Time Value of Money Introduction

Time Value of MoneyIntroduction

TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

TVM Questions What will my investment grow to? How much do I need today? How fast must my investment grow? How long will it take?

Compare and Contrast TVM 4.98% 5.29% 3.14% 2.88%

TVM Basic Concepts Simple vs. Compound Interest Simple Interest = interest earned only on principal (amount loaned) Compound Interest = interest earned on principal and any unpaid interest earned in an earlier time period

Simple Interest Calculation

Interest Example Principal $1,000 Interest Rate 10% Term 5 years

Interest Example FV = (1,000 x .10 x 5) + 1,000 FV = 500 +1,000 FV = 1,500

Simple Interest Example Principal $1,000 Total Interest 500 Ending Balance $1,500

Compound Interest Calculation

Compound Interest Example

Compound Interest Example Principal $1,000 Total Interest Rate 611 Ending Balance $1,611

Time Value of Money

Calculator Tips Set Calculator to 4 decimal points Set P/Yr to 1 and do not change Clear calculator before calculation Use recommended format Learn to use special features Read carefully Know the concepts of TVM

TVM Concepts Use a time line Use + or - to indicate cash flow Periodic Cash flows can be at Beginning or End of Period Calculators use Percentages Excel uses decimals

Lump Sum Single Payment At time zero Present Value OR Single Payment At end of time Future Value Periodic Payment Ordinary Annuity Pmt at end of periods For life of investment Annuity Due Pmt at beg. of periods For life of investment PMT Lump Sum vs. Periodic Pmts

Annuities Must be Equal Amounts Occurring in every compounding period Ordinary Annuity – End of Period Annuity Due – Beginning of Period

Annuity?

Lump Sum & Periodic Payment Combination Single Payment With periodic payments for life of investment PV & PMT

Recommended Structure

Future Value of Lump Sum
If you invest $1,000 in a savings account earning 10% compounded annually, how much will you have after 5 years?

If you invest $10,000 in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 50 years?

Future Value

Future Value of an Annuity
If you invest $10,000 at the end of each year in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 5 years?

If you invest $10,000 at the beginning of each year in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 5 years?

Ordinary Annuity

Annuity Due

Future Value of a Combination
If you invest $10,000 today and $1,000 at the end of each year in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 5 years?

Future Value of a Combination

Future Value

Combination Investment

Annual Rate of Return
TVM can also solve for the rate of return required for a PV to reach a FV in n years.

What rate of return is required for $10,000 to grow to $16,000 in 5 years?

If you invest $2,000 at the end of each year for 5 years, what rate of return must your investment earn for you to have $16,000 at the end of that period?

If you invest $10,000 today and $500 at the end of each year for the next 5 years, what rate of return must you earn to have $16,000 at the end of that period?

Number of Periods
TVM can also solve for the holding period required for a PV, a series of Payments or a combination of PV and Payments to reach a FV given a specific rate of return

Number of Periods
How long will it take for a $10,000 investment to grow to $24,000 if it earns 11.25% compounded annually?

Number of Periods

Number of Periods
If you deposit $3,000 at the beginning of each year in a savings account earning 9.75%, how long will it take for you to save for a $20,000 down payment for a house?

Number of Periods

Present Value
TVM can also solve for the price you would pay for a FV, a series of Payments, or a combination of a series of Payments and a FV given a specific rate of return and holding period.

Present Value of a Future Amount
What would you pay for the right to collect $8,000 in 7 years, if your required return is 8.75%?

Present Value of a Future Amount

Present Value of Periodic Payments
What would you pay for the right to collect $8,000 at the beginning of each year for 7 years, if your required return is 8.75%?

Present Value of Periodic Payment

Present Value of a Combination
What would you pay for the right to collect $800 at the end of each year for 7 years and an additional $10,000 at the end of the period, if your required return is 7.25%?

Present Value of a Combination

Time Value of Money
Compounding Periods Shorter than One Year

Compounding Periods Cash Flows are often more frequent than annually Monthly, quarterly, semi-annually If Compound periods < annual Effective Interest Rate is higher FV is higher and PV is lower

Compound Interest Formula with Compounding Periods less than 1 Year Where m = the number of compounding periods within the year.

