What Is an Annuity Table?

An annuity table is a tool for determining the present value of an annuity or other structured series of payments. Such a tool, used by accountants, actuaries, and other insurance personnel, takes into account how much money has been placed into an annuity and how long it has been there to determine how much money would be due to an annuity buyer or annuitant.

Figuring the present value of any future amount of an annuity may also be performed using a financial calculator or software built for such a purpose.

How an Annuity Table Works

An annuity table provides a factor, based on time, and a discount rate (interest rate) by which an annuity payment can be multiplied to determine its present value. For example, an annuity table could be used to calculate the present value of an annuity that paid $10,000 a year for 15 years if the interest rate is expected to be 3%.

According to the concept of the time value of money, receiving a lump sum payment in the present is worth more than receiving the same sum in the future. As such, having $10,000 today is better than being given $1,000 per year for the next 10 years because the sum could be invested and earn interest over that decade. At the end of the 10-year period, the $10,000 lump sum would be worth more than the sum of the annual payments, even if invested at the same interest rate.

Annuity Table and the Present Value of an Annuity

Present Value of an Annuity Formulas

The formula for the present value of an ordinary annuity, as opposed to an annuity due, is as follows:


$\begin{aligned}&\text{P} =\text{PMT}\times\frac{ 1 – (1 + r) ^ -n}{r}\\&\textbf{where:}\\&\text{P} = \text{Present value of an annuity stream}\\&\text{PMT} =\text{Dollar amount of each annuity payment}\\&r = \text{Interest rate (also known as the discount rate)}\\&n = \text{Number of periods in which payments will be made}\end{aligned}$​P=PMT×r1−(1+r)−n​where:P=Present value of an annuity streamPMT=Dollar amount of each annuity paymentr=Interest rate (also known as the discount rate)​

Assume an individual has an opportunity to receive an annuity that pays $50,000 per year for the next 25 years, with a discount rate of 6%, or a lump sum payment of $650,000. He needs to determine the more rational option. Using the above formula, the present value of this annuity is:


$\begin{aligned}&\text{PVA} = \$50,000 \times \frac{1 – (1 + 0.06) ^ -25}{0.06} = \$639,168\\&\textbf{where:}\\&\text{PVA}=\text{Present value of annuity}\end{aligned}$​PVA=$50,000×0.061−(1+0.06)−25​=$639,168where:​

Given this information, the annuity is worth $10,832 less on a time-adjusted basis, and the individual should choose the lump sum payment over the annuity.

Note, this formula is for an ordinary annuity where payments are made at the end of the period in question. In the above example, each $50,000 payment would occur at the end of the year, each year, for 25 years. With an annuity due, the payments are made at the beginning of the period in question. To find the value of an annuity due, simply multiply the above formula by a factor of (1 + r):


$\begin{aligned}&\text{P} = \text{PMT} \times\left(\frac{1 – (1 + r) ^ -n}{r}\right) \times (1 + r)\end{aligned}$​P=PMT×(r1−(1+r)−n​)×(1+r)​

If the above example of an annuity due, its value would be:


$\begin{aligned}&\text{P}= \$50,000\\&\quad \times\left( \frac{1 – (1 + 0.06) ^ -25}{0.06}\right)\times (1 + 0.06) = \$677,518\end{aligned}$​P=$50,000​

In this case, the individual should choose the annuity due, because it is worth $27,518 more than the lump sum payment.

Present Value of an Annuity Table

Rather than working through the formulas above, you could alternatively use an annuity table. An annuity table simplifies the math by automatically giving you a factor for the second half of the formula above. For example, the present value of an ordinary annuity table would give you one number (referred to as a factor) that is pre-calculated for the (1 – (1 + r) ^ – n) / r) portion of the formula.

The factor is determined by the interest rate (r in the formula) and the number of periods in which payments will be made (n in the formula). In an annuity table, the number of periods is commonly depicted down the left column. The interest rate is commonly depicted across the top row. Simply select the correct interest rate and number of periods to find your factor in the intersecting cell. That factor is then multiplied by the dollar amount of the annuity payment to arrive at the present value of the ordinary annuity.

