TVM - Finance pt 1

Time Value of Money (TVM) Concepts Overview

  • Importance of understanding Time Value of Money (TVM) in financial decisions.

TVM Overview

  • Lecture slides available in the course modules.

  • TVM quiz:

    • Unlimited attempts for students.

    • Strive for a perfect score, as each quiz is unique and covers different TVM problems.

    • The quiz is accessible during the semester, but closed during exams.

Fundamental Money Principles

  • Time Value of Money Principle:

    • A dollar today is worth more than a dollar received in the future.

  • Compounding Interest Principle:

    • The "magical power of compounding interest" is considered one of the most valuable lessons a student can learn in college.

  • Albert Einstein Quote:

    • "The most powerful force in the Universe is compound interest."

Mastering Time Value of Money Concepts

  • Corporations and individuals must apply TVM concepts to make informed financial decisions. Key questions include:

    • How much money will I have at retirement?

    • How long will my money last in retirement?

    • Should I refinance my mortgage?

    • Should I take a cash rebate on my car or choose 0% financing?

    • Should I prepay something for a discount?

    • What is the real rate of return on my investments?

Opportunity Cost

  • Understanding that receiving $1 today is more valuable than receiving it in the future, due to opportunity costs.

  • Opportunity Cost Definition: The interest that could be earned if the money were received earlier.

  • Note that the terms: interest rate, discount rate, and opportunity cost are interchangeable.

Measuring Opportunity Cost

  • If opportunity cost can be measured, it allows us to:

    • Translate $1 today into its future equivalent via compounding.

    • Translate $1 in the future into its present equivalent via discounting.

Future Value Concepts

Future Value - Single Sums Example 1

  • Problem Statement: If you deposit $100 in an account earning 6%, how much will you have after 1 year?

  • Calculator Solution Setup:

    • P/Y = 1

    • I = 6

    • N = 1

    • PV = -100

    • FV = ? (to be calculated)

  • Final Calculation Result: FV = $106.

Future Value - Single Sums Example 2

  • Problem Statement: If you deposit $100 in an account earning 6%, how much will you have after 5 years?

  • Calculator Solution Setup:

    • P/Y = 1

    • I = 6

    • N = 5

    • PV = -100

    • FV = ? (to be calculated)

  • Final Calculation Result: FV = $133.82.

Positive and Negative Numbers in Cash Flow

  • Concept of cash flows:

    • If PV is negative, FV will be positive, or vice versa.

    • NPV (Net Present Value) is the exception where negative values may indicate losses.

    • Cash flows illustrated through an example: Giving $100 today (cash out, negative; PV) results in receiving $106 back in the future (cash in, positive; FV).

Future Value Calculation Methodology

  • Formula Overview:

    • The future value is determined by multiplying the principal by

    • $(1 + r/n)^{nt}$ where

    • $r$ = annual interest rate

    • $n$ = number of compounding periods per year

    • $t$ = number of years.

  • Example with Large Investments:

    • Warren Buffett Example:

    • Net worth increase primarily credited to compounding effect over time.

    • Starting at a young age, investing for decades leads to exponential growth.

    • By age 50, his net worth was approximately $300 million, with $140.8 billion earned post-50 by time and compounding.

Periodic Interest Rates Explained

  • Definition of Periodic Interest Rate: The annual rate of interest divided by the number of periods it’s compounded during the year.

  • For example:

    • $1,000 at 10% compounded annually:

    • Periodic rate = 10%/1 = 10% (equals $100/year)

    • $1,000 at 10% compounded quarterly:

    • Periodic rate = 10%/4 = 2.5% (equals $25/quarter)

Future Value with Different Compounding Frequencies

Quarterly Compounding Example

  • Problem Statement: If you deposit $100 in an account at 6% interest compounded quarterly, what would be the balance after 5 years?

  • Calculator Solution Setup:

    • P/Y = 4

    • I = 6

    • N = 20

    • PV = -100

    • Calculated FV Result: $134.69.

Monthly Compounding Example

  • Problem Statement: If you deposit $100 in an account at 6% interest compounded monthly, what would be the balance after 5 years?

  • Calculator Solution Setup:

    • P/Y = 12

    • I = 6

    • N = 60

    • PV = -100

    • Calculated FV Result: $134.89.