Question

Mason-Dixon Stores has two bond issues outstanding. The first issue has a coupon rate of 9 percent, matures in 4 years, has a total face value of $10 million, and is quoted at 109 percent of face value. The second issue has a 7 percent coupon, matures in 11 years, has a total face value of $22 million, and is quoted at 101 percent of face value. Both bonds pay interest semiannually. What is the weighted average after-tax cost of debt if the tax rate is 35 percent?

Select one:

a. 4.37 percent

b. 6.72 percent

c. 4.98 percent

d. 2.35 percent

Answer 1

Answer : Correct option is a. 4.37 %

Calculation of After Tax Cost of Debt

After Tax Cost of Debt = (After tax cost of Debt 1 * Weight of Debt 1) + (After tax cost of Debt 2 * Weight of Debt 2 )

After Tax Cost of Debt 1

Using Excel function of Rate

=RATE(nper,pmt,pv,fv)

where nper is Number of years to maturity i.e = 4 * 2 = 8 years (As Coupons are paid semiannually)

pmt is Interest payment i.e 1000 * 9% =90/2 = 45 (As Coupons are paid semiannually)

pv is Current Market Price

= - 1090 (1000 * 109%)

Note : pv should be taken as negative.

fv is face value i.e 1000

=RATE(8,45,-1090,1000)

therefore ,Before tax cost of Debt is 3.20669% (As Coupons are paid semiannually)

Before tax cost of Debt is 3.20669%* 2 = 6.41338% (Annual)

After tax cost of Debt = 6.41338% * (1 - Tax rate )

= 6.41338% * (1 - 0.35)

= 4.16870%

Calculation of Cost of Debt 2

where nper is Number of years to maturity i.e = 11 * 2 = 22 years (As Coupons are paid semiannually)

pmt is Interest payment i.e 1000 * 7% =70/2 = 35 (As Coupons are paid semiannually)

pv is Current Market Price

= - 1010 (1000 * 101%)

Note : pv should be taken as negative.

fv is face value i.e 1000

=RATE(22,35,-1010,1000)

therefore ,Before tax cost of Debt is 3.43449% (As Coupons are paid semiannually)

Before tax cost of Debt is 3.43449%* 2 = 6.86898% (Annual)

After tax cost of Debt = 6.86898% * (1 - Tax rate )

= 6.86898% * (1 - 0.35)

= 4.46484%

Market Value of Debt 1 = 10 million * 109% = 10.9 million

Market Value of Debt 2 = 22 million * 101% = 22.22 million

Total Market Value = 10.9 + 22.22 = 33.12 million

Weight of Debt 1 = 10.9 / 33.12 = 0.32910628019 or 32.91%

Weight of Debt 2= 22.22 / 33.12 = 0.6708937198 or 67.09%

After Tax Cost of Debt = (After tax cost of Debt 1 * Weight of Debt 1) + (After tax cost of Debt 2* Weight of Debt 2)

= (4.16870% * 0.32910628019) + (4.46484% * 0.6708937198 )

= 1.371945% + 2.99543%

= 4.367375% or 4.37%