## David has \$2,500 that he wishes to invest for one

David has \$2,500 that he wishes to invest for one year. He has narrowed his choices down to one of the following two actions:

a1: Buy bonds of X Ltd., a company that has a very high debt-equity ratio. These bonds pay 8% interest, unless X defaults, in which case David will receive no interest but will recover his principal.

a2: Buy Government Savings Bonds, paying 3% interest.

David assesses his prior probability of X Ltd. defaulting as 0.45, and of the savings bonds defaulting as zero. His utility for money is given by the square root of the amount of his net payoff. That is, if he buys the savings bonds his net payoff is \$75, yielding utility of v’7s = 8.66, etc. David is a rational decision maker.

Required

a . Based on his prior probabilities, which action should David take? Show your calculations.

b. Before making a final decision, David decides he needs more information. He obtains X Ltd’s current financial statements and examines its times-interest-earned ratio. This ratio can be either “HI” or “LO.” Upon calculating the ratio, David observes that it is HI. On the basis of his prior experience in bond investments, David knows the following conditional probabilities:

Which action should David now take ? Show your calculations, taken to two decimal places.

c. An accounting standard allows X Ltd. to value its property, plant, and equipment at fair value, providing this can be done reliably. The company plans to adopt this option, since it will reduce its debt-equity ratio. Evaluate (in words only) the likely impact of this adoption on the main diagonal probabilities of the information system in part b.

## Prudent plans to invest \$6,000 in one of the following

Prudent plans to invest \$6,000 in one of the following instruments:

• Bonds of J ltd., yielding 12% (a1)

• Canada Savings Bonds, yielding 9% (a2)

On the basis of his knowledge of current economic conditions and the outlook for the industry of J ltd., Prudent assesses the prior probability that J l td. will go bankrupt as 0.05. If this happens, Prudent will lose both principal and interest and receive no money at the end of the year. If J ltd. does not go bankrupt, Prudent plans to sell the bonds, plus interest, at the end of one year.

Prudent assesses the probability that the Canada Savings Bonds will fail to pay off as zero. Prudent also plans to sell these, plus interest, one year later. Prudent is risk -a verse and decides to choose the investment that yields the highest expected utility. Assume that Prudent’s utility for an amount of \$x is given by √x. where x is the gross payoff.

Required

a. On the basis of his prior probabilities. which investment should Prudent choose?

b . Rather than choosing on the bas is of his prior probabilities. assume that Prudent decides to analyze the current financial statements of J Ltd. These financial statements can look “good” (G) or “bad” (B). After his analysis, Prudent realizes that the statements look good. On the basis of his extensive understanding of financial statement analysis, he knows that the probability that the financial statements would look good given that the firm was actually heading for bankruptcy is 0.10:

Prob(GIS1) = 0.10

where S1 denotes the state of heading for bankruptcy.

Similarly, Prudent knows that

Prob(G IS2) = 0.80

where s2 denotes the state of not heading for bankruptcy.

Which investment should Prudent now take? Explain why. Use Bayes’ theorem.

## The following RRA information is taken from the 2019 annual

The following RRA information is taken from the 2019 annual report of Moonglo Energy Inc.

Balance of proved reserves: beginning of year……………………\$ 1,010
Sales, net of production costs…………………………………………………(477)
Sales of reserves in place……………………………………………………………(6)
Accretion of discount………………………………………………………………..135
Extensions and discoveries, net of related costs……………………….162
Development costs incurred in year………………………………………….619
Changes in estimates……………………………………………………………….147
Balance of proved reserves: end of year………………………………\$1,590

Required

a. Prepare 2019 income statements for Moonglo on an RRA basis.

b. Moonglo reports a profit on its 2019 oil and gas operations, on a historical cost basis, of \$185. Explain (in words only) why this profit differs from the RRA income you calculated in part a.

c. Which income number (RRA or historical cost basis) is more relevant? Which is more reliable? Explain why.

