Definition
Content
Definition of 'Lump-Sum Payment'
A one-time payment for the total or partial value of an asset. A lump-sum payment is usually taken in lieu of recurring payments that would otherwise be received over a period of time. The value of a lump-sum payment is generally less than the sum of all payments that the party would otherwise receive, since the party paying the lump-sum payment is being asked to provide more funds up front than it otherwise would have been required to.
Lump sum
From Wikipedia, the free encyclopedia
A lump sum is a single payment of money, as opposed to a series of payments made over time (such as an annuity).[1][2][3][4] The United States Department of Housing and Urban Development distinguishes between "price analysis" and "cost analysis" by whether the decision maker compares lump sum amounts, or subjects contract prices to an itemized cost breakdown.[5] In 1911, American union leaders including Samuel Gompers of the American Federation of Labor expressed opposition to lump sums being awarded their members pursuant to a new workers compensation law, saying that when they received lump sums rather than periodic payments the risk of them squandering the money was greater.[6] USA Today reported in 2003 that experts said that retirees tend to handle lump sum payments to them by either being overly frugal, or alternatively by using a lot of the lump sum payment quickly for travel and bigticket items.[7] The Financial Times reported in July 2011 that research by Prudential had found that 79% of polled pensioners collecting a company or private pension that year took a lump sum at their retirement, as compared to 76% in 2008.[8] Prudential was of the view that for many retirees, a lump sum at the time of retirement was the most tax-efficient option.[8] However, Prudential's head of business development, Vince Smith Hughes, said "some pensioners are beginning to regret the way they used the tax-free cash. The days of buying a shiny new car or going on a once-in-a-lifetime holiday may be gone."[8]
Present Value About This Tool
The online Present Value of Lump Sum Calculator helps you calculate the present value of lump sum based on a fixed interest rate per period.
Lump Sum
A lump sum is a complete payment consisting of a single sum of money, as opposed to a series of payments made over time (such as an annuity).
Formula
The present value of lump sum calculation formula is as following:
Where: PV = present value of lump sum FV = future value of lump sum r = interest rate per period t = number of compounding periods
B Future Value
About This Tool
The online Future Value of Lump Sum Calculator helps you calculate the future value of lump sum based on a fixed interest rate per period.
Lump Sum
A lump sum is a complete payment consisting of a single sum of money, as opposed to a series of payments made over time (such as an annuity).
Formula
The future value of lump sum calculation formula is as following:
Where: FV = future value of lump sum PV = future value of lump sum r = interest rate per period t = number of compounding periods
Sinking fund
From Wikipedia, the free encyclopedia
A sinking fund is a fund established by a government agency or business for the purpose of reducing debt by repaying or purchasing outstanding loans and securities held against the entity. It helps keep the borrower liquid so it can repay the bondholder.
Historical context[edit source | editbeta]
The sinking fund was first used in Great Britain in the 18th century to reduce national debt. While used by Robert Walpole in 1716 and effectively in the 1720s and early 1730s, it originated in the commercial tax syndicates of the Italian peninsula of the 14th century, where its function was to retire redeemable public debt of those cities. The fund received whatever surplus occurred in the national Budget each year. However, the problem was that the fund was rarely given any priority in Government strategy. The result of this was that the funds were often raided by the Treasury when they needed funds quickly. In 1772, the nonconformist minister Richard Price published a pamphlet on methods of reducing the national debt. The pamphlet caught the interest of William Pitt the Younger, who drafted a proposal to reform the Sinking Fund in 1786. Lord North recommended "the Creation of a Fund, to be appropriated, and invariably applied, under proper Direction, in the gradual Diminution of the Debt." Pitt's way of securing "proper Direction" was to introduce legislation that prevented ministers from raiding the fund in crises. He also increased taxes to ensure that a £1 million surplus could be used to reduce the national debt. The legislation also placed administration of the fund in the hands of "Commissioners for Reducing the National Debt." The scheme worked well between 1786 and 1793 with the Commissioners receiving £8 million and reinvesting it to reduce the debt by more than £10 million. However, the event of war with France in 1793 "destroyed the rationale of the Sinking Fund" (Eric Evans). The fund was abandoned by Lord Liverpool's government only in the 1820s. Sinking funds were also seen commonly in investment in the 1800s in the United States, especially with highly-invested markets like railroads. An example would be the Central Pacific Railroad Company, which challenged the constitutionality of mandatory sinking funds for companies in the case In Re Sinking [1] Funds Cases in 1878.
Modern context[edit source | editbeta]
In modern finance, a sinking fund is a method by which an organization sets aside money over time to retire its indebtedness. More specifically, it is a fund into which money can be deposited, so that over time preferred stock, debentures or stocks can be retired. Sinking funds can also be used to set aside money for purposes of replacing capital equipment as it becomes obsolete. In some US states, Michigan for example, school districts may ask the voters to approve a taxation for the purpose of establishing a sinking fund. The State Treasury Department has strict guidelines for expenditure of fund dollars with the penalty for misuse being an eternal ban on ever seeking the tax levy again. See also sinking fund provision in bonds.
Types[edit source | editbeta]
A sinking fund may operate in one or more of the following ways: 1. The firm may repurchase a fraction of the outstanding bonds in the open market each year. 2. The firm may repurchase a fraction of outstanding bonds at a special call price associated with the sinking fund provision (they are callable bonds). 3. The firm has the option to repurchase the bonds at either the market price or the sinking fund price, whichever is lower. To allocate the burden of the sinking fund call fairly among bondholders, the bonds chosen for the call are selected at random based on serial number. The firm can only repurchase a limited fraction of the bond issue at the sinking fund price. At best some indentures allow firms to use a doubling option, which allows repurchase of double the required number of bonds at the sinking fund price. 4. A less common provision is to call for periodic payments to a trustee, with the payments invested so that the accumulated sum can be used for retirement of the entire issue at maturity: instead of the debt amortizing over the life, the debt remains outstanding and a matching asset accrues. Thus the balance sheet consists of Asset = Sinking fund, Liability = Bonds..
Benefits and drawbacks[edit source | editbeta]
For the organization retiring debt, it has the benefit that the principal of the debt or at least part of it, will be available when due. For the creditors, the fund reduces the risk the organization will default when the principal is due: it reduces credit risk. However, if the bonds are callable, this comes at a cost to creditors, because the organization has an option on the bonds: The firm will choose to buy back discount bonds (selling below par) at their market price, while exercising its option to buy back premium bonds (selling above par) at par.
Therefore, if interest rates fall and bond prices rise, a firm will benefit from the sinking fund provision that enables it to repurchase its bonds at below-market prices. In this case, the firm's gain is the bondholder's loss – thus callable bonds will typically be issued at a higher coupon rate, reflecting the value of the option.
Amortization (or amortisation) is the process of decreasing, or accounting for, an amount over a period. The word comes from Middle English amortisen to kill, alienate in mortmain, from AngloFrench amorteser, alteration of amortir, from Vulgar Latin admortire to kill, from Latin ad- + mort-, mors death.
Applications of amortization[
When used in the context of a home purchase, amortization is the process by which loan principal decreases over the life of a loan, typically an amortizing loan. With each mortgage payment that is made, a portion of the payment is applied towards reducing the principal, and another portion of the
payment is applied towards paying the interest on the loan. An amortization schedule, a table detailing each periodic payment on a loan, shows this ratio of principal and interest and demonstrates how a loan's principal amount decreases over time. An amortization schedule can be generated by an amortization calculator. Negative amortization is an amortization schedule where the loan amount actually increases through not paying the full interest. In business, amortization allocates a lump sum amount to different time periods, particularly for loans and other forms of finance, including related interest or other finance charges. Amortization is also applied to capital expenditures of certain assets under accounting rules, particularly intangible assets, in a manner analogous to depreciation. In tax law, amortization refers to the cost recovery system for intangible property. In computer science, amortized analysis is a method of analyzing the execution cost of algorithms over a sequence of operations. In the context of zoning regulations, amortization is the time in which a property owner has to conform or relocate when the property's use constitutes a preexisting nonconforming use under amended zoning regulations.
