Answer to Question #121979 in Financial Math for Jain

Question

Explain in a paragraph of about 100-150 words when and why would a bond be sold on a premium or discount? You may use graphs, equations, or other aids to assist your explanation.

Answer 1

The discount, or premium, when buying a bond is the difference between the nominal price of the bond and the cost of its purchase. If paper is sold cheaper than face value, then they say that it is sold at a discount, and if it is more expensive, then with a premium.

Each bond has its own nominal value, that is, the amount that the issuer must pay to the investor at maturity. At the same time, the market value of the security differs from the nominal, primarily because the coupon size is determined when the security is issued, and lending rates are constantly changing. In addition, the market situation of the borrower and the level of trust in it may change. To compensate for these changes helps increase or decrease the price of bonds.

For example, a company issued bonds with a yield of 10%. But there have been changes in the market. Suppose that the normal rate is close to 7% per annum. It is profitable for an investor to buy this security, the demand for it is great. And then the market reevaluates the bond, its price rises by the difference between the coupon interest and the market one, that is 10-7 = 3%. Most likely, such a bond will be sold with a premium of 3% of the face value.

The converse is also true. Suppose a bond is issued with a coupon of only 3%, that is, with an interest payment that is obviously lower than the market one - it would be uninteresting for investors to invest money for such income. And then the bond will be sold cheaper than face value, that is, at a discount. The size of this discount will be such that the income from investing in the securities of this issuer is at the level of profit from investments in similar alternative assets.

Moreover, bonds are issued without coupon payments at all, the so-called coupon-free. In this case, all investor income consists of a discount. In order to calculate the total yield of such a bond, it is necessary to divide the discount by face value, without forgetting to make an adjustment for the period until the bond's maturity in order to obtain an annualized percentage.