Adjustments for Compounding Periods < Annual Compounding Periods = m Divide Annual rate by m i/m Multiply Years by m n x m Input i/m for I/Y Input (n x m) for N

If you invest $6,000 in a savings account earning 10% compounded quarterly, how much will you have after 5 years?

If you invest $1,000 in a savings account earning 10% compounded daily, how much will you have after 5 years?

If you invest $1,000 at the end of each month in a mutual fund that is expected to earn a 12% after-tax return, how much will you have at the end of 5 years?

If you invest $1,000 at the beginning of each month in a mutual fund that is expected to earn a 12% after-tax return, how much will you have at the end of 5 years?

If you invest $2,000 at the end of each quarter for 5 years, what rate of return must your investment earn for you to have $60,000 at the end of that period?

If you invest $10,000 today and $500 at the end of each month for the next 5 years, what rate of return must you earn to have $60,000 at the end of that period?

Number of Periods
If you deposit $300 at the beginning of each month in a savings account earning 9.75%, how long will it take for you to save for a $20,000 down payment for a house?

Number of Periods

Uneven Cash Flows How do you calculate Present Value when your required return is 9.0% and you expect to receive the following cash flows: Year 1 2,000 Year 2 3,000 Year 5 1,000

Uneven Cash Flows Alternative One – TheHardWay Draw a Time Line Calculate the PV of each cash flow Total the Present Values

Uneven Cash Flows

Uneven Cash Flows Alternative Two – Use the CF Register Draw Time Line Input Cash Flows into CF Register Go to NPV Register Input Rate of Return Compute NPV

Uneven Cash Flows Example 1 – Alternative Two Draw Time Line Push CF button Clear CF register 2nd CLR Work Input Cash Flows

Cash Flow Register Inputs CF0 = Investment, Price, Cost at Time 0 We are solving for PV so CF0 should be 0 Since CF0 already = 0,  C01 = Cash Flow at the end of Period 1 F01 = Frequency of C01 The number of times that C01 occurred consecutively

Uneven Cash Flows Example 1 Draw Time Line Clear the CF Register Input Cash Flows CF0 = 0,  C01 = 2,000; F01 = 1,  C02 = 3,000; F02 =1,  C03 = 0; F03 = 2,  C04 = 1,000; F04 = 1, 

Uneven Cash Flows Example 1 Check Inputs Go To NPV Register Input I 9 ENTER,  CPT NPV = 5,009.83

Uneven Cash Flows Example 2
What would you be willing to pay for a real estate investment that has the following expected cash flows: Yr. 1 $500, Yrs. 2-6 $1,000, Yr. 7-10 $1,500, and Yr. 11 $30,000? Assume your required return for this type of investment is 17.0%.

Uneven Cash Flows Example 2 Draw Time Line Input Cash Flows CF0 = 0 C01 = 500; F01 = 1 C02 = 1,000; F02 = 5 C03 = 1,500; F03 = 4 C04 = 30,000; F04 = 1

Uneven Cash Flows Example 2 Check your Inputs Go to “NPV” Register Enter I = 17.0;  Press “CPT” NPV = ?

Uneven Cash Flows Example 2 NPV = 10,100.25

Uneven Cash Flows The CF Register can also be used to find the rate of return associated with uneven cash flows. This cannot be done easily any other way.

Uneven Cash Flows Inputs CF Register Steps are the same Go to IRR Register CPT IRR IRR = the Internal Rate of Return IRR = the rate of return on the investment

Effective Interest Rate Calculation

Effective Interest Rate Calculation
The annual rate of return actually earned when compounding or payment periods are less than 1 year.

Effective Interest Rate Nominal rate = i The nominal rate is the rate “named” in the information. “The credit card rate is for 18.0% compounded monthly.” 18.0% is the nominal rate

EIR Calculations
What is the Effective Interest Rate for a credit card with an 18% nominal interest rate if the card is not paid off each month?

Effective Interest Rate with Compounding Periods < 1 Year Where m = the number of compounding periods within the year.

EIR Calculations

EIR CALCULATIONS
Use “I Conv” Register for easy Effective Interest Rate calculations.

I Conv Register Steps 2nd I Conv Input Nominal Rate, ENTER Arrow Down Twice Input C/Y (Compounding Periods per Year) Arrow Up CPT EFF (Effective Interest Rate)

Time Value of Money Introduction