How to work out the “magic price” of a bond

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

11 October 2009

Last week, we calculated the price at which an investor can sell a KenGen Infrastructure Bond and recover the interest earned up to the date of selling. It turned out that the (fair) selling price depends on the date that the sale is concluded.

The calculation revealed that on the first trading day (9th November 2009), the fair selling price of this bond will be Sh100.24 per Sh100 of face value. We may want to know what kind of return the buyer will realise at that price.

For the buyer, the important period is the number of days remaining until the next interest payment. Now the interest will be paid on 30th April 2010 – 176 days from the first trading day (9th November 2009).

Therefore the buyer will calculate the return for the first period as follows: First divide the interest paid (Sh6,250) by the amount invested (Sh100,240); then multiply the result by 100 percent. The answer is 6.24 percent.

The next step is to “annualise” this value. This is done by first dividing 6.24 percent by the number of days remaining (176); then multiplying the result by 365 days (one year). The answer is 12.93 percent.

Now that’s an interesting outcome: it is not only higher than the return gained by the seller, but also greater than that offered by the bond itself! Remember; the quoted interest rate is 12.5 percent.

This leads to an interesting question: if the buyer wanted to get an annualised return of 12.5 percent during the 176 days remaining till the next interest payment, how much would they offer for the bond in this secondary market?

The calculation is similar to previous one only that, this time, the price is the unknown. Thus we start by dividing the interest (Sh6,250) by 12.5 percent; then we divide the answer the days remaining (176); and finally multiply the result by 365 days of the year.

The answer is that at Sh103.693 per Sh100, the buyer makes an annualised return equal to the 12.5 percent paid by the bond. At this price, the seller will be making the equivalent of 192 percent per annum!

Think about it this way: he only keeps the Sh100,000 in the bond for seven days and makes Sh3,693 out of it. That is very good by any standards. It is more than what you might expect to get by investing the same amount in a Treasury Bill for three months!

Now it is important to recapitulate the findings so far:

First: if the seller wants to get just the interest earned on the date of selling, then he asks for Sh100.24 per Sh100. At that price, the buyer makes an annualised return equivalent to 12.93 percent.

Second: if the buyer wants to earn the same rate of interest as that offered by the bond, then he offers Sh103.693 per Sh100. At that price, the seller’s annualised return will be 192 percent.

It is clear, then, that somewhere between Sh100.24 and Sh103.693 there must be a “magic price” that gives both the buyer and the seller equal annualised returns. The process of determining that value is not straightforward. It can be done by trial and error starting from Sh100.24 working upwards in increments of, say one cent.

A more elegant method would involve writing down the equations for the returns realised by the buyer and the seller at different prices; then equating the formulae and extracting the magic price.

The result (by either method) is that on 9th November 2009, a price of Sh100.248 per Sh100, will give both the buyer and the seller the equivalent of 12.929 percent per annum…from a bond that pays 12.5 percent interest. Interesting, isn’t it?