Limited time offer 20% OFF StudySoup Subscription details

Penn State - RUS 100 - Study Guide

Created by: Reid Moncada Elite Notetaker

> > > > Penn State - RUS 100 - Study Guide

Penn State - RUS 100 - Study Guide

School: Pennsylvania State University
Department: Russian
Course: Corporate Finance
Term: Spring 2014
Tags:
Description: Chapter 5: How to Value Bonds and Stocks 5
Uploaded: 07/08/2017
This preview shows pages 1 - 4 of a 14 page document. to view the rest of the content
background image Chapter 5: How to Value Bonds and Stocks 5.1 The present value of any pure discount bond is its face value discounted back to the present. a. PV  = F / (1+r) 10   = $1,000 / (1.05) 10   $613.91 b. PV  = $1,000 / (1.10) 10 $385.54 c. PV  = $1,000 / (1.15) 10 $247.19 5.2 First, find the amount of the semiannual coupon payment.     Semiannual Coupon Payment  = Annual Coupon Payment / 2
= (0.08 
 $1,000) / 2 = $40 a. Since the stated annual interest rate is compounded semiannually, simply divide this rate 
by two in order to calculate the semiannual interest rate.  
Semiannual Interest Rate  = 0.08 / 2 = 0.04 The bond has 40 coupon payments (=20 years   2 payments per year).  Apply the annuity formula to calculate the PV of the 40 coupon payments.  In addition, the $1,000 payment 
at maturity must be discounted back 40 periods.  
= C A T r  + F / (1+r) 40 = $40 A 40 0.04  + $1,000 / (1.04) 40 $1,000 The price of the bond is $1,000.  Notice that whenever the coupon rate and the 
market rate are the same, the bond is priced at par.  That is, its market value is 
equal to its face value.  
b. Semiannual Interest Rate  = 0.10 / 2 = 0.05 = $40 A 40 0.05  + $1,000 / (1.05) 40 $828.41 The price of the bond is $828.41.  Notice that whenever the coupon rate is below the 
market rate, the bond is priced below par.    
c. Semiannual Interest Rate = 0.06 / 2 = 0.03 = $40 A 40 0.03  + $1,000 / (1.03) 40 $1,231.15 The price of the bond is $1,231.15.  Notice that whenever the coupon rate is above 
the market rate, the bond is priced above par.  
Copyright 2003, McGraw-Hill.  All rights reserved.
background image 5.3 Since the payments occur semiannually, discount them at the semiannual interest rate.  Convert the
effective annual yield (EAY) to a semiannual interest rate.    
Semiannual Interest Rate  = (1+EAY) 1 / T  – 1 = (1.12) 1/2  – 1 = 0.0583 a. Calculate the semiannual coupon payment.   Semiannual Coupon Payment  = Annual Coupon Payment / 2
= (0.08 
 $1,000) / 2 = $40 Apply the annuity formula to calculate the PV of the 40 coupon payments (=20 years   2  payments per year).  In addition, the $1,000 payment at maturity must be discounted back
40 periods. The appropriate discount rate is the semiannual interest rate.  
= C A T r  + F / (1+r) 40 = $40 A 40 0.0583  + $1,000 / (1.0583) 40 $718.65 The price of the bond is $718.65.   b. Calculate the semiannual coupon payment.   Semiannual Coupon Payment  = (0.10   $1,000) / 2 = $50 Apply the annuity formula to calculate the PV of the 30 coupon payments (=15 years   2  payments per year).  In addition, the $1,000 payment at maturity must be discounted back
30 periods. The appropriate discount rate is the semiannual interest rate.  
= $50 A 30 0.0583  + $1,000 / (1.0583) 30 $883.64  The price of the bond is $883.64.  5.4 First, calculate the semiannual interest rate.   Semiannual Interest Rate  = (1+EAY) 1 / T  – 1 = (1.10) 1 / 2  – 1 = 0.04881 Next, find the semiannual coupon payment.   Semiannual Coupon Payment  = (0.08   $1,000) / 2 = $40 The bond has 40 payments (=20 years   2 payments per year).  Apply the annuity formula to find  the PV of the coupon payments.  In addition, discount the $1,000 payment at maturity back 40 
periods.  The appropriate discount rate is the semiannual interest rate.
= C A T r  + F / (1+r) 40 = $40 A 40 0.04881  + $1,000 / (1.04881) 40 $846.33 Copyright 2003, McGraw-Hill.  All rights reserved.
background image The price of the bond is $846.33. 5.5 First, calculate the semiannual interest rate.   Semiannual Interest Rate  = 0.10 / 2 = 0.05 Set the price of the bond equal to the sum of the PV of the 30 semiannual coupon payments (=15 
years 
 2 payments per year) and the PV of the payment at maturity.  The PV of the semiannual  coupon payments should be expressed as an annuity.  Solve for C, the semiannual coupon 
payment.    
= C A T r  + F / (1+r) 30 $923.14  = C A 30 0.05  + $1,000 / (1.05) 30 [$923.14 – $1,000 / (1.05) 30 ] / A 30 0.05 = C $45 = C To find the coupon rate on the bond, set the semiannual coupon payment, $45, equal to the product
of the coupon rate and face value of the bond, divided by two.  
