Options:
(A) 90 (B) 95 (C) 100 (D) 105 (E) 110
Answer:
(A) 90
Step-by-step explanation:
par value = $100
coupon rate 6%, semiannual
market price $110
YTM = 4%
similar coupon:
par value = $100
coupon rate 3%, semiannual
market price $???
YTM = 4%
first of all, since the market rate is higher than the coupon rate, the bond will be sold at a discount, therefore, options C, D and E can be eliminated.
that leaves us with options A ($90) and B ($95)
now we can use the YTM formula to find n for both options:
YTM = [coupon + [(face value - market value)/n]} / [(face value + market value)/2]
0.04 = 3 + [(100 - 90)/n]} / [(100 + 90)/2]
0.04 = (3 + 10/n) / 95
3.8 = (3n + 10) / n
3.8n = 3n + 10
0.8n = 10
n = 10/.8 = 12.5 years
0.04 = 3 + [(100 - 95)/n]} / [(100 + 90)/2]
0.04 = (3 + 5/n) / 95
3.8 = (3n + 5) / n
3.8n = 3n + 5
0.8n = 5
n = 5/.8 = 6.25 years
now we must replace n in the YTM formula for the first bond:
bond price $90
YTM = 3 + [(100 - 110)/12.5]} / [(100 + 110)/2]
YTM = 2.2 / 105 = 2.09% X 2 = 4.18% ≈ 4%
bond price $95
YTM = 3 + [(100 - 110)/6.25]} / [(100 + 110)/2]
YTM = 1.4 / 105 = 1.33% X 2 = 2.67% WRONG