Unit quiz: Long-Dated Money: Escalation, Depreciation, Pensions and Estates

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Question 1

A three-year services contract starts at GBP 240,000 a year with an indexation clause of CPI with a 1 percent floor and a 3 percent cap. CPI prints 0.2 percent, 0.4 percent and 1.1 percent in the three review years. Compute the annual charges and the total contract value.The floor binds in the first two reviews, so the charges are GBP 240,000, 242,400, 244,824 and 247,517.06, a total of GBP 974,741.06, which is GBP 254,741.06 above three years at the base rateThe charges are GBP 240,000, 240,480, 241,442 and 244,098, a total of GBP 966,020, because each year applies the printed CPI to the base amount

Question 2

A business buys equipment for $150,000, depreciates it as five-year property under MACRS with the half-year convention, and pays tax at 25 percent. The first-year deduction is $30,000 and the six annual deductions total $150,000. Compute the present value of the tax shield at 7 percent and the effective after-tax cost. Then compute the tax on a sale for $100,000 after two years.The shield is worth $37,500 because $150,000 of deductions at 25 percent is $37,500, and the sale produces a $28,000 capital gain taxed at the lower capital rateThe shield is worth $31,183.06 in present value, so the effective cost is $118,816.94, and a sale for $100,000 after two years produces a $28,000 gain on a $72,000 basis, taxed at 25 percent as ordinary recapture, which is $7,000

Question 3

A pension promises GBP 18,000 a year for 20 years, indexed at 2.5 percent, with the first payment one year from now. Compute its present value at a 5 percent discount rate, the value of the same promise with no indexation, and the discount rate implied by a transfer value of GBP 260,000.The indexed promise is worth GBP 275,344.34, the level promise GBP 224,319.79, and a transfer value of GBP 260,000 implies a discount rate of about 5.63 percent, which is above the 5 percent used to value the promiseThe promise is worth GBP 360,000 because 18,000 a year for 20 years is 360,000, so a transfer value of 260,000 is poor by 100,000 and should be refused on that basis

Question 4

A UK estate is worth GBP 2,150,000 including a home of GBP 620,000 left to the deceased's children. The nil-rate band is GBP 325,000, the residence nil-rate band is GBP 175,000, and the residence band tapers by GBP 1 for every GBP 2 of estate above GBP 2,000,000. Compute the tax at 40 percent and the effective rate.The allowance is GBP 500,000 because the home passes to direct descendants, so the taxable estate is GBP 1,650,000 and the tax is GBP 660,000The residence band is reduced by GBP 75,000 to GBP 100,000, so the allowance is GBP 425,000, the taxable estate is GBP 1,725,000, the tax is GBP 690,000 and the effective rate is 32.09 percent

Question 5

A firm has EBITDA of $900,000 and four committed annual charges: mortgage payments of $27,600, an equipment lease of $29,460, an indexed services contract starting at $600,000 with a 4 percent annual cap, and pension contributions of $60,000. Compute the coverage ratio in year one, then in year five when the contract has escalated three times.Year one charges are $717,060, so coverage is 1.26 times, and in year five the contract reaches $701,915.14, charges reach $818,975.14 and coverage falls to 1.10 times, which is a 12 percent reduction in cover from escalation aloneCoverage is 1.26 times and stays there, because the contract is capped at 4 percent and a cap protects the firm from the cost of escalation

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