Problem Set 4

AF, Inc. announced yesterday that they earned $27,000,000 million this year. They also stated the firm's return on equity is 12% percent. AF retains 60% percent of their earnings. What is the firms earnings growth rate? Earnings =$27,000,000 ROE =12% Retention ratio =60%

7.2% is the firms earnings growth rate. Growth rate = ROE x retention ratio = 12% x 0.60 = 7.2%

What is the percentage change in the price of the bonds if interest rates suddenly rise by 5%? Airline 1, Inc. Coupon rate =7% Settlement date 1/1/2000 Maturity date 1/1/2002 Face value =1,000 # of coupons per year =2 Airline 2, Inc. Coupon rate =7% Settlement date 1/1/2000 Maturity date 1/1/2015 Face value =1,000 # of coupons per year =2 Change in interest rate =5%

Airline 1, Inc. Percentage change in the price = (913.37-1000)/ 1000 *100% =-8.66% Airline 2 Inc. Percentage change in the price = (655.88-1000)/ 1000* 100% =-34.41%

C Inc., issued 15 Year bonds 2 years ago at a coupon rate of 6.40% percent. The bonds make semi- annual payments. If these bonds currently sell for 106 percent of par value, what is the YTM? Settlement date 1/1/2000 Maturity date 1/1/2013 Annual coupon rate =6.40% Coupons per year =2 Face value (% of par) =100 Bond price (% of par) =106

Bond price is the present value of the annuity interest plus the present value of the face value $1000 Bond price =C* [ 1-(1+r)^-n ] / r + $1000/ (1+r)^n Note: Semi-annual coupon bond Coupon payment = 0.064/2 * $1000= 32 N= 13 years*2=26 r=YTM? Price PV = - 1 060 FV=$1000 $1 060= $32 *[ 1-(1+r)^26]/ r + $1000/ (1+r)^26 Using Excel =Rate() function is determined as follows : =Rate ( Nper, PMT, PV, FV) =Rate( 26 , 32, -1060, 1000)*2 YTM =5.74%

What is the price of the bond? Par Value =1,000 Settlement date 1/1/2000 Maturity date 1/1/2015 Annual coupon rate =7.00% Coupons per year =2 Yield to maturity =7%

Semi annual coupon = (7%/2)*1000 = 35 Semi annual Yield to maturity = 7%/2 = 0.035 Time = (2015-2000)*2 = 30 The price of the bond = Coupon*((1-(1+r)^-n)/r + F/(1+r)^n The price of the bond = ((35*((1-1.035^-30)/0.035) + 1000/1.035^30 The price of the bond =643.72 + 356.28 The price of the bond = $1000

Air Taxi, Inc. has issued a bond with the following characteristics: Par Value 1,000 Settlement date 1/1/2000 Maturity date 1/1/2015 Annual coupon rate 7.00% Coupons per year 2 Yield to maturity 9% What is the price of the bond?

The price of the bond = $837.11 Semi annual coupon = (7%/2)*1000 = 35 Semi annual Yield to maturity = 9%/2 = 0.045 Time = (2015-2000)*2 = 30 The price of the bond = Coupon*((1-(1+r)^-n)/r + F/(1+r)^n The price of the bond = ((35*((1-1.045^-30)/0.045) + 1000/1.045^30 The price of the bond =570.11 + 267.00 The price of the bond = $837.11

Given the following information, what would you expect the Treasury Bill rate to be? Real rate 2.20% Inflation rate 3.20%

Using the Fisher equation, the real return is: (1 + N) = (1 + r)(1 + h) N = nominal interest rate r = Real interest rate h = expected inflation rate (1+N) = ((1+0.022)*(1.032)) 1+N = 1.054704 N = 5.47%

CT Air Inc., just paid a dividend of $5.00 per share on its stock. The dividends are expected to grow at a constant rate of 7% percent per year, indefinitely. If investors require a return of 15% percent, what is the current price? Dividend paid =$5.00 Dividend growth rate =7% Required return =15% Requested year =0

current price = $66.88 current price = (D1/(r-g) current price = ((5*1.07)/(0.15-0.07) current price = $66.88