Prudential Insurance Company must pay you $50,000 once a year for a 2-year perio

Question

Prudential Insurance Company must pay you $50,000 once a year for a 2-year period. The first payment will be made in exactly 5 years. The yield curve is flat at 10%. What is the present value and duration of Prudential's obligation to you? (Hpoints) a. b. There are currently 2-year zero-coupon bonds and perpetuities sold in the market. How much of each of 2-year zeros and perpetuities (in present value) will Prudential want to hold to both fully fund and immunize your obligation? (6 points) Suppose that one year passed and the interest rate remains at 10%. Is the position still fully fuided? Is it still immunized? If not, what actions are required? points) c.

Explanation / Answer

a) Present Value of Obligation-

1st payment will be after 5 years , and discounted @ 10%

2nd Payment will be after 6 years , and discounted @ 10%

Year

Cash Flow

Discounted @ 10%

Weight of Payment

Weight * year

Year 5

50000

31046

0.52

2.62

Year 6

50000

28224

0.48

2.86

Total

100000

59270

1

5.48

So, Present Value of Obligation is $ 59270

Duration of obligation is 5.48 Years

b) Since Zero Coupon bonds are redeemed at once, It is assumed that 1st year's payment will be done with Zero Coupon Bond & Second Year's Payment will be done through perpetual Bond.

Present value of Zero Coupon Bond, with discount rate of 10%-

Obligation amount = 50000 discounted @ 10% for 2 years we get-

50000/1.10/1.10 = $ 41322.31

If Zero Coupon Bond is for 2 years period, the bond will be issued at Year 3, therefore it needs to be discounted for 3 years to get the Present value-

Therefore , PV of Zero Coupon bond- $ 31046

Valuation of perpetual Bond can be calculated using below formula-

Value = Yearly Cash flow/yield = 50000/0.1 = $ 500000

Discounted @ 10 % for present value for 6 years, because payment will be needed in 6th year -

Present value = $ 282236.965

c) If above method is used for funding, then the obligation will be fully funded & immunized even if the yield remains at 10% in the 2nd year. No further action would be required, but if interest rate changes, then there may be a need to further take action to fully fund the obligation

Year

Cash Flow

Discounted @ 10%

Weight of Payment

Weight * year

Year 5

50000

31046

0.52

2.62

Year 6

50000

28224

0.48

2.86

Total

100000

59270

1

5.48

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