Question

A bond has a face value (and redemption value) of $504,000, and pays coupons annually. The effective annual yield is 2 times the coupon rate. The present value of the redemption amount is 2 times the present value of the coupon stream. What is the price of the bond?

Answer 1

The face value of the bond (or redemption value) is $504,000.
The effective annual yield (EAY) is 2 times the coupon rate. [ Mathematically, we can express this as:

EAY = 2 * (C / $504,000)

Simplifying this equation, we get:

C = EAY * ($504,000 / 2) = 0.02 * $252,000 = $5,040

The present value of the redemption amount is 2 times the present value of the coupon stream. Mathematically, we can express this as:

PV(redemption) = 2 * PV(coupons)

Using the formula for the present value of an annuity, we can write:

PV(coupons) = C * (1 - (1 + r)^(-n)) / r
So, we have:

r = EAY = 0.04

Substituting the values we know, we get:

PV(coupons) = $5,040 * (1 - (1 + 0.04)^(-n)) / 0.04

PV(redemption) = 2 * $5,040 * (1 - (1 + 0.04)^(-n)) / 0.04
Simplifying this expression, we get:

Price = $5,040 * (1 + 2/(1+0.04)^n) * (1 - (1 + 0.04)^(-n))

Solving this equation for n, we find that n is approximately 18.1 years.

Therefore, the price of the bond is:

Price = $5,040 * (1 + 2/(1+0.04)^18.1) * (1 - (1 + 0.04)^(-18.1)) = $473,212.42

Therefore, the price of the bond is approximately $473,212.42. ]

Answer 2

$288,009.26

Step-by-step explanation:

Present value on Face value = 3 x Present value of the coupon stream

F / (1+i) = 3 x CF / (1+i)

3C = 1

C = 0.3333 = 33.33%

i = 4 x C = 4 x 33.33% = 133.32%

P = {CF / (1+i)} + {F / (1+i)}

= {0.3333 X 504000 / (1 + 1.3332)} + {504000 / ((1 + 1.3332))}

= $288,009.26