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
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:
Find the value of the un-levered firm.
Calculate the net value of debt financing.
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.
Key Takeaways
APV is the NPV of a project or company if financed solely by equity plus the present value of financing benefits.
APV shows an investor the benefit of tax shields from tax-deductible interest payments.
It is best used for leverage transactions, such as leveraged buyouts, but is more of an academic calculation.
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.
The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. Unlike simple interest, compounding interest is calculated periodically and the amount is immediately added to the balance. With each period going forward, the account balance gets a little bigger, so the interest paid on the balance gets bigger as well.
Key Takeaways
APY is the actual rate of return that will be earned in one year if the interest is compounded.
Compound interest is added periodically to the total invested, increasing the balance. That means each interest payment will be larger, based on the higher balance.
The more often interest is compounded, the higher the APY will be.
APY has a similar concept as annual percentage rate (APR), but APR is used for loans.
The APY on checking, savings, or certificate of deposit holdings will vary across product and may have a variable or fixed rate.
APR vs. APY: What’s the Difference?
Formula and Calculation of APY
APY standardizes the rate of return. It does this by stating the real percentage of growth that will be earned in compound interest assuming that the money is deposited for one year. The formula for calculating APY is:
Where:
r = period rate
n = number of compounding periods
What Annual APY Can Tell You
Any investment is ultimately judged by its rate of return, whether it’s a certificate of deposit (CD), a share of stock, or a government bond. The rate of return is simply the percentage of growth in an investment over a specific period of time, usually one year. But rates of return can be difficult to compare across different investments if they have different compounding periods. One may compound daily, while another compounds quarterly or biannually.
Comparing rates of return by simply stating the percentage value of each over one year gives an inaccurate result, as it ignores the effects of compounding interest. It is critical to know how often that compounding occurs, since the more often a deposit compounds, the faster the investment grows. This is due to the fact that every time it compounds the interest earned over that period is added to the principal balance and future interest payments are calculated on that larger principal amount.
Comparing the APY on 2 Investments
Suppose you are considering whether to invest in a one-year zero-coupon bond that pays 6% upon maturity or a high-yield money market account that pays 0.5% per month with monthly compounding.
At first glance, the yields appear equal because 12 months multiplied by 0.5% equals 6%. However, when the effects of compounding are included by calculating the APY, the money market investment actually yields (1 + .005)^12 – 1 = 0.06168 = 6.17%.
Comparing two investments by their simple interest rates doesn’t work as it ignores the effects of compounding interest and how often that compounding occurs.
APY vs. APR
APY is similar to the annual percentage rate (APR) used for loans. The APR reflects the effective percentage that the borrower will pay over a year in interest and fees for the loan. APY and APR are both standardized measures of interest rates expressed as an annualized percentage rate.
However, APY takes into account compound interest while APR does not. Furthermore, the equation for APY does not incorporate account fees, only compounding periods. That’s an important consideration for an investor, who must consider any fees that will be subtracted from an investment’s overall return.
Example of APY
If you deposited $100 for one year at 5% interest and your deposit was compounded quarterly, at the end of the year you would have $105.09. If you had been paid simple interest, you would have had $105.
The APY would be (1 + .05/4) * 4 – 1 = .05095 = 5.095%.
It pays 5% a year interest compounded quarterly, and that adds up to 5.095%. That’s not too dramatic. However, if you left that $100 for four years and it was being compounded quarterly then the amount your initial deposit would have grown to $121.99. Without compounding it would have been $120.
X = D(1 + r/n)n*y
= $100(1 + .05/4)4*4
= $100(1.21989)
= $121.99
where:
X = Final amount
D = Initial Deposit
r = period rate
n = number of compounding periods per year
y = number of years
Special Considerations
Compound Interest
The premise of APY is rooted in the concept of compounding or compound interest. Compound interest is the financial mechanism that allows investment returns to earn returns of their own.
Imagine investing $1,000 at 6% compounded monthly. At the start of your investment, you have $1,000.
After one month, your investment will have earned one month worth of interest at 6%. Your investment will now be worth $1,005 ($1,000 * (1 + .06/12)). At this point, we have not yet seen compounding interest.
