Investments
Investments
11th Edition
ISBN: 9781259277177
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Chapter 9, Problem 8PS

a.

Summary Introduction

To determine: NPV (Net Present Value) of the project

Introduction: The net present value helps to an organization for taking decisions regarding the growth of investment and the business. It analyzes the profitability of the project through capital budgeting.

a.

Expert Solution
Check Mark

Answer to Problem 8PS

$18,092,131.90 is the Net Present Value

Explanation of Solution

Given Information:

The beta value, risk free rate of interest, expected return on market is given.

Net present value is the discounting of present value of cash inflow and outflow at a specified rate. When the NPV becomes positive, then the investment is profitable. It analyzes the profitability of the project.

Calculation of net Present Value,

  NetPresentValue=i=0NC(1+i)

  =[C0+C1(1+i)1+C2(1+i)2+C3(1+i)3+C4(1+i)4+C5(1+i)5+C6(1+i)6+C7(1+i)7+C8(1+i)8+C9(1+i)9+C10(1+i)10]

“C” refers to the cash flow,

“I” refers to discount rate

“t” refers to the time for cash flow

The CAPM equation ism

  ExpectedReturn=RiskFreeRate+Beta[ExpectedMarketRiskRiskFreeRate]

  =rf+β[E(rM)rf]

  Er , the expected return

  rf , the risk free rate of interest

  β , the systematic risk

  rM , return on market index

  Er=rf+β[E(rM)rf]=8%+1.8[16%8%]=8%+1.8[8%]=22.4%

Calculating the NPV of the project,

  NetPresentValue=i=0NC(1+i)

  =[C0+C1(1+i)1+C2(1+i)2+C3(1+i)3+C4(1+i)4+C5(1+i)5+C6(1+i)6+C7(1+i)7+C8(1+i)8+C9(1+i)9+C10(1+i)10]

  =[$40,000,000+$15,000,000(1+0.224)1+$15,000,000(1+0.224)2+$15,000,000(1+0.224)3+$15,000,000(1+0.224)4+$15,000,000(1+0.224)5+$15,000,000(1+0.224)6+$15,000,000(1+0.224)7+$15,000,000(1+0.224)8+$15,000,000(1+0.224)9+$15,000,000(1+0.224)10]

  =$18,092,131.90

So the Net Present Value is $18,092,131.90

b.

Summary Introduction

To determine: The highest possible beta for the project

Introduction: The net present value helps to an organization for taking decisions regarding the growth of investment and the business. It analyzes the profitability of the project through capital budgeting.

b.

Expert Solution
Check Mark

Answer to Problem 8PS

3.47 is the highest possible value of beta for the project.

Explanation of Solution

Given Information:

The risk free rate of interest, expected return on market is given.

Net present value is the discounting of present value of cash inflow and outflow at a specified rate. When the NPV becomes positive, then the investment is profitable. It analyzes the profitability of the project.

At internal rate of return, the NPV will be zero. So first calculate internal rate of return,

    YEARCASH FLOW ($)
    0-40,000,000
    115,000,000
    215,000,000
    315,000,000
    415,000,000
    515,000,000
    615,000,000
    715,000,000
    815,000,000
    915,000,000
    1015,000,000
    IRR35.7333%

The calculation of Beta,

  Er=rf+β[E(rM)rf]35.7333%=8%+βi[16%8%]35.7333%=8%+βi[8%]35.7333%8%=βi[8%]27.7333%=βi[8%]βi[8%]=27.7333%βi=27.7333%8%=3.47

Before the NPV becomes negative, the highest value of beta is 3.47

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