Question

A pension plan is obligated to make disbursements of $1 million, 2 million and 1 million...

A pension plan is obligated to make disbursements of $1 million, 2 million and 1 million every six months during the next 1.5 years. What is the duration if the market interest rate is 10%?

Homework Answers

Answer #1

Given about a pension plan

disbursements of $1 million, 2 million and 1 million every six months during the next 1.5 years

Cash flow in 0.5 year = $1 million

Cash flow in 1 year = $2 million

Cash flow in 1.5 year = $1 million

Market interest rate r = 10%

Duration is calculated as below table:

PV of Cash flow = cash flow/(1 + r/2)^period

Total PV = sum of all PV = $3630277.51

weight = PV of cash flow/Total PV

duration of each Cash flow = year*weight

duration of the pension fund = sum of all duration = 0.99 years

Year Period Cash flow PV of Cash flow=cash flow/(1+r)^period weight = PV of coupon/Total PV Duration = weight*year
0.5 1 $ 10,00,000.00 $    9,52,380.95 0.2623 0.1312
1 2 $ 20,00,000.00 $ 18,14,058.96 0.4997 0.4997
1.5 3 $ 10,00,000.00 $    8,63,837.60 0.2380 0.3569
Total PV $ 36,30,277.51 Duration 0.99
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
A pension plan is obligated to make disbursements of $6 million, $4 million, and $3 million...
A pension plan is obligated to make disbursements of $6 million, $4 million, and $3 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 13.0% annually. (Round your answer to 4 decimal places.)   Duration years
A corporate pension plan has to make the following payments over the next few years: Year...
A corporate pension plan has to make the following payments over the next few years: Year 1 2 3 4 Amount ($ 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...
2. Alpha Insurance Company is obligated to make payments of $2 million, $3 million, and $4...
2. Alpha Insurance Company is obligated to make payments of $2 million, $3 million, and $4 million at the end of the next three years, respectively. The market interest rate is 8% per annum. Suppose the company’s payment obligations are fully funded and immunized using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds the company will hold in the portfolio.
Consider a pension plan that pays beneficiaries in the following manner: at the end of the...
Consider a pension plan that pays beneficiaries in the following manner: at the end of the retirement year of a beneficiary the value of all benefits are transferred to his or her personal account. This means that at the end of every year the pension plan makes lump-sum payments of pension benefits to its beneficiaries. The pension plan’s actuarial team concluded that the pension’s obligation stream could not be estimated beyond an 80-year horizon. They further estimate that the plan...
Herring Wholesale Company has a defined benefit pension plan. On January 1, 2018, the following pension...
Herring Wholesale Company has a defined benefit pension plan. On January 1, 2018, the following pension related data were available: ($ in 000s) Net gain–AOCI $350 Accumulated benefit obligation 2,770 Projected benefit obligation 2,600 Fair value of plan assets 2,300 Average remaining service period of active employees (expected to remain constant for the next several years) 15 years The rate of return on plan assets during 2018 was 8%, although it was expected to be 10%. The actuary revised assumptions...
Herring Wholesale Company has a defined benefit pension plan. On January 1, 2018, the following pension...
Herring Wholesale Company has a defined benefit pension plan. On January 1, 2018, the following pension related data were available: ($ in 000s) Net gain–AOCI $300 Accumulated benefit obligation 1,670 Projected benefit obligation 2,200 Fair value of plan assets 1,600 Average remaining service period of active employees (expected to remain constant for the next several years) 16 years The rate of return on plan assets during 2018 was 9%, although it was expected to be 10%. The actuary revised assumptions...
Lewis Industries adopted a defined benefit pension plan on January 1, 2021. By making the provisions...
Lewis Industries adopted a defined benefit pension plan on January 1, 2021. By making the provisions of the plan retroactive to prior years, Lewis incurred a prior service cost of $3 million. The prior service cost was funded immediately by a $3 million cash payment to the fund trustee on January 2, 2021. However, the cost is to be amortized (expensed) over 10 years. The service cost—$290,000 for 2021—is fully funded at the end of each year. Both the actuary's...
Pension plan assets were $2,100 million at the beginning of the year and $2,272 million at...
Pension plan assets were $2,100 million at the beginning of the year and $2,272 million at the end of the year. At the end of the year, retiree benefits paid by the trustee were $46 million and cash invested in the pension fund was $50 million. What was the percentage rate of return on plan assets?
Pension plan assets were $1,500 million at the beginning of the year and $1,609 million at...
Pension plan assets were $1,500 million at the beginning of the year and $1,609 million at the end of the year. At the end of the year, retiree benefits paid by the trustee were $34 million and cash invested in the pension fund was $38 million. What was the percentage rate of return on plan assets?
It is now January 1. You plan to make a total of 5 deposits of $150...
It is now January 1. You plan to make a total of 5 deposits of $150 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 4% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. How much will be in your account after 10 years?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT