Question

Question 2 (15 marks) Two years ago, MTR issued $1,000 ten-year bonds that carry a coupon rate of 8% payable semi-annually. Required: a. If you require an effective annual rate of return of 12%, how much are you willing to pay for the bond today? b. What will be the bond price if the yield to maturity falls to 6% in one year?. c. From the answer computed in above part (b), identify, with brief explanation (within 30 words), whether the bond is issued at par, premium or discount without involving any calculation.

Answer 1

Semiannual Yield to Maturity, RATE # of Semiannuals to Maturity, NPER Semiannual coupons, PMT Bond's Maturity Value at the end, FV Semiannual coupon payment type, TYPE Bond Price Part-(a) Today 6% 20 $40 $1,000 Part-(b) 1 year later 0.5% [Part-(a) = 12% / 2 = 6%; Part-(b) = 6% / 2 = 3%] 18 [Part-(a) = 10 semiannuals x 2 = 20; Part-(b) = 9 years x 2 = 18] $40 ($1,000 x 8% / 2 --> As there will be two semiannual coupon payments per year] $1,000 [Par value recievable at the end] 0 = 0 if paid at the end of each period; 1 if paid at the beginning of each period. $1,601.05 [Ref: NOTE] O $770.60 Part-(c): Bond is issued initially at discount because bond price of $770.60 is less than bond's par value of $1000; Bond is issued after 1 year at premium because bond price of $1601.050 is more than bond's par value of $1000; NOTE:

Bond Price Today is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=6%; nper=20; pmt=-40; fv=-1000; type=0; Here, pmt & fv are negative as they denote cash inflows; type=0 as coupons are paid at the end of each semiannual only. Bond Price 1 year later is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=0.5%; nper=18; pmt=-40; fv=-1000; type=0; Here, pmt & fv are negative as they denote cash inflows; type=0 as coupons are paid at the end of each semiannual only. Α. B 3 Semiannual Yield to Maturity, RATE 4 # of Semiannuals to Maturity, NPER 5 Semiannual coupons, PMT 6 Bond's Maturity Value at the end, FV 7 Semiannual coupon payment type, TYPE 8 Bond Price 9 E F G H I Part-(a) Part-(b) Today 1 year later =12%/2 =6%/12 [Part-(a) = 12% / 2 = 6%; Part-(b) = 6% / 2 = 3%] =10*2 =(10-1)*2 [Part-(a) = 10 semiannuals x 2 = 20; Part-(b) = 9 years x 2 = 18] =1000*8%/2 =1000*8%/2 [$1,000 x 8% / 2 --> As there will be two semiannual coupon payments per year] $1,000 $1,000 [Par value recievable at the end] 0 = 0 if paid at the end of each period; 1 if paid at the beginning of each period. =PV(B3,B4,-B5,-B6,B7) =PV(C3,C4,-C5,-C6,c7) (Ref: NOTE]