Below is an example of a present value of an ordinary annuity table:

What Is Adjusted Present Value (APV)?

The adjusted present value is the net present value (NPV) of a project or company if financed solely by equity plus the present value (PV) of any financing benefits, which are the additional effects of debt. By taking into account financing benefits, APV includes tax shields such as those provided by deductible interest.

The Formula for APV Is


$\begin{aligned} &\text{Adjusted Present Value = Unlevered Firm Value + NE}\\ &\textbf{where:}\\ &\text{NE = Net effect of debt}\\ \end{aligned}$​Adjusted Present Value = Unlevered Firm Value + NEwhere:NE = Net effect of debt​

The net effect of debt includes tax benefits that are created when the interest on a company’s debt is tax-deductible. This benefit is calculated as the interest expense times the tax rate, and it only applies to one year of interest and tax. The present value of the interest tax shield is therefore calculated as: (tax rate * debt load * interest rate) / interest rate.

How to Calculate Adjusted Present Value (APV)

To determine the adjusted present value:

1. Find the value of the un-levered firm.
2. Calculate the net value of debt financing.
3. Sum the value of the un-levered project or company and the net value of the debt financing.

How to Calculate APV in Excel

An investor can use Excel to build out a model to calculate the net present value of the firm and the present value of the debt.

What Does Adjusted Present Value Tell You?

The adjusted present value helps to show an investor the benefits of tax shields resulting from one or more tax deductions of interest payments or a subsidized loan at below-market rates. For leveraged transactions, APV is preferred. In particular, leveraged buyout situations are the most effective situations in which to use the adjusted present value methodology.

The value of a debt-financed project can be higher than just an equity-financed project, as the cost of capital falls when leverage is used. Using debt can actually turn a negative NPV project into one that’s positive. NPV uses the weighted average cost of capital as the discount rate, while APV uses the cost of equity as the discount rate.

Example of How to Use Adjusted Present Value (APV)

In a financial projection where a base-case NPV is calculated, the sum of the present value of the interest tax shield is added to obtain the adjusted present value.

For example, assume a multi-year projection calculation finds that the present value of Company ABC’s free cash flow (FCF) plus terminal value is $100,000. The tax rate for the company is 30% and the interest rate is 7%. Its $50,000 debt load has an interest tax shield of $15,000, or ($50,000 * 30% * 7%) / 7%. Thus, the adjusted present value is $115,000, or $100,000 + $15,000.

The Difference Between APV and Discounted Cash Flow (DCF)

While the adjusted present value method is similar to the discounted cash flow (DCF) methodology, adjusted present cash flow does not capture taxes or other financing effects in a weighted average cost of capital (WACC) or other adjusted discount rates. Unlike WACC used in discounted cash flow, the adjusted present value seeks to value the effects of the cost of equity and cost of debt separately. The adjusted present value isn’t as prevalent as the discounted cash flow method.

Limitations of Using Adjusted Present Value (APV)

In practice, the adjusted present value is not used as much as the discounted cash flow method. It is more of an academic calculation but is often considered to result in more accurate valuations.

Learn More About Adjusted Present Value (APV)

To dig deeper into calculating the adjusted present value, check out Investopedia’s guide to calculating net present value.

What Is Annuity Due?

An annuity due is an annuity whose payment is due immediately at the beginning of each period. A common example of an annuity due payment is rent, as landlords often require payment upon the start of a new month as opposed to collecting it after the renter has enjoyed the benefits of the apartment for an entire month.

How Annuity Due Works

An annuity due requires payments made at the beginning, as opposed to the end, of each annuity period. Annuity due payments received by an individual legally represent an asset. Meanwhile, the individual paying the annuity due has a legal debt liability requiring periodic payments.

Because a series of annuity due payments reflect a number of future cash inflows or outflows, the payer or recipient of the funds may wish to calculate the entire value of the annuity while factoring in the time value of money. One can accomplish this by using present value calculations.

