Question

Arco Industries has a bond outstanding with 15 years to maturity, an 8.25% nominal coupon, semiannual payments, and a $1,000 par value. The bond has a 7.70% yield to maturity, but it can be called in 6 years at a price of $1,045. What is the bond's yield to call? Hint: Calculate the bond's price based on the YTM, and then use that price to find the YTC. Your answer should be between 4.08 and 10.64, rounded to 2 decimal places, with no special characters.

Answer 1

First we need to find the price of the bond assuming that it wont be called:

FV Price = Sum of Discounted coupons +7 (1 + frequency)" )-nx frequency 1- (1+ Price = Coupon x par valuex— - + 1000 1000 (1 + 0.077)15x2 frequency Price = (0.0825 x Price = 1048.43 100 1-(1 + 0.077)-15x2 2)x= 0.077 1000 + ( 0,077 15x2

r= YTM

Now using this price, we can calculate the YTC

Price = Sum of Discounted coupons +7 d coupons FV YTC )nx frequency (1+ Frequency 1-(1+ 1048.43 = Coupon x par valuex— YTC )-nx frequency frequency YTC frequency 1000 (1 + YTC )6x2 1000 1-(1 + YTC) -6x2 1048.43 = (0.0825 x 1000 (1 + YTC)6x2 YTC = 7.24%

YTC can be calculated using either a financial calculator or excel or through hit and trial:
Using Excel we get the YTC= 7.24% rounded to two decimal places

We can verify the same through the below schedule:

Year	CF	Discount Factor		Discounted CF
1	$       41.25	1/(1+0.0724054653114327)^1=	0.965062114	0.965062114280541*41.25=	$       39.81
2	$       41.25	1/(1+0.0724054653114327)^2=	0.931344884	0.931344884419628*41.25=	$       38.42
3	$       41.25	1/(1+0.0724054653114327)^3=	0.898805663	0.898805663282373*41.25=	$       37.08
4	$       41.25	1/(1+0.0724054653114327)^4=	0.867403294	0.867403293734611*41.25=	$       35.78
5	$       41.25	1/(1+0.0724054653114327)^5=	0.837098057	0.837098056585429*41.25=	$       34.53
6	$       41.25	1/(1+0.0724054653114327)^6=	0.80785162	0.807851620348466*41.25=	$       33.32
7	$       41.25	1/(1+0.0724054653114327)^7=	0.779626993	0.779626992758452*41.25=	$       32.16
8	$       41.25	1/(1+0.0724054653114327)^8=	0.752388474	0.752388473981651*41.25=	$       31.04
9	$       41.25	1/(1+0.0724054653114327)^9=	0.726101611	0.726101611461042*41.25=	$       29.95
10	$       41.25	1/(1+0.0724054653114327)^10=	0.700733156	0.700733156339102*41.25=	$       28.91
11	$       41.25	1/(1+0.0724054653114327)^11=	0.676251021	0.67625102140309*41.25=	$       27.90
12	$ 1,041.25	1/(1+0.0724054653114327)^12=	0.65262424	0.652624240499642*1041.25=	$     679.54
				Price = Sum of all Discounted CF	$ 1,048.43