After the second month, your investment will have earned a second month of interest at 6%. However, this interest is earned on both your initial investment as well as your $5 interest earned last month. Therefore, your return this month will be greater than last month because your investment basis will be higher. Your investment will now be worth $1,010.03 ($1,005 * (1 + .06/12)). Notice that the interest earned this second month is $5.03, different from the $5.00 from last month.
After the third month, your investment will earn interest on the $1,000, the $5.00 earned from the first month, and the $5.03 earned from the second month. This demonstrates the concept of compound interest: the monthly amount earned will continually increase as long as the APY doesn’t decrease and the investment principal is not reduced.
Banks in the U.S. are required to include the APY when they advertise their interest-bearing accounts. That tells potential customers exactly how much money a deposit will earn if it is deposited for 12 months.
Variable APY vs. Fixed APY
Savings or checking accounts may have either a variable APY or fixed APY. A variable APY is one that fluctuates and changes with macroeconomic conditions, while a fixed APY does not change (or changes much less frequently). One type of APY isn’t necessarily better than the other. While locking into a fixed APY sounds appealing, consider periods when the Federal Reserve is raising rates and APYs increase each month.
Most checking, savings, and money market accounts have variable APYs, though some promotional bank accounts or bank account bonuses may have a higher fixed APY up to a specific level of deposits. For example. a bank may reward 5% APY on the first $500 deposited, then pay 1% APY on all other deposits.
APY and Risk
In general, investors are usually awarded higher yields when they take on greater risk or agree to make sacrifices. The same can be said regarding the APY of checking, saving, and certificate of deposits.
When a consumer holds money in a checking account, the consumer is asking to have their money on demand to pay for expenses. At a given notice, the consumer may need to pull out their debit card, buy groceries, and draw down their checking account. For this reason, checking accounts often have the lowest APY because there is no risk or sacrifice for the consumer.
When a consumer holds money in a savings account, the consumer may not have immediate need. The consumer may need to transfer funds to their checking account before it can be used. Alternatively, you cannot write checks from normal savings accounts. For this reason, savings accounts usually have higher APYs than checking accounts because consumers face greater limits with savings accounts.
Last, when consumers hold a certificate of deposit, the consumer is agreeing to sacrifice liquidity and access to funds in return for a higher APY. The consumer can’t use or spend the money in a CD (or they can after paying a penalty to break the CD). For this reason, the APY on a CD is highest of three as the consumer is being rewarded for sacrificing immediate access to their funds.
What Is APY and How Does It Work?
APY is the annual percent yield that reflects compounding on interest. It reflects the actual interest rate you earn on an investment because it considers the interest you make on your interest.
Consider the example above where the $100 investment yields 5% compounded quarterly. During the first quarter, you earn interest on the $100. However, during the second quarter, you earn interest on the $100 as well as the interest earned in the first quarter.
What Is a Good APY Rate?
APY rates fluctuate often, and a good rate at one time may no longer be a good rate due to shifts in macroeconomic conditions. In general, when the Federal Reserve raises interest rates, the APY on savings accounts tends to increase. Therefore, APY rates on savings accounts are usually better when monetary policy is tight or tightening. In addition, there are often low-cost, high-yield savings accounts that consistently deliver competitive APYs.
How Is APY Calculated?
APY standardizes the rate of return. It does this by stating the real percentage of growth that will be earned in compound interest assuming that the money is deposited for one year. The formula for calculating APY is: (1+r/n)n – 1, where r = period rate and n = number of compounding periods.
How Can APY Assist an Investor?
Any investment is ultimately judged by its rate of return, whether it’s a certificate of deposit, a share of stock, or a government bond. APY allows an investor to compare different returns for different investments on an apples-to-apples basis, allowing them to make a more informed decision.
What Is the Difference Between APY and APR?
APY calculates that rate earned in one year if the interest is compounded and is a more accurate representation of the actual rate of return. APR includes any fees or additional costs associated with the transaction, but it does not take into account the compounding of interest within a specific year. Rather, it is a simple interest rate.
The Bottom Line
APY in banking is the actual rate of return you will earn on your checking or savings account. As opposed to simple interest calculations, APY considers the compounding effect of prior interest earned generating future returns. For this reason, APY will often be higher than simple interest, especially if the account compounds often.
