EBK CORPORATE FINANCE
EBK CORPORATE FINANCE
11th Edition
ISBN: 8220102798878
Author: Ross
Publisher: YUZU
Question
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Chapter 22, Problem 30QP

a.

Summary Introduction

To compute: Value of a risk free bond.

Bonds:

Bond is that item, which is similar to stock but the bonds carries some sort of interest and discount elements as well. It can be zero coupon bond, risk free or any other. There are various types of bonds, which changes according to the company on which type of bond they want to use.

a.

Expert Solution
Check Mark

Explanation of Solution

Given,

Face value of the bond is $75,000.

Risk free rate is 0.05.

Time to maturity is 2 years.

Formula to calculate value of a risk free bond is:

PV=FVeRT

Where,

  • PV is present value of a risk free bond.
  • FV is face value of the bond.
  • R is risk free rate.
  • T is time to expire.

Substitute $75,000 for FV, 0.05 for R and 2 for T,

PV=$75,000×e0.05×2=$75,000×0.904837=$67,862.77

Thus, the value of the risk free bond of ML Industries is $67,862.77.

b.

Summary Introduction

To compute: Price paid by the bondholders for put option.

b.

Expert Solution
Check Mark

Explanation of Solution

Given,

Stock price is $46,000.

Exercise price is $75,000.

Risk free rate is 0.05.

Time to maturity is 2 years.

Formula to calculate price of a call option is:

Priceofcalloption(C)=SN(d1)Ee-RtN(d2)

Where,

  • S is stock price.
  • E is exercise price.
  • R is risk free rate.
  • T is time to expire.

Substitute $46,000 for S, $75,000 for E, 0.05 for R and 2 for T,

Priceofcalloption(C)=($46,000×0.488)($75,000e0.05×2×0.1894)=($22,448)($75,000×0.904837×0.1894)=$9,594.80

Formula to calculate price of put option by put call parity is:

C-P=S-EeRT

Where,

  • C is price of call option.
  • P is price of put option.
  • S is stock price.
  • E is exercise price.
  • R is risk free rate.
  • T is time to expire.

Substitute $9,594.80 for C, $46,000 for S, $75,000 for E, 0.05 for R and 2 for T,

$9,594.80P=$46,000$75,000e0.05×2$9,594.80$46,000=P($75,000×0.904837)P=$31,457.57

Working notes:

Calculation of d1 ,

d1=In(SE)+(R+σ22)tσ2t=In($46,000$75,000)+(0.05+0.622)×20.62×2=0.48885+0.23×20.6×1.414=0.0339

From normal distribution table N(d1)=0.488

Formula to calculate d2 is:

d2=d1σ2t

Calculation of d2 :

d2=0.03390.62×2d2=0.03390.8485=0.8824

From normal distribution table N(d2)=0.1894

Hence, price that would the bondholders have to pay for a put option on the company’s assets is $31,457.57.

c.

Summary Introduction

To compute: Value of company’s debt and the continuously compounded yield on the company’s debt.

c.

Expert Solution
Check Mark

Explanation of Solution

Given,

Value of risk free bond is $67,862.77.

Value of put option is $31,457.57.

Future value of debt is $75,000.

Time to maturity is 2 years.

Formula to calculate the value of firm’s debt is:

Valueoffirm’sdebt=ValueofriskfreebondValueofputoption

Substitute $67,862.77 for value of risk free bond and $31,457.57for value of put option,

Valueoffirm’sdebt=$67,862.77$31,457.57=$36,405.2

Formula to calculate present value of firm’s debt is:

Presentvalueoffirm'sdebt=Futurevalueofdebt×eRT

Substitute $36,405.2 for the present value of firm’s debt, $75,000 for future value of debt and 2 for T,

$36,405.2=$75,000×e2R$36,405.2$75,000=e2R0.47304=2RR=0.3614 or 36.14%

Hence, value of the company’s debt is $36,405.2 and the continuous compounded yield on company’s debt is 36.14%

d.

Summary Introduction

To compute: Value of debt under proposed plan and the new continuously compounded yield on the debt.

d.

Expert Solution
Check Mark

Explanation of Solution

Given,

Face value of the bond is $75,000.

Stock price is $46,000.

Risk free rate is 0.05.

Time to maturity is 5 years.

Formula to calculate value of a risk free bond is:

PV=FVe-RT

Where,

  • PV is present value of a risk free bond.
  • FV is face value of the bond.
  • R is risk free rate.
  • T is time to expire.

Substitute $75,000 for FV, 0.05 for R and 5 for T,

PV=75,000×e0.05×5=$75,000×0.778800=$58,410

Formula to calculate price of a call option is:

Priceofcalloption(C)=SN(d1)Ee-RtN(d2)

Where,

  • S is stock price.
  • E is exercise price.
  • R is risk free rate.
  • T is time to expire.

Substitute $46,000 for S, $75,000 for E, 0.05 for R and 5 for T,

Priceofcalloption(C)=($46,000×0.6879)($75,000e0.05×5×0.2005)=($31,643.4)($75,000×0.778800×0.2005)=$19,932.195

Formula to calculate price of put option by put call parity is:

C-P=S-EeRT

Where,

  • C is price of call option.
  • P is price of put option.
  • S is stock price.
  • E is exercise price.
  • R is risk free rate.
  • T is time to expire.

Substitute $19,932.195 for C, $46,000 for S, $75,000 for E, 0.05 for R and 5 for T,

$19,932.195P=$46,000$75,000e0.05×5$19,932.195$46,000=P($75,000×0.778800)P=$32,342.2

Formula to calculate the value of firm’s debt is:

Valueoffirm’sdebt=ValueofriskfreebondValueofputoption

Substitute $58,410for value of risk free bond and $32,342.2 for value of put option,

Valueoffirm’sdebt=$58,410$32,342.2=$26,067.8

Substitute $26,067.8 for the present value of firm’s debt, $75,000 for future value of debt and 5 for T,

$26,067.8=$75,000×e5R$40,497.94$75,000=e5R0.53997=5RR=0.2113 or 21.13%

Working notes:

Calculation of d1 :

d1=In(SE)+(R+σ22)tσ2t=In($46,000$75,000)+(0.05+0.622)×50.62×5=0.48885+0.23×50.6×2.23606=0.4927

From normal distribution table N(d1)=0.6879

Calculation of d2 :

d2=d1σ2t=0.49270.62×5=0.8489

From normal distribution table N(d2)=0.2005

Hence, value of the company’s debt under given plan is $26,067.8 and the continuous compounded yield on company’s debt is 21.13%.

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Chapter 22 Solutions

EBK CORPORATE FINANCE

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