Finance Chapter 5: Time Value of Money

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Questions and Answers

What is the maximum total fee a borrower would accumulate when rolling over an initial $100 payday loan four times over a 10-week period?

$50

$75 (correct)

$150

$100

What is the annualized nominal rate derived from a 2-week payday loan rate of 15%?

195%

420%

750%

391% (correct)

What is the necessary annual cash payment to accumulate a future value of $30,000 in 5 years at an annual interest rate of 6%?

$5,000 (correct)

$6,000

$4,500

$6,500

What is the primary purpose of a loan amortization schedule?

Illustrate the breakdown of payments to interest and principal (D) Signup and view all the answers

What is the present value of $1,700 to be received in 8 years with an opportunity cost of 8%?

$918.46 (A) Signup and view all the answers

If a loan of $6,000 is borrowed at 10% over 4 years, what is the componenet that must be calculated to determine the size of payments?

Present value of future payments (B) Signup and view all the answers

How does rolling over a payday loan affect total fees paid by the borrower?

It increases total fees (D) Signup and view all the answers

In what manner does an annuity due differ from an ordinary annuity?

An annuity due has cash flows at the beginning of each period. (D) Signup and view all the answers

What does loan amortization primarily involve?

Finding equal periodic loan payments (B) Signup and view all the answers

What impact does compounding interest for an additional period have on an annuity due compared to an ordinary annuity?

An annuity due will always be greater than an ordinary annuity. (A) Signup and view all the answers

Which equation can be used to find the future value of an ordinary annuity?

FV = CF × [(1 + r)^n - 1] / r (A) Signup and view all the answers

Which factor is important when calculating the effective annual interest rate for a payday loan?

The frequency of fee charges (B) Signup and view all the answers

If Fran Abrams chooses an ordinary annuity earning 7% annually, what will be the method to calculate her future savings?

Use the future value formula for ordinary annuities. (B) Signup and view all the answers

How are cash flows defined in the context of annuities?

They are uniform periodic payments over a specified duration. (C) Signup and view all the answers

Which statement accurately reflects the nature of annuities?

Both inflows and outflows can be considered annuities. (A) Signup and view all the answers

What is the total cash flow for both annuity A and annuity B in Fran Abrams' example?

$5,000 (A) Signup and view all the answers

What does the variable FVn represent in the future value equation?

Future value at the end of period n (D) Signup and view all the answers

If Jane Farber invests $800 at an interest rate of 6%, what will be the future value after 5 years?

$1,070.58 (D) Signup and view all the answers

What is the primary principle behind present value?

A dollar today is worth more than a dollar tomorrow. (C) Signup and view all the answers

In the calculation of present value, what role does the discount rate play?

It reflects the opportunity cost of capital. (D) Signup and view all the answers

How is present value (PV) calculated using the future value (FVn)?

PV = FVn / (1 + r) (B) Signup and view all the answers

What can be inferred if an amount invested today earns no interest over time?

The present value will equal the future value. (C) Signup and view all the answers

Which of the following describes the process of discounting cash flows?

Finding the present values of future amounts. (C) Signup and view all the answers

If Paul Shorter can earn an interest rate of 6%, what is the maximum he should pay now for a future amount of $300?

$283.02 (B) Signup and view all the answers

What is the main advantage of compounding interest more frequently than annually?

It results in a higher effective interest rate. (D) Signup and view all the answers

If Frey Company expects an investment return of at least 9%, what should it consider when determining how much to pay for the cash flow opportunity?

The present value of the cash flows discounted at 9%. (A) Signup and view all the answers

How does earning interest on interest impact the effective interest rate?

It raises the effective interest rate. (C) Signup and view all the answers

What is considered a mixed stream of cash flows?

A series of varying payments received at different times. (C) Signup and view all the answers

What would be the effect of a higher discount rate on the present value of future cash flows?

It would decrease the present value significantly. (C) Signup and view all the answers

When is the best time to invest cash flows to maximize future value?

Immediately upon receiving the cash flows. (B) Signup and view all the answers

What is the relationship between nominal interest rate and effective interest rate when compounding occurs more frequently than annually?

The effective rate is always higher than the nominal rate. (A) Signup and view all the answers

If Shrell Industries receives cash flows over 5 years and invests them immediately at 8%, what method can be used to determine how much they will accumulate?

Using the future value formula for mixed streams. (B) Signup and view all the answers

What happens to a borrower with an adjustable-rate mortgage (ARM) when home prices begin to decline?

They may not have refinancing options available. (B) Signup and view all the answers

What is the formula used to calculate the compound annual rate of return?

r = (Investment Value / Initial Value)^(1/n) - 1 (B) Signup and view all the answers

How much is Ray Noble's investment worth after four years if it was initially purchased for $1,250?

$1,520 (A) Signup and view all the answers

If Jan Jacobs borrows $2,000 and pays back $514.14 annually for 5 years, what method is being used to repay the loan?

Equal end-of-year payments (B) Signup and view all the answers

How much equity can help a homeowner reduce their mortgage payment?

Equity can be used for refinancing to adjust payments. (D) Signup and view all the answers

What percentage rate did Ray earn annually on his investment worth $1,520 after 4 years from an initial amount of $1,250?