## The following RRA information is taken from the December 31,

The following RRA information is taken from the December 31, 2019, annual report of AY Energy, Inc.

Required

a. Prepare an RRA income statement for AY Energy for 2019.

b. AY Energy reports elsewhere in its annual report an (historical cost-based) operating loss from exploration and production for 2019 of \$5,389. While this amount may exclude certain administrative cost allocations, take this operating loss as a reasonable historical cost-based analogue of the RRA income you calculated in part a. Explain why RRA income for 2019 is different from the \$5,389 loss under historical cost.

c . The standardized measure is applied only to proved reserves under RRA, using average oil and gas prices for the year. Explain why.

d. RRA mandates a discount rate of 10 percent for the RRA present value calculations, rather than allowing each firm to choose its own rate. Why? Can you see any disadvantages to mandating a common discount rate?

## On January 1, 2019, Drill Deep Ltd. started its business

On January 1, 2019, Drill Deep Ltd. started its business by purchasing a productive oil well. The proved oil reserves from the well are expected to generate \$8,000 cash flow at the end of 2019, \$7,000 at the end of 2020, and \$6,000 at the end of 2021. Net sales is gross revenues less production costs. Net sales equals cash flows. On January 1, 2023, the oil well is expected to be dry, with no environmental liabilities. The management of Drill Deep Ltd. wishes to prepare financial statements on a present value basis with an interest rate of 10 percent. The following information is known about the well at the end of 2019.

• Actual cash flows in 2019 amounted to \$7 ,500-that is, \$500 less than expected.

• Changes in estimates: Due to improved recovery (of oil from the well). end of year cash flows for 2020 and 2021 are estimated to be \$7,500 and \$7,000 respectively.

Required

a. Prepare the income statement of Drill Deep Ltd. for 2019 from its proved oil reserves.

b. Managements of some firms have expressed serious concerns about the reliability of present value information for oil and gas companies. Outline two of these concerns.

## SC Ltd. operates under ideal conditions of uncertainty. On January

SC Ltd. operates under ideal conditions of uncertainty. On January 1, 2019, it purchased a capital asset that will last for two full years and then will be retired with no salvage. The purchase price was financed with an issue of common stock. SC Ltd. plans to pay no dividends until after the end of 2020. The interest rate in the economy is 6 percent.

SC Ltd. is certain that net cash flow from its only asset will be \$100 in 2019. However, net cash flow in 2020 is uncertain. Net cash flows in 2020 will be \$200 (the high state) with objective probability 0.80 and \$50 (the low state) with objective probability 0.20. All cash flows are received at their respective year-ends. At the end of year 2 it becomes known that the high state is realized.

Required

a. How much did SC Ltd. pay for its capital asset at the beginning of 2019? Show calculations.

b. Prepare. in good form, a current value-based income statement for SC Ltd. for the second year of operations- that is, 2020.

c . Prepare. in good form, a current value-based balance sheet for SC Ltd. at the end of 2020 (before any dividend payments).

## AltCoins Ltd. has just begun operating under ideal conditions of

AltCoins Ltd. has just begun operating under ideal conditions of uncertainty. Its cash flows will depend on the state of the economy. On January 1, 2019, the company acquired plant and equipment that will last two years, with a nil salvage value. AltCoins financed the plant and equipment purchase by issuing common shares.

In 2019, net cash flows will be \$800 if the state of the economy is good and \$600 if it is poor. In 2020, cash flows will rise to \$1,200 if the economy is good and remain at \$600 if it is bad. Cash flows are received at year-end. In each year. the probability that the economy is good is 0.6. The interest rate in the economy is 4 percent in both years. AltCoins pays a dividend of \$70 at the end of 2020.

Required

a . How much did AltCoins Ltd. pay for its plant and equipment on January 1, 2019?

b. In 2019, the economy is good. Prepare a current value-based balance sheet at the end of 2019 and an income statement for 2019.

c . In North America, most property, plant, and equipment is usually accounted for under historical cost accounting, rather than at current value as above. Suggest why.

