Question

percent: What is the yield to maturity on a 10-year, 9 percent annual coupon, $1,000 par value bond that sells for $887.002 That sells for $1,134.202 What does the fact that a bond sells at a discount or at a premium te e. (1) ll about the relationship between ra and the bond's coupon rate? you
I need all parts answered using step by step. Not excel. E 1&2 and also F.

Answer 1

e)

1)

time to maturity = n = 10 years

coupon rate , c = 9% = 0.09

par value of bond , m = $1000

coupon value, x = c*m = 0.09*1000 = 90

price, p = 887

yield to maturity(ytm1) = (x+((m-p)/n))/((0.6*m)+(0.4*p)) = (90+((1000-887)/10))/((0.6*1000)+(0.4*887)) = 0.1087 or 10.87% 0r 10.9% (after rounding off)

if price , p = 1134.20

yield to maturity(ytm2) = (x+((m-p)/n))/((0.6*m)+(0.4*p)) = (90+((1000-1134.20)/10))/((0.6*1000)+(0.4*1134.20)) = 0.0708 or 7.08% (after rounding off)

when a bond sells at

a) premium , rd < coupon rate

b) discount , rd > coupon rate

2)

current yield ( for p = 887) = x/p = 90/887 = 10.15% or 10.2%

current yield ( for p = 1134.20) = x/p = 90/1134.20 = 7.94% or 7.9%

capital gains yield ( for p = 887) = ytm1 - current yield = 10.9 - 10.2 = 0.7%

capital gains yield ( for p = 1134.20) = ytm1 - current yield = 7.08 - 7.94 = -0.86%

total return ( for p = 887) = ytm1 = 10.9%

total return ( for p = 1134.20) = ytm2 = 7.08%

F)

time until bond becomes callable , n = 5

call price , m = 1090

a) price, p = 887

YTC= (x+((m-p)/n))/((0.6*m)+(0.4*p)) = (90+((1090-887)/5))/((0.6*1090)+(0.4*887)) = 0.135% or 13.5%

if price , p = 1134.20

YTC = (x+((m-p)/n))/((0.6*m)+(0.4*p)) = (90+((1090-1134.20)/5))/((0.6*1090)+(0.4*1134.20)) = 0.073 or 7.3%

Note: the above formula used to calculate YTM and YTC is an approximate formula , and hence the answers will be approximates of the real values