Question

The questions below are all based on the following assumptions:

1. Assume you are the CFO of a publicly traded corporation

2. Assume you are seeking to borrow and/or raise some money

3. Assume you have two options:

Option A: Sign with a bank for a 30-yr $100,000 bank loan at 3% APR

Option B: Issue a 30-yr $100,000 bond with a 3% coupon rate

Question 1) Which of the two options has the higher duration?

Question 2) In which of the options would you pay more interest over the full 30 years?

Question 3) Assuming that you knew interest rates were going to increase in the future, which of the two options would provide you with more free cash flow and flexibility to re-invest at the higher interest rate over the first 20 years?

Answer 1

Question 1)

The duration is a measure that gives the approximate sensitivity of the bond value to the changes in interest rates. As the interest rate changes, the bond value also changes. The change depends on the interest rate, frequency of interest, number of periods and price of the bond. Duration is also the period. Hence, the duration of a bond depends on all these parameters like coupon rate, maturity, frequency of payment etc.

In the question above, if the interest frequency is annual for both the bank loan and the bond, then the two securities are identical from the perspective of duration measure. Hence, the duration will be same for both the securities or liabilities.

However, if the bond pays coupon semi-annual which is usually the case, then the duration of the bond will be LESS than the duration of the bank loan. This is because the price sensitivity of the bond will be greater with its greater interest frequency even though the annual rate is same. To understand this, you also need to remember another concept behind duration which is actually its purpose. This is about interest rate risk and reinvestment risk. The duration measure of a bond can also be defined as the measure which when kept equal to the investment horizon, the interest rate risk and reinvestment risk will be eliminated.

The reinvestment risk will be greater whenever the frequency of interest payments is higher as there is a more probability that greater amount of interest may be reinvested at a lower than the yield. Hence, duration of a security when calculated can be shown to be always lower whenever its interest payment frequency is greater.

Hence, if the bond requires payment of interest semi-annual as against annual interest required for bank loan, then the duration of the bond will be LESS than the duration of the bank loan.

2) Since the bond requires semi-annual coupon, its effective interest rate will be greater than the bank loan, due to compounding effect, as bank loan only requires annual interest payment, even though annual nomial interest rates are same. Your net interest cost will be higher whenever the interest frequency is higher for same nominal annual interest. Hence, you will end up paying more interest in the case of a bond than the bank loan.

3) If the interest rates are going to increase in the future, bank loan offers higher flexibility since it requires annual interest payment as against bond which might require semi-annual coupon. Instead of paying interest semi-annual, the interest can be kept in money market instruments to earn higher interest than bank loan interest, to be paid at the end of the year. Hence, bank loan with lesser frequency of payment would allow highe flexibility for reinvestment of idle cash.

(Note however, the answer is opposite in the case of interest rates coming down. If you project that interest rates will fall over the future years, in order to take benefit of the fall in interest rate, if only you had taken debt by issuing bonds, you can call off the bonds and redeem them and issue new bonds with lower interest for remaining years. However, a bank loan may not necessarily offer a pre-closure and even if it offers, it might attract a hefty penalty. Hence, raising debt by issue of debt securities (with call / put options) will provide you with greater flexibility than raising bank loan especially if you predict interest rates to fall down in future)