Annuity Payment (PV)
Annuity Payment PV Calculator (Click Here or Scroll Down)
More Sharing ServicesShare|Share on facebookShare on emailShare on favoritesShare on print
Start with the Basics Present Value Future Value Compound Interest Simple Interest
The annuity payment formula is used to calculate the periodic payment on an annuity. An annuity is a series of periodic payments that are received at a future date. The present value portion of the formula is the initial payout, with an example being the original payout on an amortized loan. The annuity payment formula shown is for ordinary annuities. This formula assumes that the rate does not change, the payments stay the same, and that the first payment is one period away. An annuity that grows at a proportionate rate would use the growing annuity payment formula. Otherwise, an annuity that changes the payment and/or rate would need to be adjusted for each change. An annuity that has its first payment due at the beginning would use the annuity due payment formula and the deferred annuity payment formula would have a payment due at a later date. The annuity payment formula can be used for amortized loans, income annuities, structured settlements, lottery payouts(see annuity due payment formula if first payment starts immediately), and any other type of constant periodic payments.
Per Period
The rate per period and number of periods should reflect how often the payment is made. For example, if the payment is monthly, then the monthly rate should be used. Likewise, the number of periods should be the number of months. This concept is important to remember with all financial formulas.
Annuity Payment Formula Explained
The annuity payment formula can be determined by rearranging the PV of annuity formula.
After rearranging the formula to solve for P, the formula would become:
This can be further simplified by multiplying the numerator times the reciprocal of the denominator, which is the formula shown at the top of the page.
A one-time payment for the total or partial value of an asset. A lump-sum payment is usually taken in lieu of recurring payments that would otherwise be received over a period of time. The value of a lump-sum payment is generally less than the sum of all payments that the party would otherwise receive, since the party paying the lump-sum payment is being asked to provide more funds up front than it otherwise would have been required to.
Lump sum
From Wikipedia, the free encyclopedia
A lump sum is a single payment of money, as opposed to a series of payments made over time (such as an annuity).[1][2][3][4] The United States Department of Housing and Urban Development distinguishes between "price analysis" and "cost analysis" by whether the decision maker compares lump sum amounts, or subjects contract prices to an itemized cost breakdown.[5] In 1911, American union leaders including Samuel Gompers of the American Federation of Labor expressed opposition to lump sums being awarded their members pursuant to a new workers compensation law, saying that when they received lump sums rather than periodic payments the risk of them squandering the money was greater.[6] USA Today reported in 2003 that experts said that retirees tend to handle lump sum payments to them by either being overly frugal, or alternatively by using a lot of the lump sum payment quickly for travel and bigticket items.[7] The Financial Times reported in July 2011 that research by Prudential had found that 79% of polled pensioners collecting a company or private pension that year took a lump sum at their retirement, as compared to 76% in 2008.[8] Prudential was of the view that for many retirees, a lump sum at the time of retirement was the most tax-efficient option.[8] However, Prudential's head of business development, Vince Smith Hughes, said "some pensioners are beginning to regret the way they used the tax-free cash. The days of buying a shiny new car or going on a once-in-a-lifetime holiday may be gone."[8]
Present Value About This Tool
The online Present Value of Lump Sum Calculator helps you calculate the present value of lump sum based on a fixed interest rate per period.
Lump Sum
A lump sum is a complete payment consisting of a single sum of money, as opposed to a series of payments made over time (such as an annuity).
