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

$1086 approx.

Step-by-step 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) = (C)/((1\ +\ YTM)^(1) ) \ +\ (C)/((1\ +\ YTM)^(2) ) \ +.....+ (C)/((1\ +\ YTM)^(n) ) \ +\ (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) = (37.5)/((1\ +\ .022)^(1) ) \ +\ (37.5)/((1\ +\ .022)^(2) ) \ +.....+ (37.5)/((1\ +\ .022)^(6) ) \ +\ (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.