Respuesta :
Answer:
$1086 approx.
Explanation:
Given: Coupon rate 7.5 % per annum i.e 3.75% semi annually
YTM = 4.4% per annum i.e 2.2% semi annually
Face value: $1000 (assumed)
No of periods to maturity = 3 years × 2 half years = 6 periods
Value of a bond is given by the following equation
[tex]B_{0} = \frac{C}{(1\ +\ YTM)^{1} } \ +\ \frac{C}{(1\ +\ YTM)^{2} } \ +.....+ \frac{C}{(1\ +\ YTM)^{n} } \ +\ \frac{RV}{(1\ +\ YTM)^{n} }[/tex]
where [tex]B_{0}[/tex] = Market value of bond
C= Coupon payment each period
YTM = Yield to maturity rate
n= no of periods
Hence, [tex]B_{0} = \frac{37.5}{(1\ +\ .022)^{1} } \ +\ \frac{37.5}{(1\ +\ .022)^{2} } \ +.....+ \frac{37.5}{(1\ +\ .022)^{6} } \ +\ \frac{1000}{(1\ +\ .022)^{6} }[/tex]
= 5.5638 × 37.5 + 1000 × .8776
= 208.64 + 877.60
= 1086.24
Market value of the bond is $1086 approx
This means, the bond is valued above par or priced at a premium. The reason being, it's rate of coupon payments being higher than it's yield to maturity rate.
