Question

 Calculate the value of a

​$5,000​-par-value

bond paying quarterly interest at an annual coupon interest rate of

10​%

and having

10

years until maturity if the required return on​ similar-risk bonds is currently a

12​%

annual rate paid

quarterly

The present value of the bond is

​$ ?

Answer 1

Present value of bond = Coupon * ((1 - (1/(1+i)^n)) / i) + Par value * (1 / (1+i)^n)

Here,

Par value = $5,000

i (Required return quarterly) = 12% * 3/12 months

i = 3% or 0.03

n (periods) = 10 years * 4 (quarter) = 40

Coupon = Par value * Coupon rate quarterly

Coupon = $5,000 * 10% * 3/12 months

Coupon = $125

Now, put the above values into formula,

Present value of bond = $125 * ((1 - (1/(1+0.03)^40)) / 0.03) + $5,000 * (1/(1+0.03)^40)

Present value of bond = $125 * ((1 - 0.3066)/0.03) + ($5,000 * 0.3066)

Present value of bond = ($125 * 23.11) + $1,533

Present value of bond = $2,888.75 + $1,533

Present value of bond = $4,421.75