An arm’s length transaction refers to a business deal in which buyers and sellers act independently without one party influencing the other. Arm’s length transactions assert that both parties act in their own self-interest and are not subject to pressure from the other party. They also assure others that there is no collusion between the buyer and seller. In the interest of fairness, both parties usually have equal access to information related to the deal.
Key Takeaways
An arm’s length transaction is a business deal that involves parties who act independently of one another.
Both parties involved in an arm’s length sale usually have no relationship with each other.
These types of deals in real estate help ensure that properties are priced at their fair market value.
Arm’s length transactions can have an effect on financing and taxes.
Deals between family members or companies with related shareholders are not considered arm’s length transactions.
Understanding Arm’s Length Transactions
Arm’s length transactions are commonly used in real estate deals because the sale affects not only those who are directly involved in the deal but other parties as well, including lenders.
If two strangers are involved in the sale and purchase of a house, the final agreed-upon price is likely close to fair market value (FMV), assuming that both parties have equal bargaining power and the same information about the property. The seller would want a price that’s as high as possible, and the buyer would want a price that is as low as possible. Otherwise, the agreed-upon price is not likely to differ from the property’s actual FMV.
As noted above, the buyer and seller aren’t the only ones involved in an arm’s length transaction. This type of transaction also has a direct impact on the financing needed from a bank as well as municipal and local taxes. The transaction can also influence comparable prices in the market.
Arm’s Length vs. Non-Arm’s Length Transactions
Family members and companies with related shareholders generally don’t engage in arm’s length sales. Instead, the deals between them are non-arm’s length transactions. This type of transaction, which is also known as an arm-in-arm transaction, refers to a business deal in which buyers and sellers have an identity of interest. Put simply, buyers and sellers have an existing relationship that is either business-related or personal.
An existing relationship tends to influence the terms of a non-arm’s length transaction. For instance, it’s unlikely that a transaction involving a father and his son would yield the same result as a deal between strangers because the father may choose to give his son a discount.
If the sale of a house between father and son is taxable, tax authorities may require the seller to pay taxes on the gain he would have realized had he been selling to a neutral third party. They would disregard the actual price paid by the son.
In the same way, international sales between non-arm’s-length companies, such as two subsidiaries of the same parent company, must be made using arm’s length prices. This practice, known as transfer pricing, assures that each country collects the appropriate taxes on the transactions.
Tax laws throughout the world are designed to treat the results of a transaction differently when parties are dealing at arm’s length and when they are not.
Arm’s Length Transactions and Fair Market Value (FMV)
As noted above, one of the main benefits of arm’s length transactions is that the transaction is fair and equitable. This is especially true when it comes to real estate deals. When the buyer and seller have no previous relationship, the terms of the deal—notably, the sale price—accurately reflect market conditions rather than being influenced by other factors. This value is referred to as the fair market value.
FMV is the best possible price that a neutral and impartial seller and buyer are willing to accept and pay to close the deal. The following are just some of the factors that are used to determine the FMV of a home:
Location (city, neighborhood)
Comparable home prices
Condition and age of home
Size and amenities
Renovations and upgrades made to the property
Of course, other factors also work into the FMV of a home, including interest rates and the condition of the overall economy.
Example of an Arm’s Length Transaction
Let’s use a hypothetical example to show how arm’s length transactions work. We can start by expanding on the example above using the father and son and the real estate transaction. For clarity’s sake, let’s say the father’s name is John and the son’s name is Henry.
Assume that John is selling his home and puts the house up for sale for $350,000. He gets an offer for that amount based on the FMV. The potential buyer looked at some of the factors affecting the value, including the location, amenities, and comparable homes. If the sale goes through, it’s considered a arm’s length transaction.
But Henry throws John a loop saying he needs a new place and would like to buy the home for himself. He offers a lower price of $275,000 since it’s his father who’s selling the house. If John decides to accept, he would be conducting a non-arm’s length transaction.
What Is the Difference Between an Arm’s Length Transaction and Other Sales?
The term “Arm’s Length Transaction” refers to transactions that are conducted between parties who are acting independently from one another and are not associated with one another outside of the transaction in question. By contrast, a transaction would not be “arm’s length” if the buyer and seller are personally related—such as being family members or personal friends. Transactions between related businesses, such as those made between a parent company and its subsidiary, would also not be arm’s length.
Why Are Arm’s Length Transactions Important?
