Question

Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated portfolio since the proceeds of the portfolio are dedicated to the future liability. In such a case, the portfolio is subject to reinvestment risk. Reinvestment risk occurs because the company will be reinvesting the coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will be reinvested at a lower interest rate, which will result in a portfolio value that is lower than desired at maturity. Of course, if interest rates increase, the portfolio value at maturity will be higher than needed.

Suppose Ice Cubes, Inc. has the following liability due in five years. The company is going to buy bonds today in order to meet the future obligation. The liability and current YTM are below.

Amount of liability: $100,000,000
Current YTM: 8%

At the current YTM, what is the face value of the bonds the company has to purchase today in order to meet its future obligation? Assume that the bonds in the relevant range will have the same coupon rate as the current YTM and these bonds make semiannual coupon payments.

Assume that the interest rates remain constant for the next five years. Thus, when the company reinvests the coupon payments, it will reinvest at the current YTM. What is the value of the portfolio in five years?

Assume that immediately after the company purchases the bonds, interest rates either rise or fall by one percent. What is the value of the portfolio in five years under these circumstances?

Answer 1

Question 1 - Face value of bond if company has to purchase today to meet future obligation

Lets understand few variables related to bond pricing -

1. Future value, FV - This is an amount bondholder is supposed to receive at the end of maturity - here its 100,000,000

2. Maturity, M - Total time period of investment - 5 years

3. Coupon, C - Intermediate payments received at regular intervals, in this example - C is equal to YTM on semi annual basis, hence YTM = 5% and considering semi annual time period, C = 8%/2 = 4%

4. Interest rate, I - stands for interest rate earned on bond - YTM = 8%

5. Present value, PV refers to present value to be invested today in order to earn FV at maturity. Here we need to calculate PV of the bond,

Formula for PV = C1/(1+I)^(m/2) + C2/(1+I)^(m/2) +....+C9/(1+I)^(m/2) + FV/(1+I)^m/2

inputting value in above formula, PV = 4%*100,000,000/(1+2.5%)^1...similarly defining other equations

The face value of bond = 100,000,000

This is because the coupon payments are equivalent to YTM of the bond. Hence based on time value of money concept, whatever interest is earned from market is paid in the form of coupon and hence FV= PV

In case of financial calculation, the value can be used in TVM as = FV = 100,000,000 I/Y = 4%, N=10, PMT = 4,000,000 CPT PV

Question 2

YTM assumes that the coupon payments received are reinvested at same interest rate. Hence considering interest rates remain constant for the year, the value of the bond will not change.

Question 3

If interest rate rise by 1% hence instead of 8% it becomes 9%

The TVM calculation changes as follows:

FV = 100,000,000 I/Y = 4.5%, N=10, PMT = 4,000,000 CPT PV Here PV = 96,043,640

As interest rate in market is higher compared to coupon payments, it will be sold at discount.

If interest rate drop by 1%, instead of 8% its 7%

FV = 100,000,000 I/Y = 3.5%, N=10, PMT = 4,000,000 CPT PV Here PV = 104,158,302

As interest rate in market is lower compared to coupon payments, it will be sold at premium.

Please feel free to drop comments in case of any questions.