Loose Leaf for Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Loose Leaf for Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
11th Edition
ISBN: 9781259709685
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe
Publisher: McGraw-Hill Education
Question
Chapter 4, Problem 1CQ
Summary Introduction

To discuss: The effect of increase in the length or period of investment on the future and present values.

Introduction:

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. Present value refers to the current worth of the future cash inflows after discounting with a discount rate.

Expert Solution & Answer
Check Mark

Explanation of Solution

Future value:

If the length of the period of investment increases, then the future value also increases. This is because the investment has a greater time to multiply. The following examples (1 and 2) justify this claim. The future value is higher when the investment period is 20 years, and the future value is lower when the investment period is 10 years.

Example 1:

The present value of a bond is $50, and the rate of return is 10 percent. Determine the future value of the bond if the investment period is 10 years.

The formula to calculate the future value:

FV=PV×(1+r)t

Here,

“FV” refers to the future value or the current market value,

 “PV” refers to the present value,

“r” refers to the simple rate of interest,

“t” refers to the number of years or periods of investment.

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.10)10=$50×2.5937=$129.6871

Hence, the future value of the investment after 10 years is $129.6871.

Example 2:

The present value of a bond is $50, and the rate of return is 10 percent. Determine the future value of the bond if the investment period is 20 years.

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.10)20=$50×6.7275=$336.3750

Hence, the future value of the investment after 20 years is $336.3750.

Present value:

If the length of the period of the investment increases, then the present value of the investment decreases. This is because a lesser present value of investment is sufficient to obtain higher future values; if the investment period is longer, a higher present value of investment is necessary to obtain higher future values in a short period.

The following examples (3 and 4) justify this claim. The present value is lower ($74.3218) when the period of investment is 20 years, and the present value is higher ($192.7716) when the period of investment is 10 years. Hence, the present value of the investment decreases as the length of the investment increases.

The formula to calculate the present value:

PV=FV(1+r)t

Here,

“PV” refers to the present value of future cash flow,

“FV” refers to the cash flow,

“r” refers to the discount rate,

“t” refers to the number of years or periods of investment.

Example 3:

The future value of a bond is $500, and the discount rate is 10 percent. Determine the present value of the bond if the investment period is 10 years.

Compute the present value:

PV=FV(1+r)t=$500(1+0.10)10=$5002.5937=$192.7716

Hence, the present value of investment is $192.7716.

Example 4:

The future value of a bond is $500, and the discount rate is 10 percent. Determine the present value of the bond if the investment period is 20 years.

Compute the present value:

PV=FV(1+r)t=$500(1+0.10)20=$5006.7275=$74.3218

Hence, the present value of the investment is $74.3218.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
As you increase the length of time involved, what happens to future values? What happens to present values?
Match each sentence to the correct concept. a)  The amount an investment is worth after one or more time periods is referred to as _______________ b)  The process of finding the present value of some future amount is called _________________.
What will an investment or a series of investment be worth after a period of time?

Chapter 4 Solutions

Loose Leaf for Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)

Ch. 4 - Simple Interest versus Compound Interest First...Ch. 4 - Prob. 2QPCh. 4 - Prob. 3QPCh. 4 - Prob. 4QPCh. 4 - Prob. 5QPCh. 4 - Prob. 6QPCh. 4 - Calculating Present Values Imprudential, Inc., has...Ch. 4 - Calculating Rates of Return Although appealing to...Ch. 4 - Perpetuities An investor purchasing a British...Ch. 4 - Prob. 10QPCh. 4 - Prob. 11QPCh. 4 - Prob. 12QPCh. 4 - Calculating Annuity Present Value An investment...Ch. 4 - Calculating Perpetuity Values The Perpetual Life...Ch. 4 - Calculating EAR Find the EAR in each of the...Ch. 4 - Calculating APR Find the APR, in each of the...Ch. 4 - Calculating EAR First National Bank charges 10.3...Ch. 4 - Interest Rates Well-known financial writer Andrew...Ch. 4 - Calculating Number of Periods One of your...Ch. 4 - Prob. 20QPCh. 4 - Prob. 21QPCh. 4 - Simple Interest versus Compound Interest First...Ch. 4 - Calculating Annuities You are planning to save for...Ch. 4 - Prob. 24QPCh. 4 - Prob. 25QPCh. 4 - Prob. 26QPCh. 4 - Prob. 27QPCh. 4 - Annuity Present Values What is the present value...Ch. 4 - Annuity Present Values What is the value today of...Ch. 4 - Balloon Payments Audrey Sanborn has just arranged...Ch. 4 - Prob. 31QPCh. 4 - Prob. 32QPCh. 4 - Growing Annuity Southern California Publishing...Ch. 4 - Growing Annuity Your job pays you only once a year...Ch. 4 - Prob. 35QPCh. 4 - Prob. 36QPCh. 4 - Prob. 37QPCh. 4 - Calculating Loan Payments You need a 30-year,...Ch. 4 - Prob. 39QPCh. 4 - Calculating Present Values You just won the TVM...Ch. 4 - Prob. 41QPCh. 4 - Prob. 42QPCh. 4 - Prob. 43QPCh. 4 - Prob. 44QPCh. 4 - Prob. 45QPCh. 4 - Prob. 46QPCh. 4 - Prob. 47QPCh. 4 - Prob. 48QPCh. 4 - Prob. 49QPCh. 4 - Prob. 50QPCh. 4 - Calculating Annuities Due You want to lease a set...Ch. 4 - Prob. 52QPCh. 4 - Prob. 53QPCh. 4 - Prob. 54QPCh. 4 - Prob. 55QPCh. 4 - Prob. 56QPCh. 4 - Prob. 57QPCh. 4 - Prob. 58QPCh. 4 - Prob. 59QPCh. 4 - Prob. 60QPCh. 4 - Prob. 61QPCh. 4 - Prob. 62QPCh. 4 - Prob. 63QPCh. 4 - Prob. 64QPCh. 4 - Calculating the Number of Periods Your Christmas...Ch. 4 - Prob. 66QPCh. 4 - Prob. 67QPCh. 4 - Prob. 68QPCh. 4 - Prob. 69QPCh. 4 - Perpetual Cash Flows What is the value of an...Ch. 4 - Prob. 71QPCh. 4 - Prob. 72QPCh. 4 - Prob. 73QPCh. 4 - Prob. 74QPCh. 4 - Rule or 69.3 A corollary to the Rule of 72 is the...Ch. 4 - Prob. 1MCCh. 4 - Prob. 2MCCh. 4 - Prob. 3MCCh. 4 - Prob. 4MCCh. 4 - Prob. 5MCCh. 4 - Prob. 6MC
Knowledge Booster
Similar questions
    • SEE MORE QUESTIONS
    Recommended textbooks for you
  • EBK CONTEMPORARY FINANCIAL MANAGEMENT
    Finance
    ISBN:9781337514835
    Author:MOYER
    Publisher:CENGAGE LEARNING - CONSIGNMENT
  • EBK CONTEMPORARY FINANCIAL MANAGEMENT
    Finance
    ISBN:9781337514835
    Author:MOYER
    Publisher:CENGAGE LEARNING - CONSIGNMENT