Business
Perpetuities
Perpetuities refer to a legal restriction on the transfer of property or assets that lasts indefinitely. In business, perpetuities can limit the ability of a company to sell or transfer ownership of certain assets, which can impact its ability to raise capital or make strategic decisions. Perpetuities are often subject to legal challenges and can be difficult to enforce.
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3 Key excerpts on "Perpetuities"
eBook - PDF- Robert Parrino, David S. Kidwell, Thomas Bates, Stuart L. Gillan(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
We then multiply the ordinary annuity value times (1 + i). Section 6.2 discusses the calculation of the present value and future value of an ordinary annuity and an annuity due. 3 Explain what a perpetuity is and where we see them in business, and calculate the value of a perpetuity. A perpetuity is like an annuity except that the cash flows are per- petual—they never end. British Treasury Department bonds, called consols, were the first widely used securities of this kind. The most common example of a perpetuity today is preferred stock. The issuer of preferred stock promises to pay fixed-rate dividends forever. The cash flows from corporations can also look like Perpetuities. To calculate the present value of a perpetuity, we simply divide the constant cash flow (CF) by the interest rate (i). 4 Discuss growing annuities and Perpetuities, as well as their application in business, and calculate their values. Financial managers often need to value cash flow streams that increase at a constant rate over time. These cash flow streams are called grow- ing annuities or growing Perpetuities. An example of a growing annuity is a 10-year lease with an annual adjustment for the expected rate of inflation over the life of the contract. If the cash flows continue to grow at a constant rate indefinitely, this cash flow stream is called a growing perpetuity. Since a C-corporation has an indefinite life, when the cash flows from such a corporation are growing at a constant rate, they can be thought of as a growing perpetuity. The calculation of the value of a cash flow stream that grows at a constant rate is discussed in Section 6.4. 5 Discuss why the effective annual interest rate (EAR) is the appropriate way to annualize interest rates, and calculate the EAR. The EAR is the annual interest rate that takes compounding into account. Thus, the EAR is the true cost of borrowing or lending money.
eBook - PDF- Peter Moles, Robert Parrino, David S. Kidwell(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
British Government bonds, called consols, were the first widely available securities of this kind. The most common example of a perpetuity today are preference shares. The issuer of preference shares promises to pay fixed-rate dividends forever. To calculate the present value of a perpetuity, we simply divide the promised constant payment (CF) by the interest rate (i). 4. Discuss growing annuities and Perpetuities, as well as their application in business and be able to calculate their value. Financial managers often need to value cash flow streams that increase at a constant rate over time. These cash flow streams are called growing annuities or growing Perpetuities. An example of CHAPTER 6 DISCOUNTED CASH FLOWS AND VALUATION 229 a growing annuity is a 10-year lease contract with an annual adjustment for the expected rate of inflation over the life of the contract. If the cash flows continue to grow at a constant rate indefinitely, this cash flow stream is called a growing perpetuity. We discuss the application and calculation of cash flows that grow at a constant rate. 5. Discuss why the effective annual interest rate (EAR) is the appropriate way to annualise interest rates, and be able to calculate EAR. The EAR is the annual growth rate that takes compounding into account. Thus, the EAR is the true cost of borrowing or lending money. When we need to compare interest rates, we must make sure that the rates to be compared have the same time and compounding periods. If interest rates are not comparable, they must be converted into common terms. The easiest way to convert rates to common terms is to calculate the EAR for each interest rate.
eBook - PDF- Robert Parrino, David S. Kidwell, Thomas Bates(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
perpetuity A series of level cash flows that continue forever. ordinary annuity An annuity in which payments are made at the ends of the periods. WEB Visit the following webform that provides an online annuity calculator http://www.feike.biz/annuity.php Present Value of an Annuity We frequently need to find the present value of an annuity (PVA) . Suppose, for example, that a financial contract pays €2 000 at the end of each year for three years and the appropriate discount rate is 8 per cent. The time line for the situation is: 3 Year 2 1 0 8% € 2 000 € 2 000 € 2 000 PV = ? What is the most we should pay for this annuity? Of course, we have worked problems like this one before. All we need to do is calculate the present value of each individual cash flow present value of an annuity (PVA) The present value of the cash flows from an annuity, discounted at the appropriate discount rate. 6.2 Level Cash Flows: Annuities and Perpetuities 187 (CF ) n and add them up. Using Equation 5.4, we find that the present value of the three-year annuity (PVA ) 3 at 8 per cent interest is: = × + ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ + × + ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ + × + ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = × ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ + × ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ + × ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = + + = i i i P VA CF 1 1 CF 1 (1 ) CF 1 (1 ) €2 000 1 1.08 €2 000 1 (1.08) €2 000 1 (1.08) €1 851.85 €1 714.68 €1 587.66 €5 514.19 3 1 2 2 3 3 2 3 This approach to computing the present value of an annuity works as long as the number of cash flows is relatively small. In many situations that involve annuities, however, the number of cash flows is large, and doing the calculations by hand would be tedious. For example, a typical 30-year home mortgage has × 360 (12 months 30 years) monthly payments. Fortunately, our problem can be simplified because the cash flows (CF) for an annuity are all the same = = = (CF CF . . . CF CF) n 1 2 .
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