The question of whether or not a transaction is arm’s length matters because it can have legal and tax implications. For example, when a multinational corporation engages in transactions with its affiliated companies throughout the world, it must ensure that those transactions are made at fair market values to ensure that the correct taxes are paid in each jurisdiction.
Similarly, conglomerates and holding companies can potentially run into legal and regulatory challenges if the companies within their organization do not transact with one another at arm’s length. Ultimately, Arm’s Length Transactions are intended to encourage fair and reasonable business practices and to protect the public at large.
What Are Some Examples of Non-Arm’s Length Transactions?
To illustrate, consider the case of a mother who wishes to sell her car to her son. She might choose to give her son a discount on the car, even though she could obtain a higher price if she sold it to an arms-length buyer. In this scenario, the transaction is not arm’s length, because the buyer and seller are already associated as family members.
Although this example is benign, other examples could be more harmful. For instance, if the founder of a publicly traded company engages in nepotism by appointing one of their family members to an important position within the company, even though other more qualified candidates were available, this decision could harm the company’s shareholders.
The Bottom Line
Every buyer and seller wants to get the best price possible for their financial transactions. One of the best ways to do so is to conduct an arm’s length transaction. Being at arm’s length means there are no personal factors that influence the price and the decision to either accept or reject an offer. Those who execute non-arm’s length transactions may not get the best price, which can also affect the overall market and lending decisions.
Adjusted gross income (AGI) is the figure that the Internal Revenue Service (IRS) uses to determine your income tax liability for the year. It is calculated by subtracting certain adjustments from gross income, such as business expenses, student loan interest payments, and other expenses. After calculating a taxpayer’s AGI, the next step is to subtract deductions to determine their taxable income.
The IRS also uses other income metrics, such as modified AGI (MAGI), for specific programs and retirement accounts.
Key Takeaways
The IRS uses your adjusted gross income (AGI) to determine how much income tax you owe for the year.
AGI is calculated by taking all of your income for the year (your gross income) and subtracting certain adjustments to income.
Your AGI can affect the size of your tax deductions as well as your eligibility for some types of retirement plan contributions, such as a Roth individual retirement account (Roth IRA).
Modified adjusted gross income (MAGI) is your AGI with some otherwise-allowable deductions added back in. For many people, AGI and MAGI will be the same.
Among the items subtracted from your gross income when calculating your AGI are alimony payments and educator expenses.
Click Play to Learn All About Adjusted Gross Income
Understanding Adjusted Gross Income (AGI)
As prescribed in the United States tax code, AGI is a modification of gross income. Gross income is simply the sum of all the money you earned in a year, which may include wages, dividends, capital gains, interest income, royalties, rental income, alimony, and retirement distributions, before tax or other deductions. AGI makes certain adjustments to your gross income to reach the figure on which your tax liability will be calculated.
Many U.S. states also use the AGI from federal returns to calculate how much individuals owe in state income taxes. States may modify this number further with state-specific deductions and credits.
AGI is an important figure because it is what is used to determine your eligibility for certain deductions and credits.
Common Adjustments
The items subtracted from your gross income to calculate your AGI are referred to as adjustments to income, and you report them on Schedule 1 of your tax return when you file your annual tax return. Some of the most common adjustments are listed here, along with the separate tax forms on which a few of them are calculated:
Alimony payments (for divorces filed before Jan. 1, 2019)
Early withdrawal penalties on savings
Educator expenses
Employee business expenses for armed forces reservists, qualified performing artists, fee-basis state or local government officials, and employees with impairment-related work expenses (Form 2106)
Health Savings Account (HSA) deductions (Form 8889)
Moving expenses for members of the armed forces (Form 3903)
Self-employed Simplified Employee Pension (SEP), Savings Incentive Match Plan for Employees of Small Employers (SIMPLE), and qualified plans
Self-employed health insurance deduction
Self-employment tax (the deductible portion)
Student loan interest deduction
How to Calculate Adjusted Gross Income
If you use software to prepare your tax return, it will calculate your AGI once you input your numbers. If you calculate it yourself, you’ll begin by tallying your reported income for the year. That might include job income, as reported to the IRS by your employer on a W-2 form, plus other income, such as dividends and miscellaneous income, reported on 1099 forms.
