Question

SHOW ALL WORK PLEASE QUESTION: An insurance company must make payments to a customer of $10...

SHOW ALL WORK PLEASE

QUESTION: An insurance company must make payments to a customer of $10 million in 5 years and $25 million in 30 years. The yield curve is flat at 8%.

A) What is the present value of its obligation?

B) What is the duration of its obligation?

C) If it wants to fully fund and immunize its obligation to this customer by buying a single issue of a zero-coupon bond, what face value the bond must have?

D) Suppose you buy a zero-coupon bond with value and duration equal to your obligation, and that rates immediately increase to 9%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation?

PLEASE SHOW WORK TO ALL PARTS AND MAKE SURE YOU CLEARLY LABEL THE ANSWER TO EACH PART

FOR EXAMPLE -

PART A= x

PART B=x

PART C=x

PART D=x

Homework Answers

Answer #1
Liabilities(L) Term(t) PV=L x 1.08^(-n) n x PV
10 5 6.81 34.03
25 30 2.48 74.53
Total 9.29 108.56

PART A

PV=L x r^(-n)

L- Liability amount

r - Rate of interest

n - Number of years

The present value of the obligations = $ 9.29 million

PART B

Duration = (n*PV) / PV

Duration = 108.56 / 9.29 = 11.69 years

Maturity of the zero coupon bond (ZCB) = duration of the liabilities calculated = 11.69 years

PART C

Face value of the ZCB that you will buy = PV * ( 1 + r )^d

Face value of the ZCB that you will buy = 9.29 x (1 + 8%)11.69 = $22.84

PART D

When YTM changes to 9%;

PV of the bonds = 22.84 / (1 + 9%)11.69 =   8.34

nd the PV of the obligations = 10 / (1 + 9%)5 + 25 / (1 + 9%)30 = 6.50 + 1.88 = 8.38

Hence, the net position = 8.34 - 8.38 = - $ 0.04 million

Thus the net position is a loss (reduction in value of) of $ 0.04 million.

Thank You....

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Additional Question 2: An insurance company must make payments to a customer of $10 million in...
Additional Question 2: An insurance company must make payments to a customer of $10 million in one year and $4 million in five years. The yield curve is flat at 10%. Use annual compounding. a) If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? b) What must be the face value and market value of that zero-coupon bond
An insurance company must make payments to a customer of $8 million in one year and...
An insurance company must make payments to a customer of $8 million in one year and $4 million in four years. The yield curve is flat at 9%. a. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? (Do not round intermediate calculations. Round your answer to 4 decimal places.) b. What must be the face value and market value of that...
1. You are managing a portfolio of $5 million. Your target duration is 10 years, and...
1. You are managing a portfolio of $5 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with a maturity of 5 years, and perpetuity, each currently yielding 8.00%. What weight of each bond will you hold to immunize your portfolio? (10 points) How will these weights change next year if the target duration is now 9 years? (15 points) If you do not rebalance your portfolio of immunizing assets over the...
You will be paying $8,600 a year in tuition expenses at the end of the next...
You will be paying $8,600 a year in tuition expenses at the end of the next two years. Bonds currently yield 7%. a. What is the present value and duration of your obligation? (Do not round intermediate calculations. Round "Present value" to 2 decimal places and "Duration" to 4 decimal places.) 1. Present Value = 2. Duration (in years) = b. What maturity zero-coupon bond would immunize your obligation? (Do not round intermediate calculations. Round "Duration" to 4 decimal places...
Part A. Suppose your firm has an obligation to pay an annuity with 18 annual payments...
Part A. Suppose your firm has an obligation to pay an annuity with 18 annual payments of $80,000. The first payment is due two years from today. Assume all interest rates are 11.5%. Write down the information requested on your answer sheet. What is the present value of the obligation? Round and express your answer to the nearest whole dollar (i.e., nearest integer). Do not include a dollar sign. Part B. What is the duration of the obligation? Please carry...
A corporate pension plan has to make the following payments over the next few years: Year...
A corporate pension plan has to make the following payments over the next few years: Year 1 2 3 4 Amount ($ million) 27 31 37 45 The appropriate interest rate is 7%. What is the present value of the liability (in $ million)? What is the duration of the liability? What is the duration of a perpetuity if the yield is 7%? The fund wants to immunize its interest rate risk by investing in a perpetuity and a 1-year...
You will be paying $12,400 a year in tuition expenses at the end of the next...
You will be paying $12,400 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%. a. What is the present value and duration of your obligation? (Do not round intermediate calculations. Round "Present value" to 2 decimal places and "Duration" to 4 decimal places.) Present value $ 22113 Duration 1.4808 years b. What is the duration of a zero-coupon bond that would immunize your obligation and its future redemption value? (Do not round...
Background: Suppose you will go to graduate school for 3 years beginning in year 5. Tuition...
Background: Suppose you will go to graduate school for 3 years beginning in year 5. Tuition is $25,109 per year, due at the end of each school year. Assume annual compounding. In the above description, if you see a flat yield curve of 0.08 for example, then it means that the yield at all maturities is 8%. Question: Suppose in the question above, the tuition obligations have a Macaulay duration of 6.36 in years, and that you wish to immunize...
You manage a pension fund that has a target duration of 10 years, you must immunize...
You manage a pension fund that has a target duration of 10 years, you must immunize your portfolio using two bonds. The first bond is a 6-year zero-coupon bond and the second bond is a perpetuity. Both securities have a 10% yield to maturity. What percentage of your assets will you invest in the zero-coupon bond?
An insurance company expects to make a one-time payout of $10 million dollars in exactly 6...
An insurance company expects to make a one-time payout of $10 million dollars in exactly 6 years to fulfil contractual agreements for an investment product. To create a portfolio that immunizes this liability, using only a 10-year zero-coupon bond and a 3 year 8% annual coupon bond with a yield to maturity of 10% and a Duration of 2.78 years, one would have to invest ________ of the portfolio value in the zero-coupon bond.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT