An insurance company has liabilities consisting of eleven annual payments of 1 million, with the first...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
An insurance company has liabilities consisting of eleven annual payments of 1 million, with the first payment due to be made in 10 years' time and the last payment due to be made in 20 years' time. The rate of interest is 6% per annum effective. (i) Show that the discounted mean term of these liabilities, to four significant figures, is 14.42 years. [3] The insurance company holds two zero-coupon bonds, one paying X in 10 years' time and the other paying Y in 20 years' time. (ii) Find values of X and Y such that Redington's first two conditions for immunisation from small changes in the rate of interest are satisfied. [6] (iii) Explain, without making any further calculations, whether you would expect Redington's third condition for immunisation to be satisfied for the values of X and Y calculated in (ii). [2] [Total 11] Two bonds paying annual coupons of 5% in arrear and redeemable at par have terms to maturity of exactly one year and two years, respectively. The gross redemption yield from the 1-year bond is 4.5% per annum effective; the gross redemption yield from the 2-year bond is 5.3% per annum effective. You are informed that the 3-year par yield is 5.6% per annum. Calculate all zero-coupon yields and all one-year forward rates implied by the yields given above. [12] A loan pays coupons of 11% per annum quarterly on 1 January, 1 April, 1 July and 1 October each year. The loan will be redeemed at 115% on any 1 January from 1 January 2015 to 1 January 2020 inclusive, at the option of the borrower. In addition to the redemption proceeds, the coupon then due is also paid. An investor purchased a holding of the loan on 1 January 2005, immediately after the payment of the coupon then due, at a price which gave him a net redemption yield of at least 8% per annum effective. The investor pays tax at 30% on income and 25% on capital gains. On 1 January 2008 the investor sold the holding, immediately after the payment of the coupon then due, to a fund which pays no tax. The sale price gave the fund a gross redemption yield of at least 9% per annum effective. Calculate the following: (i) The price per 100 nominal at which the investor bought the loan. [6] (ii) The price per 100 nominal at which the investor sold the loan. [4] (iii) The net yield per annum convertible quarterly that was actually obtained by the investor during the period of ownership of the loan. [5] [Total 15] The force of interest (1) at time is a+b where a and b are constants. An amount of 100 invested at time = 0 accumulates to 130 at time = 5 and 200 at time t=10. (i) Calculate the values of a and b. (ii) [6] Calculate the constant rate of interest per annum convertible monthly that would give rise to the same accumulation from time 1-0 to time 1-5. (iii) Calculate the constant force of interest that would give rise to the same accumulation from time 15 to time = 10. [2] [2] [Total 10] (i) Distinguish between a future and an option. [2] An investor wishes to purchase a one year forward contract on a risk-free bond which has a current market price of 97 per 100 nominal. The bond will pay coupons at a rate of 7% per annum half yearly. The next coupon payment is due in exactly six months and the following coupon payment is due just before the forward contract matures. The six-month risk-free spot interest rate is 5% per annum effective and the 12-month risk-free spot interest rate is 6% per annum effective. Stating all necessary assumptions: (ii) (a) Calculate the forward price of the bond. (b) Calculate the six-month forward rate for an investment made in six months' time. (c) Calculate the purchase price of a risk-free bond with exactly one year to maturity which is redeemed at par and which pays coupons of 4% per annum half-yearly in arrears. (d) Calculate the gross redemption yield from the bond in (c). (e) Comment on why your answer in (d) is close to the one-year spot rate. [10] [Total 12] An insurance company has liabilities consisting of eleven annual payments of 1 million, with the first payment due to be made in 10 years' time and the last payment due to be made in 20 years' time. The rate of interest is 6% per annum effective. (i) Show that the discounted mean term of these liabilities, to four significant figures, is 14.42 years. [3] The insurance company holds two zero-coupon bonds, one paying X in 10 years' time and the other paying Y in 20 years' time. (ii) Find values of X and Y such that Redington's first two conditions for immunisation from small changes in the rate of interest are satisfied. [6] (iii) Explain, without making any further calculations, whether you would expect Redington's third condition for immunisation to be satisfied for the values of X and Y calculated in (ii). [2] [Total 11] Two bonds paying annual coupons of 5% in arrear and redeemable at par have terms to maturity of exactly one year and two years, respectively. The gross redemption yield from the 1-year bond is 4.5% per annum effective; the gross redemption yield from the 2-year bond is 5.3% per annum effective. You are informed that the 3-year par yield is 5.6% per annum. Calculate all zero-coupon yields and all one-year forward rates implied by the yields given above. [12] A loan pays coupons of 11% per annum quarterly on 1 January, 1 April, 1 July and 1 October each year. The loan will be redeemed at 115% on any 1 January from 1 January 2015 to 1 January 2020 inclusive, at the option of the borrower. In addition to the redemption proceeds, the coupon then due is also paid. An investor purchased a holding of the loan on 1 January 2005, immediately after the payment of the coupon then due, at a price which gave him a net redemption yield of at least 8% per annum effective. The investor pays tax at 30% on income and 25% on capital gains. On 1 January 2008 the investor sold the holding, immediately after the payment of the coupon then due, to a fund which pays no tax. The sale price gave the fund a gross redemption yield of at least 9% per annum effective. Calculate the following: (i) The price per 100 nominal at which the investor bought the loan. [6] (ii) The price per 100 nominal at which the investor sold the loan. [4] (iii) The net yield per annum convertible quarterly that was actually obtained by the investor during the period of ownership of the loan. [5] [Total 15] The force of interest (1) at time is a+b where a and b are constants. An amount of 100 invested at time = 0 accumulates to 130 at time = 5 and 200 at time t=10. (i) Calculate the values of a and b. (ii) [6] Calculate the constant rate of interest per annum convertible monthly that would give rise to the same accumulation from time 1-0 to time 1-5. (iii) Calculate the constant force of interest that would give rise to the same accumulation from time 15 to time = 10. [2] [2] [Total 10] (i) Distinguish between a future and an option. [2] An investor wishes to purchase a one year forward contract on a risk-free bond which has a current market price of 97 per 100 nominal. The bond will pay coupons at a rate of 7% per annum half yearly. The next coupon payment is due in exactly six months and the following coupon payment is due just before the forward contract matures. The six-month risk-free spot interest rate is 5% per annum effective and the 12-month risk-free spot interest rate is 6% per annum effective. Stating all necessary assumptions: (ii) (a) Calculate the forward price of the bond. (b) Calculate the six-month forward rate for an investment made in six months' time. (c) Calculate the purchase price of a risk-free bond with exactly one year to maturity which is redeemed at par and which pays coupons of 4% per annum half-yearly in arrears. (d) Calculate the gross redemption yield from the bond in (c). (e) Comment on why your answer in (d) is close to the one-year spot rate. [10] [Total 12]
Expert Answer:
Answer rating: 100% (QA)
i To calculate the values of a and b Given Amount invested at time 0 100 Accumulates to 130 at time 15 Accumulates to 200 at time 10 We can use the formula for compound interest to solve for a and b A... View the full answer
Related Book For
Intermediate Accounting
ISBN: 978-0470161012
9th Canadian Edition, Volume 2
Authors: Donald E. Kieso, Jerry J. Weygandt, Terry D. Warfield.
Posted Date:
Students also viewed these accounting questions
-
Kahn Inc. has a target capital structure of 65% common equity and 35% debt to fund its $10 billion in operating assets. Furthermore, Kahn Inc. has a WACC of 15%, a before-tax cost of debt of 12%, and...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
1.WarsingWare produces specialized shipping containers for food products. The shipping containers help protect the food and keep it from spoiling. In addition, the shipping containers have security...
-
After deducting capital allowances for the year to 31 December 2019, the tax written down values of a company's plant and machinery were as follows: Calculate the capital allowances available for the...
-
Terminal value refers to the valuation attached to the end of the planning period; it captures the value of all subsequent cash flows. Estimate the value today for each of the following sets of...
-
D'Eon Corporation reports the following January 1, 2017 balances for its defined benefit pension plan, which it accounts for under IFRS: plan assets, $460,000; defined benefit obligation, $460,000....
-
The following is a list of assets and claims of a manufacturing business at a particular point in time: Required: Write out a statement of financial position in the standard format incorporating...
-
1. What type of property was at the center of the dispute in this case? How did that property become involved in the dispute? 2. On what ground did the plaintiffs argue that the bank should not have...
-
Question Tent 11 km - 3 km Shoreline Coral reef A visitor is staying in a tent that is 11 kilometers west of the closest point on a shoreline to a coral reef. Th coral reef is 3 kilometers due south...
-
2. Suppose that we have an AR(2) model as follows: yt = 0.1 + 1yt1 + 2yt2 + ut, where ut follows a white noise process with mean zero and variance 2 u = 0.2. Please compute the following: (b)....
-
Differentiate the money market from the capital market. Your answer must include: a review of their key characteristics provide a minimum of 2 financial instruments in each market. Save First...
-
What are the differences and similarities between permanent funds and trust funds. The criteria for establishing a business fund. Develop at least two paragraphs for each of the topics in your...
-
Bob Newhart operates a bed and breakfast hotel in Vermont. Depreciation on the hotel is $12,000 per year. Bob employs a maintenance person, George Utley, at an annual salary of $48,000 and a cleaning...
-
A company is setting its direct materials and direct labor standards for its leading product. Direct materials cost from the supplier are $5.00 per square foot, net of purchase discount. Freight-in...
-
Brown Printing, a small family-owned business, began operations on March 1, manufacturing premium quality books. The owners have expertise in printing but no accounting knowledge or experience. The...
-
A data analyst has spreadsheets numbered 1 , 2 , databases numbered 1 , 2 , 3 , and presentations numbered 1 , 2 , 3 , 4 to work on this week. If a single item is picked at random to work on, what is...
-
The relationship described in question 7 does not always appear to hold. What factors, besides the number of firms in the market, might affect margins?
-
Is Russia experiencing a net capital inflow? Use the following balance of payments data for Russia (Russian Federation) from the IMF to answer this problem. Assumptions (million US$) 2000 2001 2002...
-
What is Russias total for Groups A and B? Use the following balance of payments data for Russia (Russian Federation) from the IMF to answer this problem. Assumptions (million US$) 2000 2001 2002 2003...
-
What is Russias total for Groups A through C? Use the following balance of payments data for Russia (Russian Federation) from the IMF to answer this problem. Assumptions (million US$) 2000 2001 2002...
Study smarter with the SolutionInn App