A present value table for an annuity due has the projected interest rate across the top of the table and the number of periods as the left-most column. The intersecting cell between the appropriate interest rate and the number of periods represents the present value multiplier. Finding the product between one annuity due payment and the present value multiplier yields the present value of the cash flow.

A whole life annuity due is a financial product sold by insurance companies that require annuity payments at the beginning of each monthly, quarterly, or annual period, as opposed to at the end of the period. This is a type of annuity that will provide the holder with payments during the distribution period for as long as they live. After the annuitant passes on, the insurance company retains any funds remaining.

Annuity Due vs. Ordinary Annuity

An annuity due payment is a recurring issuance of money upon the beginning of a period. Alternatively, an ordinary annuity payment is a recurring issuance of money at the end of a period. Contracts and business agreements outline this payment, and it is based on when the benefit is received. When paying for an expense, the beneficiary pays an annuity due payment before receiving the benefit, while the beneficiary makes ordinary due payments after the benefit has occurred.

The timing of an annuity payment is critical based on opportunity costs. The collector of the payment may invest an annuity due payment collected at the beginning of the month to generate interest or capital gains. This is why an annuity due is more beneficial for the recipient as they have the potential to use funds faster. Alternatively, individuals paying an annuity due lose out on the opportunity to use the funds for an entire period. Those paying annuities thus tend to prefer ordinary annuities.

Examples of Annuity Due

An annuity due may arise due to any recurring obligation. Many monthly bills, such as rent, car payments, and cellphone payments, are annuities due because the beneficiary must pay at the beginning of the billing period. Insurance expenses are typically annuities due as the insurer requires payment at the start of each coverage period. Annuity due situations also typically arise relating to saving for retirement or putting money aside for a specific purpose.

How to Calculate the Value of an Annuity Due

The present and future values of an annuity due can be calculated using slight modifications to the present value and future value of an ordinary annuity.

Present Value of an Annuity Due

The present value of an annuity due tells us the current value of a series of expected annuity payments. In other words, it shows what the future total to be paid is worth now.

Calculating the present value of an annuity due is similar to calculating the present value of an ordinary annuity. However, there are subtle differences to account for when annuity payments are due. For an annuity due, payments are made at the beginning of the interval, and for an ordinary annuity, payments are made at the end of a period. The formula for the present value of an annuity due is:

With:

• C = Cash flows per period
• i = interest rate
• n = number of payments

Let’s look at an example of the present value of an annuity due. Suppose you are a beneficiary designated to immediately receive $1000 each year for 10 years, earning an annual interest rate of 3%. You want to know how much the stream of payments is worth to you today. Based on the present value formula, the present value is $8,786.11.

Future Value of an Annuity Due

The future value of an annuity due shows us the end value of a series of expected payments or the value at a future date.

Just as there are differences in how the present value is calculated for an ordinary annuity and an annuity due, there are also differences in how the future value of money is calculated for an ordinary annuity and an annuity due. The future value of an annuity due is calculated as:

Using the same example, we calculate that the future value of the stream of income payments to be $11,807.80.

Annuity Due FAQs

Which Is Better, Ordinary Annuity or Annuity Due?

Whether an ordinary annuity or an annuity due is better depends on whether you are the payee or payer. As a payee, an annuity due is often preferred because you receive payment up front for a specific term, allowing you to use the funds immediately and enjoy a higher present value than that of an ordinary annuity. As a payer, an ordinary annuity might be favorable as you make your payment at the end of the term, rather than the beginning. You are able to use those funds for the entire period before paying.

Often, you are not afforded the option to choose. For example, insurance premiums are an example of an annuity due, with premium payments due at the beginning of the covered period. A car payment is an example of an ordinary annuity, with payments due at the end of the covered period.

What Is an Immediate Annuity?

An immediate annuity is an account, funded with a lump sum deposit, that generates an immediate stream of income payments. The income can be for a stated amount (e.g., $1,000/month), a stated period (e.g., 10 years), or a lifetime.