Semiannual Coupon Payment  = (Coupon Rate   Face Value) / 2 $45 = (Coupon Rate   $1,000) / 2 $90 = Coupon Rate   $1,000 $90 / $1,000 = Coupon Rate 0.09 = Coupon Rate The annual coupon rate is 9 percent.   5.6 a. The market interest rate and the coupon rate are equal because the bond is selling 
at par.  Since the face value of the bond is $1,000 and the semiannual coupon payment is 
$60, the semiannual coupon rate is six percent (=$60 / $1,000).  Thus, the semiannual 
interest rate is also six percent.  Calculate the yield, expressed as an effective annual 
yield, by compounding the semiannual interest rate over two periods.  
Yield = (1+r) 2   – 1 = (1.06) 2  – 1 0.1236 The yield is 0.1236.   b. You are willing to pay a price equal to the PV of the bond’s payments.  To find the PV of 
the 12 coupon payments, apply the annuity formula, discounted at the semiannual rate of 
return.  Also, discount the $1,000 payment made at maturity back to the present.  The 
discount rate, r, is the same as calculated in part (a).   
= C A T + F / (1+r) 12 = $30 A 12 0.06  + $1,000 / (1.06) 12 $748.49 The price of the bond is $748.49. c. If the five-year bond pays $40 in semiannual payments and is priced at par, the 
semiannual rate of return will be different from that in part (a).  Since the face value of 
the bond is $1,000 and the semiannual coupon payment is $40, the semiannual interest 
Copyright 2003, McGraw-Hill.  All rights reserved.
background image rate is four percent (=$40 / $1,000).  To calculate the price of the bond, apply the annuity 
formula, discounted at the semiannual interest rate.  In addition, discount the $1,000 
payment made at maturity back 12 periods.   
= C A T + F / (1+r) 12 = $30 A 12 0.04  + $1,000 / (1.04) 12 $906.15 The price of the bond is $906.15.  5.7 a. Since the coupon rates of the bonds are equal to the market interest rate, the bonds are 
priced at face value.  Both bonds have face values of $1,000.   
P A   $1,000 P B $1,000 b. Discount the cash flows of the bonds at 12 percent.  Since the coupon rates of both bonds 
are less than the market interest rate, the bonds will be priced at a discount.  
P A   = $100 A 20 0.12  + $1,000 / (1.12) 20 $850.61 P B   = $100 A 10 0.12  + $1,000 / (1.12) 10 $887.00 c. Discount the cash flows of the bonds at eight percent.  Since the coupon rates of both 
bonds are greater than the market interest rate, the bonds will be priced at a premium.  
P A   = $100 A 20 0.08  + $1,000 / (1.08) 20 $1,196.36 P B   = $100 A 10 0.08  + $1,000 / (1.08) 10 $1,134.20 5.8 a. The prices of long-term bonds should fall.  The price of any bond is the PV of the cash 
flows associated with the bond.  As the interest rate increases, the PV of those cash flows 
falls.  This can be easily seen by looking at a one-year, pure discount bond.  
= $1,000 / (1+i) As i increases, the denominator, (1 + i), rises, thus reducing the value of the numerator 
($1,000).  The price of the bond decreases.  
b. The effect on stocks is not as clear-cut as the effect on bonds.  The nominal interest rate is
a function of both the real interest rate, r, and the inflation rate, i.e.,
(1+i)  =  (1+r) (1+Inflation) From this relationship it is easy to conclude that, as inflation rises, the nominal interest 
rate, i, rises.  However, stock prices are a function of dividends and future prices as well 
as the interest rate.  Those dividends and future prices are determined by the earning 
power of the firm.  Inflation may increase or decrease firm earnings.  Thus, a rise in 
interest rates has an uncertain effect on the general level of stock prices.  
Copyright 2003, McGraw-Hill.  All rights reserved.

This is the end of the preview. Please to view the rest of the content
Join more than 18,000+ college students at Pennsylvania State University who use StudySoup to get ahead
14 Pages 69 Views 55 Unlocks
  • Better Grades Guarantee
  • 24/7 Homework help
  • Notes, Study Guides, Flashcards + More!
Join more than 18,000+ college students at Pennsylvania State University who use StudySoup to get ahead
School: Pennsylvania State University
Department: Russian
Course: Corporate Finance
Term: Spring 2014
Tags:
Description: Chapter 5: How to Value Bonds and Stocks 5
Uploaded: 07/08/2017
14 Pages 69 Views 55 Unlocks
  • Better Grades Guarantee
  • 24/7 Homework help
  • Notes, Study Guides, Flashcards + More!
Join StudySoup for FREE
Get Full Access to Penn State - RUS 100 - Study Guide
Join with Email
Already have an account? Login here
×
Log in to StudySoup
Get Full Access to Penn State - RUS 100 - Study Guide

Forgot password? Reset password here

Reset your password

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here