Question

Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the table below.

Bond	Coupon Rate	Price Quote	Maturity	Face Value
1	8.70%	105.2	7 years	$22,000,000
2	7.00	95.2	10 years	42,000,000
3	8.40	104.0	17.5 years	47,000,000
4	8.90	105.9	27 years	62,000,000

If the corporate tax rate is 22 percent, what is the aftertax cost of the company’s debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:
Bond 1:
Face Value = $22,000,000
Current Price = 105.20% * $22,000,000 = $23,144,000

Annual Coupon Rate = 8.70%
Semiannual Coupon Rate = 4.35%
Semiannual Coupon = 4.35% * $22,000,000 = $957,000

Time to Maturity = 7 years
Semiannual Period to Maturity = 14

Let semiannual YTM be i%

$23,144,000 = $957,000 * PVIFA(i%, 14) + $22,000,000 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -23144000
PMT = 957000
FV = 22000000

I = 3.8622%

Semiannual YTM = 3.8622%
Annual YTM = 2 * 3.8622%
Annual YTM = 7.7244%

Before-tax Cost of Debt = 7.7244%
After-tax Cost of Debt = 7.7244% * (1 - 0.22)
After-tax Cost of Debt = 6.03%

Bond 2:
Face Value = $42,000,000
Current Price = 95.2% * $42,000,000 = $39,984,000

Annual Coupon Rate = 7.00%
Semiannual Coupon Rate = 3.50%
Semiannual Coupon = 3.50% * $42,000,000 = $1,470,000

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$39,984,000 = $1,470,000 * PVIFA(i%, 20) + $42,000,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -39984000
PMT = 1470000
FV = 42000000

I = 3.8485%

Semiannual YTM = 3.8485%
Annual YTM = 2 * 3.8485%
Annual YTM = 7.6970%

Before-tax Cost of Debt = 7.6970%
After-tax Cost of Debt = 7.6970% * (1 - 0.22)
After-tax Cost of Debt = 6.00%

Bond 3:
Face Value = $47,000,000
Current Price = 104.0% * $47,000,000 = $48,880,000

Annual Coupon Rate = 8.40%
Semiannual Coupon Rate = 4.20%
Semiannual Coupon = 4.20% * $47,000,000 = $1,974,000

Time to Maturity = 17.5 years
Semiannual Period to Maturity = 35

Let semiannual YTM be i%

$48,880,000 = $1,974,000 * PVIFA(i%, 35) + $47,000,000 * PVIF(i%, 35)

Using financial calculator:
N = 35
PV = -48880000
PMT = 1974000
FV = 47000000

I = 3.9861%

Semiannual YTM = 3.9861%
Annual YTM = 2 * 3.9861%
Annual YTM = 7.9722%

Before-tax Cost of Debt = 7.9722%
After-tax Cost of Debt = 7.9722% * (1 - 0.22)
After-tax Cost of Debt = 6.22%

Bond 4:
Face Value = $62,000,000
Current Price = 105.9% * $62,000,000 = $65,658,000

Annual Coupon Rate = 8.90%
Semiannual Coupon Rate = 4.45%
Semiannual Coupon = 4.45% * $62,000,000 = $2,759,000

Time to Maturity = 27 years
Semiannual Period to Maturity = 54

Let semiannual YTM be i%

$65,658,000 = $2,759,000 * PVIFA(i%, 54) + $62,000,000 * PVIF(i%, 54)

Using financial calculator:
N = 54
PV = -65658000
PMT = 2759000
FV = 62000000

I = 4.1734%

Semiannual YTM = 4.1734%
Annual YTM = 2 * 4.1734%
Annual YTM = 8.3468%

Before-tax Cost of Debt = 8.3468%
After-tax Cost of Debt = 8.3468% * (1 - 0.22)
After-tax Cost of Debt = 6.51%

Total Value of Debt = $23,144,000 + $39,984,000 + $48,880,000 + $65,658,000
Total Value of Debt = $177,666,000

Weight of Bond 1 = $23,144,000 / $177,666,000
Weight of Bond 1 = 0.1303

Weight of Bond 2 = $39,984,000 / $177,666,000
Weight of Bond 2 = 0.2250

Weight of Bond 3 = $48,880,000 / $177,666,000
Weight of Bond 3 = 0.2751

Weight of Bond 4 = $65,658,000 / $177,666,000
Weight of Bond 4 = 0.3696

After tax Cost of Debt = (Weight of Bond 1* After Tax Cost of Debt of Bond 1) + (Weight of Bond 2* After Tax Cost of Debt of Bond 2) + (Weight of Bond 3* After Tax Cost of Debt of Bond 3) + (Weight of Bond 4* After Tax Cost of Debt of Bond 4)
After Tax Cost of Debt = (0.1303 * 6.03%) + (0.2250 * 6.00%) + (0.2751 * 6.22%) + (0.3696 * 6.51%)
After Tax Cost of Debt = 6.25%