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.

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,

  $Net\mathrm{Pr}esentValue={\displaystyle \sum _{i=0}^N\frac{C}{(1+i)}}$

  $=\left[C_0+\frac{C_1}{{(1+i)}^1}+\frac{C_2}{{(1+i)}^2}+\frac{C_3}{{(1+i)}^3}+\frac{C_4}{{(1+i)}^4}+\frac{C_5}{{(1+i)}^5}+\frac{C_6}{{(1+i)}^6}+\frac{C_7}{{(1+i)}^7}+\frac{C_8}{{(1+i)}^8}+\frac{C_9}{{(1+i)}^9}+\frac{C_{10}}{{(1+i)}^{10}}\right]$

“C” refers to the cash flow,

“I” refers to discount rate

“t” refers to the time for cash flow

The CAPM equation ism

  $Expected\mathrm{Re}turn=RiskFreeRate+Beta[ExpectedMarketRisk-RiskFreeRate]$

  $=r_f+\beta [E(r_M)-r_f]$

  $E_r$ , the expected return

  $r_f$ , the risk free rate of interest

  $\beta$ , the systematic risk

  $r_M$ , return on market index

  $\begin{array}{l}{E}_r=r_f+\beta [E(r_M)-r_f]\\ =8\%+1.8[16\%-8\%]\\ =8\%+1.8[8\%]\\ =22.4\%\end{array}$

Calculating the NPV of the project,

  $Net\mathrm{Pr}esentValue={\displaystyle \sum _{i=0}^N\frac{C}{(1+i)}}$

  $=\left[C_0+\frac{C_1}{{(1+i)}^1}+\frac{C_2}{{(1+i)}^2}+\frac{C_3}{{(1+i)}^3}+\frac{C_4}{{(1+i)}^4}+\frac{C_5}{{(1+i)}^5}+\frac{C_6}{{(1+i)}^6}+\frac{C_7}{{(1+i)}^7}+\frac{C_8}{{(1+i)}^8}+\frac{C_9}{{(1+i)}^9}+\frac{C_{10}}{{(1+i)}^{10}}\right]$

  $=\left[-\$40,000,000+\frac{\$15,000,000}{{(1+0.224)}^1}+\frac{\$15,000,000}{{(1+0.224)}^2}+\frac{\$15,000,000}{{(1+0.224)}^3}+\frac{\$15,000,000}{{(1+0.224)}^4}+\frac{\$15,000,000}{{(1+0.224)}^5}+\frac{\$15,000,000}{{(1+0.224)}^6}+\frac{\$15,000,000}{{(1+0.224)}^7}+\frac{\$15,000,000}{{(1+0.224)}^8}+\frac{\$15,000,000}{{(1+0.224)}^9}+\frac{\$15,000,000}{{(1+0.224)}^{10}}\right]$

  $=\$18,092,131.90$

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.

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,

YEAR	CASH FLOW ($)
0	-40,000,000
1	15,000,000
2	15,000,000
3	15,000,000
4	15,000,000
5	15,000,000
6	15,000,000
7	15,000,000
8	15,000,000
9	15,000,000
10	15,000,000
IRR	35.7333%

The calculation of Beta,

  $\begin{array}{l}{E}_r=r_f+\beta [E(r_M)-r_f]\\ \Rightarrow 35.7333\%=8\%+{\beta }_i[16\%-8\%]\\ \Rightarrow 35.7333\%=8\%+{\beta }_i[8\%]\\ \Rightarrow 35.7333\%-8\%={\beta }_i[8\%]\\ \Rightarrow 27.7333\%={\beta }_i[8\%]\\ \Rightarrow {\beta }_i[8\%]=27.7333\%\\ \Rightarrow {\beta }_i=\frac{27.7333\%}{8\%}\\ =3.47\end{array}$

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