Question

Sunland, Inc., has issued a three-year bond that pays a coupon rate of 7.5 percent. Coupon payments are made semiannually. Given the market rate of interest of 4.4 percent, what is the market value of the bond?

Answer 1

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

$B_{0} = \frac{C}{(1\ +\ YTM)^{1} } \ +\ \frac{C}{(1\ +\ YTM)^{2} } \ +.....+ \frac{C}{(1\ +\ YTM)^{n} } \ +\ \frac{RV}{(1\ +\ YTM)^{n} }$

where $B_{0}$ = Market value of bond

          C= Coupon payment each period

          YTM = Yield to maturity rate

          n= no of periods

Hence,  $B_{0} = \frac{37.5}{(1\ +\ .022)^{1} } \ +\ \frac{37.5}{(1\ +\ .022)^{2} } \ +.....+ \frac{37.5}{(1\ +\ .022)^{6} } \ +\ \frac{1000}{(1\ +\ .022)^{6} }$

= 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.