Question

NTR issue a bond in January 2014 in the UK that has coupon of 3% paid annually and the face value of $10,000. The face value is paid out in December 2019.

Required:

a.If the interest rate is 4% at the time of issue, determine the bond price.

b.If the interest rate reduces to 3% after one year, determine the total rate of return if you sell the bond at the market.

Answer 1

a) Aannual Yield to Maturity, RATE # of years to maturity, NPER Annual coupons payments, PMT Bond's Maturity Value at the end, FV Annual coupon type, TYPE Bond's price when it was issued in 2014 4% [Annual interest rate] 6 [Time gap between Jan. 1, 2014 and Dec. 31, 2019 --> 1 year will be counted for 2014 also] $300 ($10,000 x 3% --> Coupons are payable on bond's par valueat annual coupon rate) $10,000 [Par value recievable at the end] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. $9,475.79 [Ref: NOTE] EXCEL SCREENSHOT: Bond's price when it was issued in 2014 is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=4%; nper=6; pmt=-300; fv=-10000; type=0; Here, pmt & fv are negative as they denote cash inflow; type=0 as coupons are paid at the end of each period only. B. 1 Aannual Yield to Maturity, RATE 2 # of years to maturity, NPER 3 Annual coupons payments, PMT 4 Bond's Maturity Value at the end, FV 5 Annual coupon type, TYPE 6 Bond's price when it was issued in 2014 D E F F G G H I J K 4% [Annual interest rate) =(2019-2014)+1 (Time gap between Jan. 1, 2014 and Dec. 31, 2019 --> 1 year will be counted for 2014 also] =10000*3% ($10,000 x 3% --> Coupons are payable on bond's par valueat annual coupon rate] $10,000 [Par value recievable at the end] 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]

b) Total rate of return (Holding Period Return) = (Change in Bond Price + Annual Coupon Payments Received) / Initial Price paid for bonds Change in bond price Annual coupon payments received Initial price paid for bonds Total rate of return earned in 1 year $524.21 ($10000 - $9475.79 --> As per workings below] $300 ($10,000 x 3% --> Coupons are payable on bond's par valueat annual coupon rate] $9,475.79 [As calculated in Part-(a)] 8.70% (($524.21 + $300) / $9475.79) x 100 = ($824.21 / $9475.79) x 100 = 0.087 x 100 = 8.70%] Workings:

Aannual Yield to Maturity, RATE # of years to maturity, NPER Annual coupons payments, PMT Bond's Maturity Value at the end, FV Annual coupon type, TYPE Bond's price after one year 3% [Annual interest rate] 5 [Time gap between Dec. 31, 2014 and Dec. 31, 2019 --> 1 year would be elapsed] $300 ($10,000 x 3% --> Coupons are payable on bond's par valueat annual coupon rate] $10,000 [Par value recievable at the end] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. $10,000.0 [Ref: NOTE] EXCEL SCREENSHOT: Bond's price after one year is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=3%; nper=5; pmt=-300; fv=-10000; type=0; Here, pmt & fv are negative as they denote cash inflow; type=0 as coupons are paid at the end of each period only. A 1 Aannual Yield to Maturity, RATE 2 # of years to maturity, NPER 3 Annual coupons payments, PMT 4 Bond's Maturity Value at the end, FV 5 Annual coupon type, TYPE 6 Bond's price after 1 year B C D E F H I J 3% [Annual interest rate] = (2019-2014) [Time gap between Dec. 31, 2014 and Dec. 31, 2019 --> 1 year would be elapsed] =10000*3% ($10,000 x 3% --> Coupons are payable on bond's par valueat annual coupon rate) $10,000 [Par value recievable at the end] 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]