100,000 in a product that would return a total of $200,000 after one year, or one that would return $220,000 after two years?


Simple Interest

• With simple interest, you don’t earn interest on interest.

• Year 1: 5% of $100 = $5 + $100 = $105

• Year 2: 5% of $100 = $5 + $105 = $110

• Year 3: 5% of $100 = $5 + $110 = $115

• Year 4: 5% of $100 = $5 + $115 = $120

• Year 5: 5% of $100 = $5 + $120 = $125


Compound Interest• With compound interest, a depositor earns interest

on interest!

• Year 1: 5% of $100.00 = $5.00 + $100.00 = $105.00

• Year 2: 5% of $105.00 = $5.25 + $105.00 = $110.25

• Year 3: 5% of $110.25 = $5 .51+ $110.25 = $115.76

• Year 4: 5% of $115.76 = $5.79 + $115.76 = $121.55

• Year 5: 5% of $121.55 = $6.08 + $121.55 = $127.63


Computational Aids

• Techniques to solve TVOM problems:

– Algebraically

– TVOM (interest factor) Tables

– Financial Calculators

– Spreadsheets

– “Rule of 72”


Time Value Terms

• PV = present value or beginning amount

• i = interest rate

• FV = future value

• n = number of periods

• Pmt = periodic payment on an annuity

• m = # of times per year interest is compounded


Four Basic Models

• FVn = PV0(1+i)n = PV x (FVIFi,n)

• PV0 = FVn[1/(1+i)n] = FV x (PVIFi,n)

• FVAn = Pmt (1+i) - 1 = Pmt x (FVIFAi,n)

i

• PVA0= Pmt 1 - [1/(1+i)n] = Pmt x (PVIFAi,n) i


Future Value of a Single Amount

• The future value technique uses compounding to find the future value of each cash flow at the end of an investment’s life and then sums these values to find the investment’s future value.

• We speak of compound interest to indicate that the amount of interest earned on a given deposit has become part of the principal at the end of the period.


Present Value of a Single Amount

• Present value is the current dollar value of a future amount of money.

• It is the amount today that must be invested at a given rate to reach a future amount.

• Calculating present value is also known as __________________________.

• The discount rate is often also referred to as the opportunity cost, the discount rate, the required return, or the cost of capital.


Annuities

• Annuities are periodic cash flows of equal size.

• Annuities can be either inflows or outflows.• An ordinary annuity has CFs that occur at

the ____________ of each period.• An annuity due has CFs that occur at the

_____________________ of each period.


Annuities


Present Value of a Mixed Stream


Future Value of a Mixed Stream


Present Value of a Perpetuity

• A perpetuity: a cash flow stream that continues forever

PV = Pmt/i

• For example, how much would I have to deposit today in

order to withdraw $1,000 each year forever if I earn 8%

on my deposit?

PV = $1,000/.08 = $12,500


Compounding Interest More Frequently Than Annually

• Compounding more frequently than once a year results in a ________________ effective interest rate because you are earning on interest on interest more frequently.

• As a result, the effective interest rate is greater than the nominal (annual) interest rate.



(cont.)



(cont.)• A General Equation for Compounding

More Frequently than Annually


EAR = (1 + i/m) m - 1

Nominal & Effective Annual Rates of Interest

• The nominal interest rate is the stated rate of interest charged by a lender or promised by a borrower.

• The effective interest rate is the rate actually paid or earned.

• In general, the effective rate > nominal rate whenever compounding occurs more than once per year


Rule of 72

• The “rule of 72” is a rule of thumb, or approximation technique that can be used for some simple TVOM problems:– An amount invested at rate i will double in

72/i years (n = 72/i) – If an investment doubles in n years, the

rate of return is 72/n (i = 72/n)

Documents

Copyright © 2003 Pearson Education, Inc. Slide 4-0 Ch 4, Time Value of Money, Learning Goals 1.Concept of time value of money (TVOM). 2.Calculate for a