Formula
The present value of lump sum calculation formula is as following:
Where: PV = present value of lump sum FV = future value of lump sum r = interest rate per period t = number of compounding periods
B Future Value
About This Tool
The online Future Value of Lump Sum Calculator helps you calculate the future value of lump sum based on a fixed interest rate per period.
Lump Sum
A lump sum is a complete payment consisting of a single sum of money, as opposed to a series of payments made over time (such as an annuity).
Formula
The future value of lump sum calculation formula is as following:
Where: FV = future value of lump sum PV = future value of lump sum r = interest rate per period t = number of compounding periods
Sinking fund
From Wikipedia, the free encyclopedia
A sinking fund is a fund established by a government agency or business for the purpose of reducing debt by repaying or purchasing outstanding loans and securities held against the entity. It helps keep the borrower liquid so it can repay the bondholder.
Historical context[edit source | editbeta]
The sinking fund was first used in Great Britain in the 18th century to reduce national debt. While used by Robert Walpole in 1716 and effectively in the 1720s and early 1730s, it originated in the commercial tax syndicates of the Italian peninsula of the 14th century, where its function was to retire redeemable public debt of those cities. The fund received whatever surplus occurred in the national Budget each year. However, the problem was that the fund was rarely given any priority in Government strategy. The result of this was that the funds were often raided by the Treasury when they needed funds quickly. In 1772, the nonconformist minister Richard Price published a pamphlet on methods of reducing the national debt. The pamphlet caught the interest of William Pitt the Younger, who drafted a proposal to reform the Sinking Fund in 1786. Lord North recommended "the Creation of a Fund, to be appropriated, and invariably applied, under proper Direction, in the gradual Diminution of the Debt." Pitt's way of securing "proper Direction" was to introduce legislation that prevented ministers from raiding the fund in crises. He also increased taxes to ensure that a £1 million surplus could be used to reduce the national debt. The legislation also placed administration of the fund in the hands of "Commissioners for Reducing the National Debt." The scheme worked well between 1786 and 1793 with the Commissioners receiving £8 million and reinvesting it to reduce the debt by more than £10 million. However, the event of war with France in 1793 "destroyed the rationale of the Sinking Fund" (Eric Evans). The fund was abandoned by Lord Liverpool's government only in the 1820s. Sinking funds were also seen commonly in investment in the 1800s in the United States, especially with highly-invested markets like railroads. An example would be the Central Pacific Railroad Company, which challenged the constitutionality of mandatory sinking funds for companies in the case In Re Sinking [1] Funds Cases in 1878.
Modern context[edit source | editbeta]
In modern finance, a sinking fund is a method by which an organization sets aside money over time to retire its indebtedness. More specifically, it is a fund into which money can be deposited, so that over time preferred stock, debentures or stocks can be retired. Sinking funds can also be used to set aside money for purposes of replacing capital equipment as it becomes obsolete. In some US states, Michigan for example, school districts may ask the voters to approve a taxation for the purpose of establishing a sinking fund. The State Treasury Department has strict guidelines for expenditure of fund dollars with the penalty for misuse being an eternal ban on ever seeking the tax levy again. See also sinking fund provision in bonds.
Types[edit source | editbeta]
A sinking fund may operate in one or more of the following ways: 1. The firm may repurchase a fraction of the outstanding bonds in the open market each year. 2. The firm may repurchase a fraction of outstanding bonds at a special call price associated with the sinking fund provision (they are callable bonds). 3. The firm has the option to repurchase the bonds at either the market price or the sinking fund price, whichever is lower. To allocate the burden of the sinking fund call fairly among bondholders, the bonds chosen for the call are selected at random based on serial number. The firm can only repurchase a limited fraction of the bond issue at the sinking fund price. At best some indentures allow firms to use a doubling option, which allows repurchase of double the required number of bonds at the sinking fund price. 4. A less common provision is to call for periodic payments to a trustee, with the payments invested so that the accumulated sum can be used for retirement of the entire issue at maturity: instead of the debt amortizing over the life, the debt remains outstanding and a matching asset accrues. Thus the balance sheet consists of Asset = Sinking fund, Liability = Bonds..
