Professor Jerry Langham
MBA 554: 262
27 January 2009
Chapter 5: Problems 1, 2, 3, 4, 7, 12, & 25
1. Bond Yields. A 30-year Treasury bond is issued with face value of $1,000, paying interest of $60 per year. If market yields increase shortly after the T-bond is issued, what happens to the bond’s a. coupon rate? The fixed rate is 6% and will not change the $60 per year. b. price? Price is dependent upon the market interest rate. If the market interest rate goes up, the bond price goes down; if the interest rate goes down, the price of the bond must increase. c. yield to maturity? If the market yield increases, the yield to maturity will increase, and vice versa. d. current yield? Current rate = coupon rate ÷ bond price. As the bond price changes the current yield will as well. If the bond price is lower, the current yield will be higher and vice versa. 2. Bond Yields. If a bond with face value of $1,000 and a coupon rate of 8 percent is selling at a price of $970, is the bond’s yield to maturity more or less than 8 percent? What about the current yield?
Because the bond is discounted, the yield to maturity must be more than 8%, so the yield to maturity is greater than the coupon rate.
Current yield = coupon payment ÷ bond price
Coupon payment = $1000 * .08 = $80
CY = 80÷ 970 = 8.247 which is greater than 8%.
3. Bond Yields. A bond with face value $1,000 has a current yield of 7 percent and a coupon rate of 8 percent. What is the bond’s price?
If x = the bond price
.07 = 80/x
x= 80/.07 = $1,142.86
4. Bond Pricing. A 6-year Circular File bond pays interest of $80 annually and sells for $950. What are its coupon rate, current yield, and yield to maturity?
Coupon rate = 80/1000 = 8%
Current yield = 80 ÷ 950 = 8.42%
Yield to maturity =
950 = 80 * ((1/r)- (1/(r*(1+r)^6)))+ (1000/(1+r)^6)
In calc…N = 6, PV = -950, PMT = 80, FV = 1000
7.Coupon Rate. General Matter’s outstanding bond issue has a coupon rate of 10 percent and a current yield of 9.6 percent, and it sells at a yield to maturity of 9.25 percent. The firm wishes to issue additional bonds to the public at face value. What coupon rate must the new bonds offer in order to sell at face value? The yield to maturity = coupon rate, so the new bond needs to be 9.25 to sell at face value. 12. Bond Pricing. A 30-year maturity bond with face value of $1,000 makes annual coupon payments and has a coupon rate of 8 percent. What is the bond’s yield to maturity if the bond is selling for 1. $900? N=30, FV=1000, PMT = 80, PV = -900 ( I/YR = 8.9708% 2. $1,000? N=30, FV=1000, PMT = 80, PV = -1000 ( I/YR = 8% 3. $1,100? N=30, FV=1000, PMT = 80, PV = -11000 ( I/YR = 7.1796% 25. Real Returns. Suppose that you buy a 1-year maturity bond for $1,000 that will pay you back $1,000 plus a coupon payment of $60 at the end of the year. What real rate of return will you earn if the inflation rate is 1. 2 percent? (1.06/1.02) – 1 = 0.039215686 = 3.92%
2. 4 percent? (1.06/1.04) – 1 = 0.019230769 = 1.92%
3. 6 percent? (1.06/1.06) – 1 = 1%
4. 8 percent? (1.06/1.08) – 1 = -0.018518519 = -1.85%
Chapter 6: Problems 1, 2, 3, 4, 13, 17, 19 and 32
1. Dividend Discount Model. Amazon.com has never paid a dividend, but in June 2005 the market value of its stock was $13 billion. Does this invalidate the dividend discount model? No.
2. Dividend Yield. Favored stock will pay a dividend this year of $2.40 per share. Its dividend yield is 8 percent. At what price is the stock selling? Dividend yield = Dividend ÷ Price
8% = 2.4/p
p=2.4/.08 = 30
The price of the stock is $30.
3.Preferred Stock. Preferred Products has issued preferred stock with an $8 annual dividend that will be paid in perpetuity. If the discount rate is 12 percent, at what price should the preferred sell? Price = Dividend ÷ rate
P = $8/.12
P = $66.67
At what price should the stock sell 1 year...