You are the financial manager in charge of the company pension fund at Cowboys I

Question

You are the financial manager in charge of the company pension fund at Cowboys Incorporated. You know that the fund must be sufficient to make the payments listed in the table below. Each payment must be made on the first day of each year, and today is currently the first day of Year 1. You are going to finance these payments by purchasing bonds, which operate differently from other investment tools: rather than allowing for any amount to be invested in the tool and then paying off only at one point it time, bonds can be purchased only in whole/integer values at a given price and then pay small amounts (coupons) over the course of several years and then pay back a larger amount at the end of the bond’s life. The prices and coupons for the bonds currently available are as follows: Bond X costs $980 in Year 1 and yields a $60 coupon in Years 2-5 and a $1,060 payment on maturity in Year 6; Bond Y costs $970 in Year 1 and yields a $65 coupon in Years 2-11 and a $1,065 payment on maturity in Year 12; and Bond Z costs $1,050 in Year 1 and yields a $75 coupon in Years 2-14 and a $1,075 payment on maturity in Year 15. For the sake of simplicity, assume the bond yields arrive on the first day of the year and can be used to make the pension fund payments. Additionally, you know that excess cash on hand will be placed in a savings account which earns an annual rate of 4. How would you allocate cash to meet the initial payment and buy enough bonds to make future payments? Construct and solve an Optimization model for this problem in Excel.

Year Pmt Year Payment Year Payments 1 $11000 6 $18,000 11 $25,000 2 12,000 7 20000 12 30000 3 14,000 8 21,000 13 31000 4 15000 9 22000 14 31000 5 16000 10 24000 15 31000

Explanation / Answer

A)

Year Years Remaining To Maturity Payment Reinvested Amount
t T=5-t 10%*1000 Payment*(1+10%)^T
1 4 100 146.41
2 3 100 133.1
3 2 100 121
4 1 100 110
5 0 1100 1100
Total Reinvested Amount 1610.51

Yes the pension fund shall have sufficient fund of $ 1610.51 to meet its future obligation of $ 1600 after 5 years.

b) Now suppose the interest rate moves down so that the yield to maturity(YTM ) is now just 5%. We recalculate the Reinvested amount at the new yield to maturity of 5% to get,

YTM decreases to 5%
Year Years Remaining To Maturity Payment Reinvested Amount
t T=5-t 10%*1000 Payment*(1+5%)^T
1 4 100 121.550625
2 3 100 115.7625
3 2 100 110.25
4 1 100 105
5 0 1100 1100
Total Reinvested Amount $                     1,552.56

Therefore when yield to maturity is moves down to 5% there are not sufficient fund available this is just $ 1552.56 not enough to meet the obligation of $ 1600.Her logic is not correct because just matching the horizon does not guarantee that the liability shall be met.What is required for immunization is that either the cash flows are matched for this she could have brought the 5 year zero coupon Bond so that the duration of bond is equal to the duration of liability which is 5 years or the Durations are matched. Here the coupon Bond Duration is lower as compared to the Duration of the liability which is 5 years therefore net Duration is negative.Thus any fall in the interest rate shall result in liability increasing by more amount as compared to the reinvested amount which result in funds fail to meet obligation. Thus there is risk of falling interest rate that can result in the reinvested amount failing to meet the liability.

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