Benefits and drawbacks[edit source | editbeta]
For the organization retiring debt, it has the benefit that the principal of the debt or at least part of it, will be available when due. For the creditors, the fund reduces the risk the organization will default when the principal is due: it reduces credit risk. However, if the bonds are callable, this comes at a cost to creditors, because the organization has an option on the bonds: The firm will choose to buy back discount bonds (selling below par) at their market price, while exercising its option to buy back premium bonds (selling above par) at par.
Therefore, if interest rates fall and bond prices rise, a firm will benefit from the sinking fund provision that enables it to repurchase its bonds at below-market prices. In this case, the firm's gain is the bondholder's loss – thus callable bonds will typically be issued at a higher coupon rate, reflecting the value of the option.
Amortization (or amortisation) is the process of decreasing, or accounting for, an amount over a period. The word comes from Middle English amortisen to kill, alienate in mortmain, from AngloFrench amorteser, alteration of amortir, from Vulgar Latin admortire to kill, from Latin ad- + mort-, mors death.
Applications of amortization[
When used in the context of a home purchase, amortization is the process by which loan principal decreases over the life of a loan, typically an amortizing loan. With each mortgage payment that is made, a portion of the payment is applied towards reducing the principal, and another portion of the
payment is applied towards paying the interest on the loan. An amortization schedule, a table detailing each periodic payment on a loan, shows this ratio of principal and interest and demonstrates how a loan's principal amount decreases over time. An amortization schedule can be generated by an amortization calculator. Negative amortization is an amortization schedule where the loan amount actually increases through not paying the full interest. In business, amortization allocates a lump sum amount to different time periods, particularly for loans and other forms of finance, including related interest or other finance charges. Amortization is also applied to capital expenditures of certain assets under accounting rules, particularly intangible assets, in a manner analogous to depreciation. In tax law, amortization refers to the cost recovery system for intangible property. In computer science, amortized analysis is a method of analyzing the execution cost of algorithms over a sequence of operations. In the context of zoning regulations, amortization is the time in which a property owner has to conform or relocate when the property's use constitutes a preexisting nonconforming use under amended zoning regulations.
Annuity Payment (PV)
Annuity Payment PV Calculator (Click Here or Scroll Down)
More Sharing ServicesShare|Share on facebookShare on emailShare on favoritesShare on print
Start with the Basics Present Value Future Value Compound Interest Simple Interest
The annuity payment formula is used to calculate the periodic payment on an annuity. An annuity is a series of periodic payments that are received at a future date. The present value portion of the formula is the initial payout, with an example being the original payout on an amortized loan. The annuity payment formula shown is for ordinary annuities. This formula assumes that the rate does not change, the payments stay the same, and that the first payment is one period away. An annuity that grows at a proportionate rate would use the growing annuity payment formula. Otherwise, an annuity that changes the payment and/or rate would need to be adjusted for each change. An annuity that has its first payment due at the beginning would use the annuity due payment formula and the deferred annuity payment formula would have a payment due at a later date. The annuity payment formula can be used for amortized loans, income annuities, structured settlements, lottery payouts(see annuity due payment formula if first payment starts immediately), and any other type of constant periodic payments.
Per Period
The rate per period and number of periods should reflect how often the payment is made. For example, if the payment is monthly, then the monthly rate should be used. Likewise, the number of periods should be the number of months. This concept is important to remember with all financial formulas.
Annuity Payment Formula Explained
The annuity payment formula can be determined by rearranging the PV of annuity formula.
After rearranging the formula to solve for P, the formula would become:
This can be further simplified by multiplying the numerator times the reciprocal of the denominator, which is the formula shown at the top of the page.
