Question

Suppose that today's date is April 15. A bond with a 10% coupon paid semiannually every January 15 and July 15 is listed in The Wall Street Journal as selling at an asked price of 101:04. If you buy the bond from a dealer today,what price will you pay for it?

Answer 1

Answer:

$1,035.4

Explanation:

To find the purchase price of the bond for today April 15, we can follow the following formula:

Purchase price = Selling price + Accrued interest

Therefore, the steps to follow are these:

1. Calculate the selling price.

Theoretically, the selling price tells us how much cash the bond will generate, but brought to present value. To find it,  we should know what the par value of the bond and the asked price are. The question only give us the former (101.04). In this case, we will assume that the par or face value - the price at which the bond is sold when it is first released - is $ 1,000, which is the average face value of a bond in the United States.

Now, we apply the following formula:

Selling price (sp) = Par value * (Asked price / 100)

$sp = 1,000 * (101.04/100)$

$sp = 1,000 * (1.0104)$

$sp = 1,010.4$

2. Calculate the accrued interest.

The accrued interest is the part of the purchase price that represents the interest accrued from the last maturity of interest charged to the purchase date. To find it, we apply this formula:

$AC = \frac{D_{c} }{D_{t} } *C$

Where C is the amount of the coupon that is paid periodically (in this case semianually), Dc is the time elapsed since the last payment and Dt is the time between the semiannual payments.

For our case, C is 50. The statement says that the bond pays a 10% coupon, that is $ 100, which is distributed on two dates, therefore, what is paid on each date is $ 50.

The purchase was made on April 15, that is, three months had passed since the last payment, which was on January 15. Therefore Dc is 3.

Finally, the time between the first payment (January 15) and the second (July 15) is six months. Therefore, Dt is 6.

We replace in the equation:

$AC=\frac{3}{6} *50$

The accrued interest is $25.

3. Clear in the purchase price equation.

Purchase price (PP)= Selling price + Accrued interest

$PP=1,010.40+25$

$PP=1,035.4$

Therefore, the price you would pay for the bond today April 15 is 1,035.4. That means the purchase price is above the par value (1,000).