An investor is facing three possible outcomes tomorrow. He can give up some cons

Question

An investor is facing three possible outcomes tomorrow. He can give up some consumption today to invest in either a stock that makes a payoff (x1, x12, x13) = (3, 5, 8) or a put on the stock with exercise price 6 or a call on the stock with exercise price 4. The agent has a utility function given by u(co, c1, c21, c31) = ln(co) + 1 /3 ln(c^11) + 1/3 ln(c12) + 1/3 ln(c^13). In equilibrium the investor consumes 2 units of consumption today and then (1,2,3) units of consumption tomorrow depending on what the outcome tomorrow is. Find the payoff of the call and put options in each possible outcome tomorrow. Find the price of each of the three assets in equilibrium.

Explanation / Answer

In determining the profits (net income) from an activity, the receipts from the activity must be reduced by appropriate costs. One such cost is the cost of assets used but not immediately consumed in the activity.[2] Such cost so allocated in a given period is equal to the reduction in the value placed on the asset, which is initially equal to the amount paid for the asset and subsequently may or may not be related to the amount expected to be received upon its disposal. Depreciation is any method of allocating such net cost to those periods in which the organization is expected to benefit from use of the asset. The asset is referred to as a depreciable asset. Depreciation is technically a method of allocation, not valuation,[3] even though it determines the value placed on the asset in the balance sheet.

Any business or income producing activity[4] using tangible assets may incur costs related to those assets. If an asset is expected to produce a benefit in future periods, some of these costs must be deferred rather than treated as a current expense. The business then records depreciation expense in its financial reporting as the current period's allocation of such costs. This is usually done in a rational and systematic manner. Generally this involves four criteria:

Depreciable basis[edit]

Cost generally is the amount paid for the asset, including all costs related to acquisition.[6] In some countries or for some purposes, salvage value may be ignored. The rules of some countries specify lives and methods to be used for particular types of assets. However, in most countries the life is based on business experience, and the method may be chosen from one of several acceptable methods.

Net basis[edit]

When a depreciable asset is sold, the business recognises gain or loss based on net basis of the asset. This net basis is cost less depreciation.

Impairment[edit]

Accounting rules also require that an impairment charge or expense be recognized if the value of assets declines unexpectedly.[7] Such charges are usually nonrecurring, and may relate to any type of asset. Many companies consider write-offs of some of their long-lived assets because some property, plant, and equipment have suffered partial obsolescence. Accountants reduce the asset's carrying amount by its fair value. For example, if a company continues to incur losses because prices of a particular product or service are higher than the operating costs, companies consider write-offs of the particular asset. These write-offs are referred to as impairments. There are events and changes in circumstances might lead to impairment. Some examples are:

Events or changes in circumstances indicate that the company may not be able recover the carrying amount of the asset. In which case, companies use the recoverability test to determine whether impairment has occurred. The steps to determine are: 1. Estimate the future cash flow of asset. (from the use of the asset to disposition) 2. If the sum of the expected cash flow is less than the carrying amount of the asset, the asset is considered impaired..

Depletion and amortization[edit]

Depletion and amortization are similar concepts for minerals (including oil) and intangible assets, respectively.

Effect on cash[edit]

Depreciation expense does not require current outlay of cash. However, since depreciation is an expense to the P&L account, provided the enterprise is operating in a manner that covers its expenses (e.g. operating at a profit) depreciation is a source of cash in a statement of cash flows, which generally offsets the cash cost of acquiring new assets required to continue operations when existing assets reach the end of their useful lives.

Accumulated depreciation[edit]

While depreciation expense is recorded on the income statement of a business, its impact is generally recorded in a separate account and disclosed on the balance sheet as accumulated depreciation, under fixed assets, according to most accounting principles. Accumulated depreciation is known as a contra account, because it separately shows a negative amount that is directly associated with another account.

Without an accumulated depreciation account on the balance sheet, depreciation expense is usually charged against the relevant asset directly. The values of the fixed assets stated on the balance sheet will decline, even if the business has not invested in or disposed of any assets. The amounts will roughly approximate fair value. Otherwise, depreciation expense is charged against accumulated depreciation. Showing accumulated depreciation separately on the balance sheet has the effect of preserving the historical cost of assets on the balance sheet. If there have been no investments or dispositions in fixed assets for the year, then the values of the assets will be the same on the balance sheet for the current and prior year (P/Y).

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