Outline: Chapter 4 Valuation of Bonds and Stocks. Financial Assets Determining Bond Values and Yields Bond valuation Interest rates and bond prices Bonds issued by the government Bonds issue by firms Determining the yield to maturity Bonds with semi-annual interest
Consider a $1,000 par value bond that has a 10% coupon rate and a 25 year maturity. If this bond has a required rate of return of 10% and pays interest annually, what is its market value?
The market price of the bond is equal to its face value because the market rate (or required rate of return) is equal to the coupon rate
Assume that the 25-year, 10% coupon rate, bond from the last example is a Government of Canada bond. Expected inflation jumps by 6%. If you own this bond what is the new market value of your $1,000 par value bond? Is your bond selling at a premium or a discount from its par value?
Your bond is selling at a discount because the market interest rate is greater than the coupon rate
Assume that expected inflation falls by 2%, such that the required return is 8% for similar government bonds issued today. What is the market value of your $1,000 par value bond? Is it selling at a premium or a discount?
Your bond is selling at a premium because the market interest rate is less than the coupon rate
Assume you own a government bond with three years to maturity (instead of 25 years). Coupon rate is still 10%. Relative to a 25-year government bond, how will an increase in expected inflation of 6% and a decrease in expected inflation of 2% affect the value of your three year bond? What can we conclude?
Given our previous answers of $634.17 and $1,213.50 we can conclude that bonds of shorter maturity are less sensitive to changes in expected inflation i.e., they have less interest rate risk.
Market value of bond ($)
25 - year bond
Par value = 1,000
3 – year bond
Market rate of interest (%)
You are told that your 20-year maturity, $1,000 par value bond with an 8% coupon rate sells for $908.32. What discount rate makes the present value of the interest of $80 per year and the maturity value of $1,000 equal to $908.32?
We know your bond is selling at a discount. This implies that the yield to maturity must be more than 8%. The yield to maturity is simply an internal rate of return
By financial calculator, kb = 9%
Consider a bond with 20 years to maturity remaining and with a 14% coupon rate that pays interest semiannually. Assume a 10% annual or a 5% semiannual rate of return is presently required on this bond. What is the value of the bond?
If the required rate of return is 7.5% and the coupon rate is 10%, then a $1,000 par value perpetual bond would be worth $100 / 0.075 = $1,333.33
If a preferred stock has a $50 par value and the dividend is 6.5% per year and the required rate of return is 9%, then the preferred stock's value is ($50)(0.065) / 0.09 = $36.11
You expect $5, $6, and $7 in dividends over the next three years, at which time you expect to sell your stock for $100. What is the current market value if the required rate of return on the stock is 14%?
P0 = $5/(1.14)1 + $6/(1.14)2 + $107/(1.14)3 = $81.22
What is Po if you expect $1.00 dividend in perpetuity and ks = 16%?
P0 = $1.00/0.16 = $6.25
The current (t=0) cash dividend of $1.00 is expected to grow to grow at 5% per year to infinity. Your required rate of return is 8%. What price would you place on this common stock?
Assume a required rate of return of 16%, Do = $1.00, and 10% growth in dividends for years 1 through 3, followed by 3% compound growth thereafter to infinity.
Step 4: Using Equation 4.4, we discount (by 16%) Dl, D2, D3 and P3 back to t = 0 and get P0 equal to about $9.46
$9.46 = P0
0.16 - 0.03
g = 0% $6.25
10% Compound growth $8.03
for years 1-3, then g = 0%
10% compound growth $9.46
for years 1-3, then g = 3%
g = 10% to infinity $18.33
NPV = $18.33 - $20 = -$1.67
He should not buy the shares
If an investor pays $15 for a share of stock today when it is expected that the current dividend (D0) of $1 will grow indefinitely at 10 percent per year. If the investor has a required rate of return of 16% should she buy the stock?
Since this is greater than her required rate of return of 16%, she should buy this stock.
FSB Inc expects to grow at 8% for the foreseeable future. The firm’s stock is currently trading at $4.63. A years ago the firm issued 15-year bonds with a face value of $1,000 and a coupon rate of 7% that are convertible into 110 shares of common stock. The issue also has a call price of $1,025. FSB will call the bonds when the share price hits $10.87. The current required rate of return is 7.5%. How much would you be willing to pay for one of FSB’s bonds?
The growth rate is 8% therefore
You would be willing to pay up to $1,051.75 for the bond
You own 100 shares of stock in Canada Ltd. and expect to receive cash dividends of $5.00 per share at time t = 1. You pay $50 per share at time t = 0. At time t = 1, the price per share is $51. What is your return?
k = [$5.00 + ($51 - $50)]/$50 = 12%
For the 100 shares, your return is $6.00 ($5 dividend and $1 capital gain) per share or $600.00 total during this time period
3. Riskiness of expected
decisions, which affect
1. Perceived risk
V = S + B
2. Required rate of
the size of the pie