Question

8. The 10 year IBM corporate bond you purchased is contracted to pay a semi-annual 6.75% coupon. If you purchase this bond for $1,089.64 it will have a yield to maturity of 5.569%. What is the expected capital gain or loss for the first year holding period?

(a) a capital loss of 0.62% (b) a capital loss of 1.18% (c) a capital loss of 3.40% (d) a capital gain of 1.18% (e) a capital gain of 0.62%

Answer 1

Capital gain yield = Change in bond price / Initial price paid for bonds Change in bond price Initial price paid for bonds Capital gain yield $6.93 [Ref: Workings] $1,089.64 -0.62% ($6.93 / $1089.64) x 100] --> Option-(a) Negative capital gain yield implies this bond suffers from a capital loss of 0.62% for the first year holding period. Workings:

Semiannual Yield to Maturity, RATE # of semiannuals to maturity, NPER Semiannual coupons payments, PMT Bond's Maturity Value at the end, FV Semiannual coupon type, TYPE Bond's price after 1 year from now 2.7845% [5.569% / 2 --> Annual interest rate is converted into semiannual rate] 18 [9 years x 2 --> As there will be 2 semiannual per year & 1 year would be elapsed out of 10 years] $33.75 ($1000 x 6.75%/2 --> As coupons are payable semiannually at coupon rate on bond's par value] $1,000 [Par value at maturity] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. $1,082.71 [Ref: NOTE] Therefore, change in bond price -$6.93 ($1082.71 - $1089.64] NOTE: Bond Price after 1 year from now is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=2.7845%; nper=18; pmt=-33.75; fv=-1000; type=0; Here, pmt & fv are negative as they denote cash inflow; type=0 as coupons are paid at the end of each year only. А L 1 Semiannual Yield to Maturity, RATE 2 # of semiannuals to maturity, NPER 3 Semiannual coupons payments, PMT 4 Bond's Maturity Value at the end, FV 5 Semiannual coupon type, TYPE 6 Bond's price after 1 year from now в C D E F G H I J K =5.569%/2 [5.569% / 2 --> Annual interest rate is converted into semiannual rate] =9*2 [9 years x 2 --> As there will be 2 semiannual per year & 1 year would be elapsed out of 10 years] =1000*6.75%/2 ($1000 x 6.75% / 2 --> As coupons are payable semiannually at coupon rate on bond's par value] $1,000 [Par value at maturity] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. =PV(B1,B2,-B3,-B4,B5) [Ref: NOTE]