How Do You Calculate the Future Value of an Annuity Due?

The future value of an annuity due is calculated using the formula:

where

• C = cash flows per period
• i = interest rate
• n = number of payments

What Does Annuity Mean?

An annuity is an insurance product designed to generate payments immediately or in the future to the annuity owner or a designated payee. The account holder either makes a lump sum payment or a series of payments into the annuity and can either receive an immediate stream of income or defer receiving payments until some time in the future, usually after an accumulation period where the account earns interest tax-deferred.

What Happens When an Annuity Expires?

Once an annuity expires, the contract terminates and no future payments are made. The contractual obligation is fulfilled, with no further duties owed from either party.

The Bottom Line

An annuity due is an annuity with payment due or made at the beginning of the payment interval. In contrast, an ordinary annuity generates payments at the end of the period. As a result, the method for calculating the present and future values differ. A common example of an annuity due is rent payments made to a landlord, and a common example of an ordinary annuity includes mortgage payments made to a lender. Depending on whether you are the payer or payee, the annuity due might be a better option.

What Is an Appraisal?

An appraisal is a valuation of property, such as real estate, a business, collectible, or an antique, by the estimate of an authorized person. The authorized appraiser must have a designation from a regulatory body governing the jurisdiction of the appraiser. Appraisals are typically used for insurance and taxation purposes or to determine a possible selling price for an item or property.

Understanding Appraisals

Appraisals are used in many types of transactions, including real estate. If a home valuation, for example, comes in below the amount of the purchase price, mortgage lenders are likely to decline to fund the deal. Unless the prospective buyer is willing and able to come up with the difference between the appraised value and the lender’s financing offer, the transaction will not go forward.

The appraiser can use any number of valuation methods to determine the appropriate value of an item or property, including comparing the current market value of similar properties or objects.

Appraisals are also done for tax purposes when determining the value of charitable donations for itemized deductions. Deductions can reduce your taxes owed to the IRS by deducting the value of your donation from your taxable income.

Appraisals can also be a helpful tool in resolving conflicts between heirs to an estate by establishing the value of the real estate or personal property to be divided.

Types of Appraisals

Home Appraisals

A home valuation is necessary during the process of buying and selling a home, as well as a refinance of an existing mortgage. A refinance is when a loan or mortgage is reevaluated and updated to current interest rates and new terms.

An appraisal determines the home’s value to ensure that the price reflects the home’s condition, age, location, and features such as the number of bathrooms. Also, valuations help banks and lenders avoid loaning more money to the borrower than the house is worth.

In the event of default, when the borrower can’t make the payments anymore, the bank uses the appraisal as a valuation of the home. If the home is in foreclosure, whereby the bank takes possession of the house, it must be resold to help the lender recoup any losses from making the mortgage loan.

It’s important to remember that when a bank lends for a mortgage, it gives the full amount of the home’s value to the seller on the date it’s sold. In other words, the bank is out the money and, in return, has a promise to pay, plus interest, from the borrower. As a result, the valuation is important to the lending process since it helps the bank avoid losses and protect itself against lending more than it might be able to recover if the borrower defaults.

Collectibles or Antiques

Professional appraisals can be done for many items, including collectibles, antiques, or grandma’s silver. Ideally, you’ll want multiple valuations for an item from an accredited professional. Appraisers might charge an hourly rate or a flat fee. 

A certified appraiser’s valuation will likely be fair and unbiased, whereas the local collectible shop has an incentive to offer you less for the item. Also, owners can get an idea of an item’s value by checking collectible magazines and online appraisal websites. Most websites charge a small fee, such as $10, to value an item. Of course, obtaining a value online is done through photos of the item and is not an official valuation, but it should give you an idea of what it’s worth before proceeding. If you decide to pursue an appraisal, the American Society of Appraisers has thousands of members and is a great place to begin searching for an accredited professional.

