Calculate the aftertax cost of debt under each of the following cond itions Yield Corporate Tax Rate a.8.0% 18% b.120% 34% c.10.6% 15% Solution: Kd Yield(1-T Yield Yield (1-T) a.8.0% (1-.18) 6.56% b.120% 792% C.10.6% 9.01% 11-4 The Millennium Charitable Foundation, which is tax-exempt, issued debt last year at 8 percent to help finance a new playground facility in Chicago. This year the cost of debt is 15 percent higher; that is, firms that paid 10 percent for debt last year would be paying 11.5 percent this year a. If the Millennium Charitable Foundation borrowed money this year, what would the aftertax cost of debt be, based on their cost last year and the 15 percent increase? b. If the Foundation was found to be taxable by the irS (at a rate of 35 percent) because it was involved in political activities, what would the aftertax cost of debt be? Solution: Millennium Charitable foundati K Yield(1-T Yield=8%X1.15=9.20% K 92%(1-0)=9.2%(1)=9.2% b K 92%(1-35)=92%(65)=5.98% CopyrightC 2005 by The McGray-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-384 11-3. Calculate the aftertax cost of debt under each of the following conditions. Yield Corporate Tax Rate a. 8.0% 18% b. 12.0% 34% c. 10.6% 15% Solution: Kd = Yield (1 – T) Yield (1 – T) Yield (1 – T) a. 8.0% (1 – .18) 6.56% b. 12.0% (1 – .34) 7.92% c. 10.6% (1 – .15) 9.01% 11-4. The Millennium Charitable Foundation, which is tax-exempt, issued debt last year at 8 percent to help finance a new playground facility in Chicago. This year the cost of debt is 15 percent higher; that is, firms that paid 10 percent for debt last year would be paying 11.5 percent this year. a. If the Millennium Charitable Foundation borrowed money this year, what would the aftertax cost of debt be, based on their cost last year and the 15 percent increase? b. If the Foundation was found to be taxable by the IRS (at a rate of 35 percent) because it was involved in political activities, what would the aftertax cost of debt be? Solution: Millennium Charitable Foundation a. Kd = Yield (1 – T) Yield = 8% x 1.15 = 9.20% Kd = 9.2% (1 – 0) = 9.2% (1) = 9.2% b. Kd = 9.2% (1 – 35) = 9.2% (65) = 5.98%
Waste Disposal Systems, Inc, has an aftertax cost of debt of 6 percent. With a tax rate of 33 percent, what can you assume the yield on the debt is? Solution: Waste Disposal Systems, Inc. K=Yield(1-T) K Yield 6%6% Yield 8.95% (1-.3)67 9% is an acceptable answer l1-6 Addison glass Company has a $1,000 par value bond outstanding with 25 years to maturity. The bond carries an annual interest payment of $88 and is currently selling for $925. Addison is in a 25 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar a. Compute the approximate yield to maturity(formula 11-1)on the old issue and use this as the yield for the new issue b. Make the appropriate tax adjustment to determine the aftertax cost of debt 385 Copyright C2005 by The McGra-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-385 11-5. Waste Disposal Systems, Inc., has an aftertax cost of debt of 6 percent. With a tax rate of 33 percent, what can you assume the yield on the debt is? Solution: Waste Disposal Systems, Inc. ( ) ( ) 8.95% .67 6% 1 .33 6% Yield 1 T K Yield K Yield (1 T) d d = = − = − = = − 9% is an acceptable answer. 11-6. Addison Glass Company has a $1,000 par value bond outstanding with 25 years to maturity. The bond carries an annual interest payment of $88 and is currently selling for $925. Addison is in a 25 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar. a. Compute the approximate yield to maturity (Formula 11-1) on the old issue and use this as the yield for the new issue. b. Make the appropriate tax adjustment to determine the aftertax cost of debt
1-6. Continued Solution: Addison Glass Company Principal payment- Price of the bond Annual interest payment Number of years to maturity 6(Price of bond)+ 4 (Principal payment) S8$1000-$925 6(925)+4($1000 $75 $88+ $555+$400 $88+$3 $955 $9l 953% $955 b Kd yield 953%(1-25) =953%(75) 7.15% CopyrightC 2005 by The McGray-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-386 11-6. Continued Solution: Addison Glass Company a. .6 (Price of bond) .4 (Principal payment) Number of years to maturity Principal payment Price of the bond Annual interest payment Y' + − + = ( ) ( ) 9.53% $955 $91 $955 $88 $3 $555 $400 25 $75 $88 .6 $925 .4 $1,000 25 $1,000 $925 $88 = = + = + + = + − + = b. Kd = Yield (1 – T) = 9.53% (1 – .25) = 9.53% (.75) = 7.15%
Hewlett Software Corporation has a $1,000 par value bond outstanding with 20 years to maturity. The bond carries an annual interest payment of $110 and is currently selling for $1, 080 per bond. Hewlett is in a 35 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar a. Compute the approximate yield to maturity( formula 11-1)on the old issue and use this as the yield for the new issue Make the appropriate tax adjustment to determine the aftertax cost of debt Solution: Hewlett Software Corporation Principal payment- Price of the bond Annual interest payment Number of years to maturity 6(Price of bond)+ 4 (Principal payment) $l10+ $1,000-$1,080 20 6($1,080)+4($1000 $l10+ $80 20 $648+$400 $l10-$4 $l.048 $106 =10.11 $l,048 iby The McGraw-Hill Co
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-387 11-7. Hewlett Software Corporation has a $1,000 par value bond outstanding with 20 years to maturity. The bond carries an annual interest payment of $110 and is currently selling for $1,080 per bond. Hewlett is in a 35 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar. a. Compute the approximate yield to maturity (Formula 11-1) on the old issue and use this as the yield for the new issue. b. Make the appropriate tax adjustment to determine the aftertax cost of debt. Solution: Hewlett Software Corporation a. .6 (Price of bond) .4 (Principal payment) Number of years to maturity Principal payment Price of the bond Annual interest payment Y' + − + = ( ) ( ) 10.11% $1,048 $106 $1,048 $110 $4 $648 $400 20 $80 $110 .6 $1,080 .4 $1,000 20 $1,000 $1,080 $110 = = − = + − + = + − + =
1-7. Continued b Kd= Yield(1-T 10.11%(1-35) 10.11%(65) 6.57% l1-8 For Hewlett Software Corporation, described in problem 7, assume that the yield on the bonds goes up by I percentage point and that the tax rate is now 4. percent a. What is the new aftertax cost of debt? b. Has the aftertax cost of debt gone up or down from problem 7? Explain wny Solution: Hewlett Software Corporation( Continued) a. Kd= Yield (1-T 11.11%(1-45) 11.11%(55) 6.11% b. It has gone down. Although the before-tax yield is higher, the larger tax deduction(45 percent versus 35 percent) more than offsets the higher rate CopyrightC 2005 by The McGray-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-388 11-7. Continued b. Kd = Yield (1 – T) = 10.11% (1 – .35) = 10.11% (.65) = 6.57% 11-8. For Hewlett Software Corporation, described in problem 7, assume that the yield on the bonds goes up by 1 percentage point and that the tax rate is now 45 percent. a. What is the new aftertax cost of debt? b. Has the aftertax cost of debt gone up or down from problem 7? Explain why. Solution: Hewlett Software Corporation (Continued) a. Kd = Yield (1 – T) = 11.11% (1 – .45) = 11.11% (.55) = 6.11% b. It has gone down. Although the before-tax yield is higher, the larger tax deduction (45 percent versus 35 percent) more than offsets the higher rate