Question

High Country Marketing Corp. issues a corporate bond that has a 10-year maturity
with a par value of $1,000 and pays interest semiannually. The quoted coupon rate is
6%.

(a) If the required rate of return on this bond is 8% per year. What should the issuing
price be?
(b) The bond is callable in 3 years at 110% of par. What is the bond's yield to call?
(c) Currently, the bond is having an ask price of $998.91, and the last coupon was
paid 35 days ago. What is the the invoice price of the bond? For simplicity,
assume there are 360 days in a year.

Answer 1

Answer :

(a.) Calculation of Issuing Price

Issuing Price = (Coupon * PVAF @ YTM for n years) + (Face value * PVF @ YTM for nth year)

where

Coupon = 1000 * 6% / 2 = 30 (As coupons paid semiannually)

YTM = 8% / 2 = 4% or 0.04 (As coupons paid semiannually)

n is the number of years to maturity i.e 10 * 2 = 20 (As coupons paid semiannually)

Face Value or Par value = 1000

Issuing Price = (30 * PVAF @ 4% for 20 years) + (1000 * PVF @ 4% for 20th year)

= (30 * 13.5903263437 ) + (1000 * 0.45638694612)

= 407.709790311 + 456.38694612

= 864.096736431 or 864.10

(b.) Calculation of Yield to call

Using Excel Function of RATE

=RATE(nper,pmt,pv,fv)

where nper is Number of years of call i.e 3 * 2 = 6 (As coupons paid semiannually)

pmt is Interest payment i.e 1000 * 6% =60/2 = 30 (As coupons paid semiannually)

pv is Current Market Price

= - 864.10 (calculated in part a)

Note : pv should be taken as negative.

fv is call price i.e 1100 (1000*110%)

=RATE(6,30,-864.10,1100)

therefore ,Yield to call is 7.26% (Semi annual)

Yield to call is 7.26% * 2 = 14.53% (Annual)

(c.) Calculation of Invoice Price = Ask Price + Last Coupon payment

As the bonds pay semiannual coupon number of days will be 180 days (360 / 2 )

Coupon = 1000 * 6% = 60 / 2 = 30 (As coupons paid semiannually)

Invoice Price = 998.91 + [30 * (35 / 180)]

= $1004.74