Appraisals and Insurance

Some types of insurance policies also require appraisals of goods being insured. Homeowners’ and renters’ insurance policies protect policyholders against the loss of personal property due to theft or damage. These blanket policies cover items up to a preset dollar limit. Obtaining an appraisal of the contents of a home creates an inventory of the owner’s property and establishes its value, which helps to ensure a swift settlement if a claim is filed.

When the value of specific items exceeds a homeowners policy limit, the policyholder may wish to obtain additional insurance that covers luxury items such as jewelry or collectibles, including art objects and antiques. Before issuing personal property insurance policies for high-end items, many insurance underwriters require applicants to have the object appraised. The appraisal creates a record of the item’s existence, along with its description. It also helps establish the item’s actual value.

Some insurance contracts include an appraisal clause that specifies the owner agrees to obtain an appraisal from a mutually agreeable expert in the event of a dispute between the owner and the insurance company. Neutral appraisals can speed the resolution of a settlement and keep disputes from escalating into lengthy and expensive lawsuits.

Home Appraisal Process and Cost

The home appraisal process typically begins after a buyer makes an offer on a home and that offer is accepted by the seller. The buyer’s mortgage lender or broker may order the appraisal on their behalf, though the buyer is typically expected to pay for it out of pocket. On average, a home appraisal for a single-family property runs between $300 and $450 while appraisals for multi-family homes can start at around $500.

Once the appraisal is ordered, the appraiser will schedule a time to visit the property. The appraiser will then conduct a thorough review of the interior and exterior of the home to determine what it’s worth. This may require them to take measurements or photos of the property. Appraisals can take a few minutes to a few hours to complete, depending on the details of the home and the appraiser’s methods.

After visiting the home, the appraiser will use the information they’ve collected to create a reasonable estimate for the home’s value. At this stage, the appraiser will also look at the values of comparable homes in the area. Using these comps and what they’ve learned from visiting the home, the appraiser will prepare an appraisal report that includes a figure that represents their perceived value of the home.

A copy of this appraisal report is then shared with the buyer and the buyer’s mortgage lender. It can take anywhere from a week to 10 days for the report to be completed. Sellers can also request a copy of the report.

If a buyer disagrees with the appraisal report, they can request a reconsideration from the lender or opt to pay for a second appraisal.

How To Improve Your Home’s Appraisal Value

The appraisal process is meant to be objective, but appraisers are human. Good curb appeal and clean, uncluttered rooms send a message of a well-maintained home. And they can be achieved without a great deal of time or expense. There are some easy ways to quickly improve the appraised value of your home:

• Lean and uncluttered rooms convey the message that a home is well-maintained.
• Minor cosmetic improvements can make a big difference.
• Point out any major improvements you’ve made to the appraiser, in case they miss them.

On the other hand, you should avoid big expensive improvements just for the sake of increasing your home’s appraisal value. They generally don’t pay off.

Make sure you know your rights as well. If you hire the appraiser to determine your home’s value, the appraisal belongs to you. If you’re refinancing your mortgage and the lender hires the appraiser, the lender is required to provide you with a copy–possibly for a reasonable fee–of the appraisal and any other home value estimates.

If you think the appraiser has the value wrong, first review the written appraisal for errors. Check whether the comps the appraiser chose are reasonably similar to your home. If you still think the price is incorrect, you can appeal the valuation with your lender or ask it to order a second appraisal. 

The Bottom Line

An appraisal is an assessment of the fair market value of a property, business, antique, or even a collectible. Appraisals are used to estimate the value of items that are infrequently traded, and are often rare or unique. The authorized appraiser must have a designation from a regulatory body governing the jurisdiction of the appraiser. Appraisals can be done for many reasons such as tax purposes when valuing charitable donations, but the most familiar form of appraisal is for a property.

Home appraisals can positively or negatively impact the sale of a house or property, and so are an important part of the process of financing a house. A home appraisal is almost always a requirement when purchasing a home with a mortgage, for example, and if you are refinancing your property your lender may hire their own appraiser to make a valuation of your home.