5.01% (D) Signup and view all the answers

What occurred in 2006 that significantly impacted subprime mortgage borrowers?

Adjustable ARMs were reset to higher rates. (B) Signup and view all the answers

Which factor contributed to lenders tightening lending standards after 2006?

Rising default rates among borrowers. (D) Signup and view all the answers

What is the method used to find the periodic deposit required to accumulate a given future sum?

Solving for the future value of an annuity (B) Signup and view all the answers

Which method is appropriate for amortizing a loan into equal periodic payments?

Solving the present value of an annuity (C) Signup and view all the answers

How can interest or growth rates be determined in financial calculations?

By finding the unknown interest rate in the present value equation (D) Signup and view all the answers

Which equation is used to estimate an unknown number of periods in a financial scenario?

Present value of a single amount or annuity equation (B) Signup and view all the answers

In loan amortization, which aspect is crucial to determine?

The periodic payment amount (A) Signup and view all the answers

What is typically not considered when estimating an unknown interest rate in financial calculations?

The future value of an annuity (D) Signup and view all the answers

What does the procedure of finding the future value of an annuity primarily assist with?

Determining periodic savings needed (B) Signup and view all the answers

Which of these statements accurately describes loan amortization?

It breaks a loan into equal periodic payments (B) Signup and view all the answers

Study Notes

Chapter 5: Time Value of Money

This chapter covers the fundamental concepts of time value in finance, including the use of computational tools and the basic patterns of cash flow.
Learning Goals (LG1-LG6): LG1 discusses the role of time value, computational tools, and cash flow patterns. LG2 explains future value and present value calculations for single amounts and their relationship. LG3 calculates future and present values of ordinary annuities and annuities due, and the present value of a perpetuity. LG4 calculates the future and present value of a mixed cash flow stream. LG5 explores the effect of compounding interest more frequently than annually on future value and the effective annual interest rate. LG6 describes methods for determining deposits needed to accumulate a future sum, loan amortization, finding interest or growth rates, and calculating unknown periods.
Future Value vs. Present Value: The text introduces the concept of valuing future cash flows in today's dollars (present value) versus today's money in future terms (future value). A timeline example of a company's cash flow is given.
Computational Tools: Financial calculators and spreadsheets offer built-in time value functions. Calculator keys and spreadsheet functions are described. Cash flows are represented as either positive (inflows) or negative (outflows).
Cash Flow Patterns: Three key patterns—single amount, annuities (level periodic cash flows), and mixed cash flows are examined.
Future Value of a Single Amount: Defined as the value at a future date of a sum invested today, earning interest over a specific period. The concept of compound interest is explored. Principal is the base amount on which interest is calculated, while a detailed example of Fred Moreno's account is provided. A general equation for the future value of a single amount is also presented for understanding.
Present Value of a Single Amount: The current value of a future amount; the amount required today to generate a given future value at a predetermined rate of interest. A personal finance example of calculating this is given; also, a personal finance example showing how computer programming and calculator keys and functions can be used to find present values is provided. A general formula is also shown.
Annuities: This section details ordinary annuities (payments at the end of each period) and annuity due (payments at the beginning). Examples, calculations, and the differences between ordinary and annuity due payments are discussed.
Finding the Future Value of an Ordinary Annuity: A formula is given to calculate the future value of an ordinary annuity, including an example. The formula for calculating the future value of an ordinary annuity is presented. Examples of problems are given to show how to calculate the future value of an annuity.
Finding the Present Value of an Ordinary Annuity: The formula to calculate the present value of an ordinary annuity is provided, along with examples.
Finding the Future Value of an Annuity Due: A formula to calculate the future value of an annuity due is presented and examples are given.
Finding the Present Value of an Annuity Due: The formula for calculating the present value of an annuity due is included, along with examples.
Perpetuities: defined as an annuity with an infinite life. The formula to calculate the present value of a perpetuity is presented. Example problems are provided to illustrate their use.
Future Value of a Mixed Stream: A method for calculating the future value of a mixed cash flow stream is demonstrated.
Finding the Present Value of a Mixed Stream: A method for calculating the present value of a mixed cash flow stream.
Compounding Interest More Frequently Than Annually: This section explains the effective annual rate (EAR) and how it differs from the stated/nominal annual rate. Specific examples, including semiannual and quarterly compounding, are given.
Continuous Compounding: The continuous compounding formula is presented, along with an example problem.
Nominal and Effective Annual Rates of Interest: Definitions and the formula for calculating the effective annual rate are provided.
Special Applications: Deposits Needed to Accumulate a Future Sum, Loan Amortization, Finding Interest or Growth Rates, Finding an Unknown Number of Periods: Formulas and examples for each are described.
Chapter Resources: MyFinanceLab with chapter cases, group exercises, and critical thinking problems.
Integrative Case: Track Software, Inc. (Tables 1-5, and related questions): The financial statements for Track Software are presented, and the corresponding analysis and practical applications of financial goals are emphasized. A case study.

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Description

This chapter explores the fundamental concepts of the time value of money in finance. It covers essential calculations of future and present values as well as the relationship between cash flow patterns and computational tools. Learn about annuities, perpetuities, and the effects of compounding interest on financial decision-making.