Question

(a)Suppose a 10 percent coupon, $1,000 bond with ten years left to maturity is selling for

$1,200. What is the yield, assuming that interest is paid semi-annually?

If, in part (a), the 10 percent coupon was paid quarterly on the bond, what would the bond

sell for, given that the effective annual yield remained unchanged?

If, in part (a), the 10 percent coupon was paid monthly on the bond, what would the bond

sell for, given that the annual yield remained unchanged.

Answer 1

a) # of semiannuals left to maturity, NPER Semiannual coupon Payment, PMT Bond's current selling price, PV Bond's maturity value at the end, FV Semiannual coupon type, TYPE Bond's Semiannual YTM Number of semiannuals in a year Bond's annual yield to maturity (YTM) 20 [10 years x 2] $50 ($1,000 x 10% / 2] $1,200 $1,000 [Par value of the bond] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period 3.5823% [Ref: EXCEL SCREENSHOT] 7.16% [3.5823% x 2] EXCEL SCREENSHOT: Bond's Semiannual YTM is calculated using EXCEL FUNCTION RATE(nper,pmt,pv,fv,type) where nper=20; pmt=-50; pv=1200; fv=-1000; type=0; Here, pmt & fv are negative as they denote cash inflows; pv is positive as it denotes cash outflow; type = 0 as coupons pad at the end of each semiannual only. D E F G H I 1 # of semiannuals left to maturity, NPER =10*2 [10 years x 2] 2 Semiannual coupon Payment, PMT =1000*10%/2 ($1,000 x 10% / 2] 3 Bond's current selling price, PV $1,200 Bond's maturity value at the end, FV $1,000 [Par value of the bond] Semiannual coupon type, TYPE 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period 6 Bond's Semiannual YTM =RATE(B1,-B2,B3,-B4,B5) [Ref: EXCEL SCREENSHOT] 7 Number of semiannuals in a year 8 Bond's annual yield to maturity (YTM) =B6*B7 [3.5823% x 2]

b&c) Periodic yield to maturity, RATE # of periods to maturity, NPER Periodic coupon payment, PMT Bond's maturity value at the end, FV Periodic coupon type, TYPE Bond should sell at Part-(b) Part-(c) 1.7911% 0.5970% [For Part-(b): 3.5853%/2 = 1.7911%; For Part-(c): 3.5823%/6 = 0.5970%] 40 120 [For Part-(b): 10 years x 4 = 40; For Part-(c): 10 years x 12 = 120] $25 $8.33 [For Part-(b): $1,000 x 10% / 4 = $25; For Part-(c): $1,000 x 10% / 12 = $8.33] $1,000 $1,000 [Par value of the bond] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. $1,201.21 $1,202.03 [Ref: NOTE] NOTE: For Part-(b): 'Bond should sell at' is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=1.7911%; nper=40; pmt=-25; fv=-1000; type=0; Here, pmt & fv are negative as they denote cash inflowz; type=0 as coupons are paid at the end of each semiannual only. For Part-(c): 'Bond should sell at' is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=0.5970%; nper=120; pmt=-8.33; fv=-1000; type=0; Here, pmt & fv are negative as they denote cash inflowz; type=0 as coupons are paid at the end of each semiannual only. Α. 2 Periodic yield to maturity, RATE 3 # of periods to maturity, NPER 4. Periodic coupon payment, PMT 5 Bond's maturity value at the end, FV 6 Periodic coupon type, TYPE 7 Bond should sell at Part-(b) =3.5853%/2 =10*4 =1000*10%/4 $1,000 0 =PV(B2,B3,-B4,-B5,36) D F G H I I J K L Part-(c) =3.5853%/6 [For Part-(b): 3.5853%/2 = 1.7911%; For Part-(c): 3.5823%/6 = 0.5970%] = 10*12 [For Part-(b): 10 years x 4 = 40; For Part-(c): 10 years x 12 = 120] =1000*10%/12 [For Part-(b): $1,000 x 10% / 4 = $25; For Part-(c): $1,000 x 10% / 12 = $8.33] $1,000 [Par value of the bond] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. =PV(C2,C3,-C4,-C5,C6) [Ref: NOTE]