Essentials of Corporate Finance
Essentials of Corporate Finance
8th Edition
ISBN: 9780078034756
Author: Stephen A. Ross, Randolph W. Westerfield, Bradford D. Jordan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 4, Problem 5QP
Summary Introduction

To determine: The number of periods of investment

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. The value increases based on the period of investment. The value of the investment will be higher if the duration of investment is longer.

Expert Solution & Answer
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Answer to Problem 5QP

The number of periods is as follows:

Particulars Present value Years Interest Rate Future value
Investment A $195 20.13 9% $1,105
Investment B $2,105 8.34 7% $3,700
Investment C $47,800 18.45 12% $387,120
Investment D $38,650 9.39 19% $198,212

Explanation of Solution

Given information:

Investment A has a present value of $195, future value of $1,105, and an interest rate of 9 percent. Investment B has a present value of $2,105, future value of $3,700, and an interest rate of 7 percent.

Investment C has a present value of $47,800, future value of $387,120, and an interest rate of 12 percent. Investment D has a present value of $38,650, future value of $198,212, and an interest rate of 19 percent.

Formula:

Derive the formula to calculate the number of periods from the present value equation as follows:

PV=FV(1+r)t(1+r)t=FVPVln(1+r)t=ln(FVPV)

The power rule of naturallogarithm states that[ln(xy) = y× ln(x)] Hence,t×ln(1+r)=ln(FVPV)Divide the right hand side and left hand side byln(1+r)

t×ln(1+r)ln(1+r)=ln(FVPV)ln(1+r)t=ln(FVPV)ln(1+r)

The formula to calculate the number of periods:

t=ln(FVPV)ln(1+r)

Where,

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

“ln” refers to the log value,

 “FV” refers to the future value,

“PV” refers to the present value,

“r” refers to the simple rate of interest.

Compute the number of periods of Investment A:

t=ln(FVPV)ln(1+r)=ln($1,105$195)ln(1+0.09)=ln(5.66)ln(1.09)=20.13 years

Hence, the number of periods of Investment A is 20.13 years.

Compute the number of periods of Investment B:

t=ln(FVPV)ln(1+r)=ln($3,700$2,105)ln(1+0.07)=ln(1.76)ln(1.07)=8.34 years

Hence, the number of periods of Investment B is 8.34 years.

Compute the number of periods of Investment C:

t=ln(FVPV)ln(1+r)=ln($387,120$47,800)ln(1+0.12)=ln(8.099)ln(1.12)=18.45 years

Hence, the number of periods of Investment C is 18.45 years.

Compute the number of periods of Investment D:

t=ln(FVPV)ln(1+r)=ln($198,212$38,650)ln(1+0.19)=ln(5.12)ln(1.19)=9.39 years

Hence, the number of periods of Investment D is 9.39 years.

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Esfandairi Enterprises is considering a new three-year expansion project that requires an initial fixed asset investment of $2,350,000. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $3,310,000 in annual sales, with costs of $2,330,000. Assume the tax rate is 23 percent and the required return on the project is 11 percent. What is the project's NPV? Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
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