Chapter 6, Problem 4PS

A

Summary Introduction

To calculate:The amount which is paid for the portfolio is 8% risk premium is to be determined.

Introduction:The present values of portfolio is defined as the contemporary values of the subsequent amount of money or called as stream of cash flow with defined rate of return.

Answer to Problem 4PS

The present values of the portfolio= $ 118,421

Explanation of Solution

The expected cash flow is determined by the summation of the product of the probability with the cash flow in two scenarios.

Cash flow = $ 70,000 with probability 0.5

Cash flow = $200,000 with probability 0.5

  $expectedcashflow=\left(0.5\times \$70,000\right)+\left(0.5\times 200,000\right)$

The assumed cash flow = $135,000

Mentioned risk premium = 8%

Mentioned risk-free rate = 6%

Mentioned rate of return = 14%

The present value of portfolio is determined by dividing assumed cash flow by stated rate of return.

  $presentvalue=\frac{expectedcashflow}{rateofreturn}$.................... Equation (1)

Put the given values in Equ (1)

  $presentvalue=\frac{\$135,000}{1.14}=\$118,421$

The present value of the portfolio = $118,421

B

Summary Introduction

To calculate:The assumed rate of return of the portfolio is to be determined.

Introduction:The present value of portfolio is defined as the present value of the future amount of money or called as stream of cash flow with identified rate of return.

Answer to Problem 4PS

The assumed rate of return = $135,000

Explanation of Solution

The assumed rate of the return is calculated by the following formula −

  $expectedrateofthereturn[E(r)]=presentvalueoftheportfolio\times [1+E(r)]$ …………Equation (2)

  $expectedrateofthereturn[E(r)]=\$118,421\times [1+0.14]$

The assumed rate of return = $135,000

C

Summary Introduction

To calculate:Theamount which is paid for the portfolio at 12% risk premium is to be determined.

Introduction:The present value of portfolio is defined as the present value of the future amount of money or called as stream of cash flow with a stated rate of return.

Answer to Problem 4PS

The present value of the portfolio = $114,407

Explanation of Solution

Given that −

Risk premium = 12%

Risk-free rate = 6%

  $Requiredrateofreturn=12\%+6\%=18\%$

The present value of portfolio is ascertained by dividing assumed cash flow by identified rate of return.

  $presentvalue=\frac{expectedcashflow}{rateofreturn}$.................... Equ (1)

Put the given values in Equ (1)

  $presentvalue=\frac{\$135,000}{1.18}=\$114,407$

The present value of the portfolio = $114,407

D

Summary Introduction

To calculate:The relation between risk portfolio and the amount at which it sell is to be determined.

Introduction:The present value of portfolio is defined as the present value of the future amount of money or called as stream of cash flow with a expected rate of return.

Answer to Problem 4PS

The portfolio with higher risk will sell at lower price. The portfolio (a) will be selling at lower price.

Explanation of Solution

The current value of the portfolio (a) = $118,421

The current value of the portfolio (c) = $114,407

The portfolio with higher risk will be selling at lower price and providing extra discount from assumed price is a consequence of risk.