Question

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

Bond		Coupon Rate				Price Quote				Maturity			Face Value
1			5.00	%			103.18			5	years		$	45,000,000
2			7.10				112.80			8	years			40,000,000
3			6.30				107.45			15	1/2 years			50,000,000
4			5.90				102.75			25	years			65,000,000

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 = $45,000,000
Current Price = 103.18% * $45,000,000 = $46,431,000

Annual Coupon Rate = 5%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50% * $45,000,000 = $1,125,000

Time to Maturity = 5 years
Semiannual Period to Maturity = 10

Let semiannual YTM be i%

$46,431,000 = $1,125,000 * PVIFA(i%, 10) + $45,000,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -46431000
PMT = 1125000
FV = 45000000

I = 2.1433%

Semiannual YTM = 2.1433%
Annual YTM = 2 * 2.1433%
Annual YTM = 4.2866%

Before-tax Cost of Debt = 4.2866%
After-tax Cost of Debt = 4.2866% * (1 - 0.22)
After-tax Cost of Debt = 3.34%

Bond 2:
Face Value = $40,000,000
Current Price = 112.80% * $40,000,000 = $45,120,000

Annual Coupon Rate = 7.10%
Semiannual Coupon Rate = 3.55%
Semiannual Coupon = 3.55% * $40,000,000 = $1,420,000

Time to Maturity = 8 years
Semiannual Period to Maturity = 16

Let semiannual YTM be i%

$45,120,000 = $1,420,000 * PVIFA(i%, 16) + $40,000,000 * PVIF(i%, 16)

Using financial calculator:
N = 16
PV = -45120000
PMT = 1420000
FV = 40000000

I = 2.5646%

Semiannual YTM = 2.5646%
Annual YTM = 2 * 2.5646%
Annual YTM = 5.1292%

Before-tax Cost of Debt = 5.1292%
After-tax Cost of Debt = 5.1292% * (1 - 0.22)
After-tax Cost of Debt = 4.00%

Bond 3:
Face Value = $50,000,000
Current Price = 107.45% * $50,000,000 = $53,725,000

Annual Coupon Rate = 6.30%
Semiannual Coupon Rate = 3.15%
Semiannual Coupon = 3.15% * $50,000,000 = $1,575,000

Time to Maturity = 15.5 years
Semiannual Period to Maturity = 31

Let semiannual YTM be i%

$53,725,000 = $1,575,000 * PVIFA(i%, 31) + $50,000,000 * PVIF(i%, 31)

Using financial calculator:
N = 31
PV = -53725000
PMT = 1575000
FV = 50000000

I = 2.7879%

Semiannual YTM = 2.7879%
Annual YTM = 2 * 2.7879%
Annual YTM = 5.5758%

Before-tax Cost of Debt = 5.5758%
After-tax Cost of Debt = 5.5758% * (1 - 0.22)
After-tax Cost of Debt = 4.35%

Bond 4:
Face Value = $65,000,000
Current Price = 102.75% * $65,000,000 = $66,787,500

Annual Coupon Rate = 5.90%
Semiannual Coupon Rate = 2.95%
Semiannual Coupon = 2.95% * $65,000,000 = $1,917,500

Time to Maturity = 25 years
Semiannual Period to Maturity = 50

Let semiannual YTM be i%

$66,787,500 = $1,917,500 * PVIFA(i%, 50) + $65,000,000 * PVIF(i%, 50)

Using financial calculator:
N = 50
PV = -66787500
PMT = 1917500
FV = 65000000

I = 2.8462%

Semiannual YTM = 2.8462%
Annual YTM = 2 * 2.8462%
Annual YTM = 5.6924%

Before-tax Cost of Debt = 5.6924%
After-tax Cost of Debt = 5.6924% * (1 - 0.22)
After-tax Cost of Debt = 4.44%

Total Value of Debt = $46,431,000 + $45,120,000 + $53,725,000 + $66,787,500
Total Value of Debt = $212,063,500

Weight of Bond 1 = $46,431,000 / $212,063,500
Weight of Bond 1 = 0.2190

Weight of Bond 2 = $45,120,000 / $212,063,500
Weight of Bond 2 = 0.2128

Weight of Bond 3 = $53,725,000 / $212,063,500
Weight of Bond 3 = 0.2533

Weight of Bond 4 = $66,787,500 / $212,063,500
Weight of Bond 4 = 0.3149

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 = (0.2190 * 3.34%) + (0.2128 * 4.00%) + (0.2533 * 4.35%) + (0.3149 * 4.44%)
After Tax Cost of Debt = 4.08%