Question

Zheng Enterprises, a multinational drug company specializing in Chinese medicines, issued $100 million of 15 percent coupon rate bonds in January 2011. The bonds had an initial maturity of 30 years. The bonds were sold at par and were callable in five years at 110 (that is, 110 percent of par value). It is now January 2016, and interest rates have declined such that bonds of equivalent remaining maturity now sell to yield 11 percent. How much would you be willing to pay for one of these bonds today? Why?

Answer 1

Sol:

Bond Issue value (FV) = $100 million or for simplification $1,000

Coupon rate = 15% = 1,000 * 15% = $150

Bond callable in five years for 110 percent of par value or = $1,100

Years to Maturity = 30 - 5 = 25 years

Yield = 11%

To compute how much you would be willing to pay for one of these bonds today (PV):

Present value (PV) = PMT * (1-(1+r)^-n)/r) + (FV/(1+r)^n)

Present value (PV) = 150 * (1-(1+11%)^-25)/11%) + (1000/(1+11%)^25)

Present value (PV) = 150 * (1-(1.11)^-25)/0.11) + (1000/(1.11)^25)

Present value (PV) = (150 * 8.4217) + 73.6081

Present value (PV) = 1,263.2617 + 73.6081

Present value (PV) = $1,336.87

Therefore the amount that you would be willing to pay will be $1,100 or a fraction higher than this, however it is nowhere near to the Present value of $1,336.87. This is due to the overhanging risk associated to the call of the bond.