Question

Question 11 5 pts Pandora Media plans to issue original issue discount (OID) bonds with a 20- year maturity, $1,000 par value, and initial yield to maturity of 8%. Since these bonds are issued below par, the total yield will come from both annual coupon payments and appreciation. If the bonds are offered at a discounted price of $840, what is their nominal coupon rate? That is, at this price, what coupon rate will result in a yield to maturity of 8%? Your answer should be between 5.12 and 8.74, rounded to 2 decimal places, with no special characters.

Answer 1

Value of bond = Interest x PVIFA(YTM%,n) + Redemption value x PVIF(YTM%,n)

Here YTM = 8% , n = no of year till maturity = 20 years

PVIFA(YTM%,n) = [1-(1/(1+r)^n / r]

PVIFA(8%,20) = [1-(1/(1+8%)^20 / 8%]

=[1-1/(1+0.08)^20 / 0.08]

=[1-1/(1.08)^20 / 0.08]

=[1-0.21455 / 0.08]

=[0.7855/0.08]

=9.8181

PVIF(YTM%,n) = 1/(1+r)^n

=1/(1+0.08)^20

=1/(1.08)^20

=0.21455

Thus Price of bond = Interest x 9.8181 + 1000 x 0.21455

=840 =Interest x 9.8181 + 214.55$

625.45 = Interest x 9.8181

Interest = 63.70 $

Thus original coupon rate = Interest / Face value of bond

=63.70/1000

=0.06370

i.e 6.37%