Question

Below is the listing of a bond issued by International Business Machines Corporation (IBM). Below the detail of the bond is the information on a recent sale of part of the bond issue. Explain what the price of $148.850 on a $100 par value bond means in this purchase. Explain how the yield to maturity of 4.058% is calculated. Contrast that with the calculation of the current yield of 4.703%. Explain why it matters to know if the bond pays interest monthly, semi-annually or annually. This bond does not mature for almost 28 years. Explain the concept of interest rate risk in context with this bond for both the issuer and the investor. Rating Issuer – CUSIP Coupon Maturity Price Yield to Maturity A1 – Moody’s International Business 7.000% 10/30/2045 $148.850 4.058% Machines Corp (IBM) Current Yield Dated Minimun Size Coupon Pd Callable 4.703% 04/30/1996 5K Semi-Annual No

Answer 1

Market Price = $ 148.85, Par Value of the Bond = $ 100, Yield to Maturity = YTM = 4.058%

Let us assume that the bond maturity is 28 years (as mentioned in the problem)

The Market Price of the bond (or any financial asset for that matter) is calculated by summing the present value of all future cash flows expected to be generated by the bond. The present value of each cash flow is calculated using the appropriate discount factor. Now the appropriate discount factor for a bond is usually the interest rate prevailing at the time of each of the bond's cash flows. The same is taken from the yield curve which is essentially a prediction of the expected future interest rate over a period of time in the future. Once, the bond is price by discounting each cash flow with the interest rate prevailing at the time of these cash flows one gets the market price of the bond which happens to be $ 148.85 in this case. As the bond market value is above the par or face value it is said to be at a premium.

The YTM is calculated by considering that the bond has a fixed interest rate during the time of its existence. Hence, all of its interim cash flows (in the form of coupons and the final face value redemption) can be discounted at the same single interest rate which is what YTM is. In other words the YTM is the return or yield promised to a bond buyer if the bond is held to maturity, compounded annually and coupon paid yearly.

The YTM in this case would be calculated as given below:

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where YTM = 4.058% per annum with the Annual Coupon Payment = Annual Coupon Rate x Par Value

It must be noted that the annual coupon payment is annual coupon rate times the par value (and not market value) of the bond. The market value of the bond would fluctuate as at any point of time, the bond's remaining cash flows would be discounted at the expected interest rates prevailing then.

Also Current Yield is simply the ratio of a bond's periodic (in this case annual) coupon payment to that of its market price. It is a measure of an investor's return or yield for any period during the bond's tenure.

If the bond pays interest monthly, then it is compounded monthly which in turn means that the bond's YTM gets divided by 12 (as there are 12 months in a year) and tenure becomes 12 times of the tenure in years.

Similarly, for semi annual, quarterly or any other rate of compounding.

The interest rate risk of a bond is related to the inverse relationship of bond prices to existing interest rates(and therefore, their discount rates). Rising interest rates reduce present value of bond cash flows thereby depressing their prices and consequently value of bond investor's holding. This impact of fluctuating interest rate on bond investor portfolio value is known as the interest rate risk.