## Contingent Corp. operates under ideal conditions of uncertainty. It has

Contingent Corp. operates under ideal conditions of uncertainty. It has just purchased a new machine, at a cost of \$3,575.10, paid for entirely from the proceeds of a stock issue. The interest rate in the economy is 8 percent. The machine is expected to last for two years, after which time it will have zero salvage value.

The new machine is an experiment al model, and its suitability for use in Contingent’s operations is not completely known. Contingent assesses a 0.75 probability that there w ill be a major machine failure during the first year of operation, and a 0.25 probability that the machine will operate as planned. If there is a major failure, cash flow for the year will be \$1,000. If the machine operates as planned, cash flow will be \$3,000 for the year. If there is no major failure in the first year, the probability of a major failure in the second year. and resulting cash flows of \$1,000, falls to 0.60. If there is no major failure in the second year, cash flows for that year will again be \$3,000. However, if there is a major failure in the first year, the lessons learned from correcting it will result in only a 0.10 probability of failure in the second year.

It turns out that there is no major failure in the first year.

Required

a. Verify that the cost of \$3,575.10 for the machine is correct.

b. Prepare a current value-based income statement for year 1.

c. Prepare a current value-based balance sheet at the end of the first year.

## Undoubtedly Corp. operates under ideal conditions of certainty. It acquired

Undoubtedly Corp. operates under ideal conditions of certainty. It acquired its sole asset on January 1, 2019. The asset will yield \$725 cash at the end of each year from 2019 to 2021, inclusive, after which it will have no market value and no disposal costs. The interest rate in the economy is 5 percent. Purchase of the asset was financed by the issuance of common shares. Undoubtedly Corp. will pay a dividend of \$50 at the end of 2019 and 2020.

Required

a. Prepare a balance sheet for Undoubtedly Corp. at the end of 2019 and an income statement for the year ended December 31, 2019.

b. Prepare a balance sheet for Undoubtedly Corp. as at the end of 2020 and an income statement for the year ended December 31, 2020.

c. Under ideal conditions, what is the relationship between present value (i.e., value in use) and market value (i.e., fair value)? Why? Under the real conditions in which accountants operate, to what extent do market values provide a way to implement fair value accounting? Explain.

d. Under real conditions, present value calculations tend to be of low reliability. Why? Does this mean that present value-based accounting for assets and liabilities is not decision useful? Explain.

## EZ Sports Ltd. plans to manufacture cross-country skiing equipment. Its

EZ Sports Ltd. plans to manufacture cross-country skiing equipment. Its cash flows are highly dependent on the winter weather. EZ operates under ideal conditions of uncertainty. On August 1, 2019, the beginning of its first year in business, EZ acquires equipment to be used in its operations. The equipment will last two years, at which time its salvage value will be zero. The company finances the equipment by means of a \$600 bank loan at 3 percent interest, with the balance financed by issuing common shares.

EZ’s annual net cash flows will be \$900 if the weather is snowy and \$300 if it is not snowy. Assume that cash flows are received at year-end. In each year, the objective probability that the weather is snowy is 0.75 and 0.25 that it is not snowy. The interest rate in the economy is 3 percent in both years.

EZ Sports Ltd. will pay a dividend of \$50 at the end of each year of operation.

Required

a. In the 2019-2020 skiing season, the weather is snowy. Prepare a current value- based balance sheet at July 31, 2020, the end of EZ Sports Ltd.’s first year of operations, and an income statement for the year.

b. What timing of revenue recognition is implicit in the income statement you have prepared in part a ? When ideal conditions do not hold, is this timing of revenue recognition relevant? Is it reliable? Explain.

c. Assume that EZ Sports Ltd . paid the present value you calculated in part a for its equipment. Calculate EZ’s net income for the year ended July 31, 2020, on a historical cost basis, assuming that equipment is amortized on a straight line basis. Under the more realistic assumption that ideal conditions do not hold, which measure of net income-present value basis or historical cost basis-is most relevant? Which is most reliable? Why?