   Chapter 5, Problem 7P Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

Solutions

Chapter
Section Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

PRESENT AND FUTURE VALUES Of A CASH FLOW STREAM An investment will pay $100 at the end of each of the next 3 stars,$200 at the end of Year 4. $300 at the end of Year 5, and$500 at the end of Year 6. if other investments of equal risk cum 8% annually, what is its present value? Its future value?

Summary Introduction

To determine: The present value and the future value.

Present Value: The present value refers to that value, which is the current value and by which the future value of the annuity is determined. The calculation of the future value depends on the present value which is calculated at a discounted rate.

Future Value: The future value means that value of the investment, which will be realized in the future. With the help of the calculation of future value, an analysis of the amount to be invested can be made. This is very useful for the financial users and investors.

Explanation

Solution:

Given,

The cash flow at the end of first 3 years is $100. The cash flow at the end of the 4th year is$200.

The cash flow at the end of 5th and 6th year is $300 and$500.

The rate of interest is 8% annually.

Calculate the present value of the cash flows.

The formula to calculate the present value of the cash flows,

PV=FV(1+I)N

Where,

• FV is the future value.
• PV is the present value.
• I is the interest rate.
• N is the time period.

Substitute $100 for FV in 1st, 2nd and 3rd year,$200 for the FV in 4th year, $300 for FV in 5th year,$500 for the FV in 6th year, 8% for I and the value of N according to the years in the above formula.

PV=($100(1+0.08)1+$100(1+0.08)2+$100(1+0.08)3+$200(1+0.08)4+$300(1+0.08)5+$500(1+0.08)6)=($92.592+$60.096+$79.383+$147.006+$204.176+$315

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