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Annuity is a fixed payment (or receipt) each year for a specified number of years. If you rent a flat and promise to make a series of payments over an agreed period, you have created an annuity.

If the annuity cash flow occurs at the end of each period, it is called regular annuity or Deferred Annuity.

If the annuity occurs at the beginning of each period, it is called Annuity Due.

Future Value of an Deferred Annuity

The future value of a Deferred Annuity is calculated as under:

The term within brackets is the compound value factor for an annuity of Re 1, which we shall refer as CVFA.

Example

Suppose that a firm deposits Rs 5,000 at the end of each year for 4 years at 6% rate of interest. How much would this annuity accumulate at the end of the fourth year?

We first find CVFA which is 4.3746. If we multiply 4.375 by Rs 5,000, we obtain a compound value of Rs 21,875:

Future Value of an Annuity Due

The future value of an Annuity Due is calculated as under:

The term within brackets is the compound value factor for an annuity of Re 1, which we shall refer as CVFA.

· Futures are traded on organized exchanges with clearing associations that act as intermediaries between the contracting parties.

· Futures are highly standardized contracts that provide for the performance of the contract either through deferred delivery of an asset or a final cash settlement.

· Both the parties pay a margin to the clearing association. This is used as a performance bond by contracting parties. The margin paid is generally market to the market price every day.

· Each futures contract has an association month which represents the month of contract delivery or final settlement, for example-a September T-bill, a March Euro, A November Nifty futures, etc.,

Both the buyer and seller of a forward contract are bound to the price decided upfront.

As there is no performance guarantee in a forward contract, there is always counter party risk.

The computation of the present value of an annuity can be written in the following general form The term within parentheses is the present value factor of an annuity of Re 1, which we would call PVFA, and it is a sum of single-payment present value factors.

Capital Recovery and Loan Amortisation

Capital recovery is the annuity of an investment made today for a specified period of time at a given rate of interest. Capital recovery factor helps in the preparation of a loan amortisation (loan repayment) schedule.

The reciprocal of the present value annuity factor is called the capital recovery factor (CRF).

Present Value of an Uneven Periodic Sum

Investments made by of a firm do not frequently yield constant periodic cash flows (annuity). In most instances the firm receives a stream of uneven cash flows. Thus the present value factors for an annuity cannot be used.

The procedure is to calculate the present value of each cash flow and aggregate all present values.

Present Value of Perpetuity

Perpetuity is an annuity that occurs indefinitely. Perpetuities are not very common in financial decision-making:

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Conglomerate transactions take many forms, ranging from short-term joint ventures to complete mergers. Whether a conglomerate merger is pure, geographical, or a product line extension, it involves firms that operate in separate markets. Therefore, a conglomerate transaction ordinarily has no direct effect on competition. There is no reduction or other change in the number of firms in either the acquiring or acquired firm’s market.Conglomerate mergers can supply a market or “demand” for firms, thus giving entrepreneurs liquidity at an open market price and with a key inducement to form new enterprises. The threat of takeover may force existing managers to increase efficiency in competitive markets. Conglomerate mergers also provide opportunities for firms to reduce capital costs and overhead and achieve other efficiencies.

Conglomerate mergers, however, may lessen future competition by eliminating the possibility that the acquiring firm would have entered the acquired firm’s market independently. A conglomerate merger also may convert a large firm into a dominant company with a decisive competitive advantage or otherwise make it difficult for other companies to enter the market. This type of merger may also reduce the number of smaller firms and increase the merged firm’s political power, thereby impairing the social and political goals of retaining independent decision-making centers, guaranteeing small business opportunities, and preserving democratic processes.

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Purchase consideration refers to the consideration payable by the purchasing company to the vendor company for taking over the assets and liabilities of Vendor Company. (Aggregate of the shares and other securities issued and the payment made in the form of cash or other assets by the transferee company to the shareholders of the transferor company).

Purchase consideration refers to total payments made by purchasing company to the shareholders of vendor company, its calculation could be in different methods, as explained below;

a. Lump sum Method – Strictly speaking, this is not a method. Where the purchase consideration amount is mentioned in the problem itself, it is called Lump sum consideration. This method, does not involve any calculation regarding purchase consideration.

b.   Net Payments Method – Under this method, the purchase consideration will be the total of payments made (in any form) by purchasing company to Vendor Company, on any basis. Generally, purchasing company decides the payment to be made towards liabilities of Vendor Company, not taken over and towards expenses. The total of such payments will be the purchase consideration.

c. Net Assets Method – Under this method, purchase consideration will be the excess of value of assets taken over by the purchasing company, over the value of liabilities taken over. That is, under this method, the purchase consideration will be – Purchase consideration = Assets taken over - Liabilities taken over (at taken over values)

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There are mainly two types of accounting for mergers they are

POOLING OF INTERESTS METHOD:

All assets and liabilities of Transferor Company will be incorporated in the books of Transferee Company. All reserves of Transferor Company will be recorded in the books of Transferee Company. The assets and liabilities of Transferor Company will be recorded in the books of Transferee Company at book values. Any difference between purchase consideration and values of assets and liabilities taken over must be adjusted against reserves.

PURCHASE METHOD:

Only assets and liabilities taken over by Transferee Company will be incorporated in its books. Other than statutory reserves (statutory reserves refers to the reserves to be maintained as per the requirements of any law or legislation) no other reserves of the transferor company will be recorded in the books of Transferee Company. The assets and liabilities of Transferor Company will be recorded in the books of Transferee Company at agreed values. Any difference between purchase consideration and value of assets and liabilities taken over must be treated as goodwill or capital reserves, as the case may be. There are three methods for purchase consideration under this method, they are; Lump sum method, Net asset method and Net payment method.

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