Next, you add any taxable income from other sources, such as profit on the sale of a property, unemployment compensation, pensions, Social Security payments, or anything else that hasn’t already been reported to the IRS. Many of these income items are also listed on IRS Schedule 1.
The next step is to subtract the applicable adjustments to the income listed above from your reported income. The resulting figure is your AGI. To determine your taxable income, subtract either the standard deduction or your total itemized deductions from your AGI. In most cases, you can choose whichever gives you the most benefit.
For example, the standard deduction for tax returns for married couples filing jointly was $25,900 in 2022, rising to $27,700 in 2023, so couples whose itemized deductions exceed that amount would generally opt to itemize, while others would take the standard deduction.
The IRS provides a list of itemized deductions and the requirements for claiming them on its website. Your AGI also affects your eligibility for many of the deductions and credits available on your tax return. In general, the lower your AGI, the more significant the number of deductions and credits you will be eligible to claim, and the more you’ll be able to reduce your tax bill.
An Example of AGI Affecting Deductions
Let’s say you had some significant dental expenses during the year that weren’t reimbursed by insurance, and you’ve decided to itemize your deductions. You are allowed to deduct the portion of those expenses that exceed 7.5% of your AGI.
This means that if you report $12,000 in unreimbursed dental expenses and have an AGI of $100,000, you can deduct the amount that exceeds $7,500, which is $4,500. However, if your AGI is $50,000, the 7.5% reduction is just $3,750, and you’d be entitled to deduct a larger amount of that $12,000, in this case $8,250.
Adjusted Gross Income (AGI) vs. Modified Adjusted Gross Income (MAGI)
In addition to AGI, some tax calculations and government programs call for using what’s known as your modified adjusted gross income, or MAGI. This figure starts with your AGI, then adds back certain items, such as any deductions you take for student loan interest or tuition and fees.
Your MAGI is used to determine how much, if anything, you can contribute to a Roth individual retirement account (Roth IRA) in any given year. It is also used to calculate your income if you apply for Marketplace health insurance under the Affordable Care Act (ACA).
Many people with relatively uncomplicated financial lives find that their AGI and MAGI are the same number or very close.
If you file your taxes electronically, the IRS form will ask you for your previous year’s AGI as a way of verifying your identity.
Adjusted Gross Income vs. Gross Income vs. Taxable Income
Your gross income is all of the money you’ve earned in a year that isn’t exempt from taxation. This can be in the form of salary, wages, interest, dividends, capital gains, and so on.
Your adjusted gross income takes that amount and takes out certain qualified expenses and adjustments.
Taxpayers can then take either the standard deduction for their filing status or itemize the deductible expenses they paid during the year. You’re not permitted to both itemize deductions and claim the standard deduction. The result is your taxable income.
Where to Find Your Adjusted Gross Income (AGI)
You report your AGI on line 11 of IRS Form 1040, which is the form you use to file your income taxes for the year. Keep that number handy after completing your taxes, because you will need it again if you e-file your taxes next year. The IRS uses it as a way to verify your identity.
Also, note that as of January 2022, almost anyone may use the IRS Free File program to file their federal (and, in some cases, state) taxes electronically at no charge.
Frequently Asked Questions
What Does Adjusted Gross Income (AGI) Mean for Tax Payments?
Adjusted gross income (AGI) is essentially your income for the year after accounting for all applicable tax deductions. It is an important number that is used by the Internal Revenue Service (IRS) to determine how much you owe in taxes. AGI is calculated by taking your gross income from the year and subtracting any deductions that you are eligible to claim. Therefore, your AGI will always be less than or equal to your gross income.
What Are Some Common Adjustments Used When Determining AGI?
There are a wide variety of adjustments that might be made when calculating AGI, depending on the financial and life circumstances of the filer. Moreover, since the tax laws can be changed by lawmakers, the list of available adjustments can change over time. Some of the most common adjustments used when calculating AGI include reductions for alimony and student loan interest payments.
What Is the Difference Between AGI and Modified Adjusted Gross Income (MAGI)?
AGI and modified adjusted gross income (MAGI) are very similar, except that MAGI adds back certain deductions. For this reason, MAGI would always be larger than or equal to AGI. Common examples of deductions that are added back to calculate MAGI include foreign earned income, income earned on U.S. savings bonds, and losses arising from a publicly traded partnership.
The Bottom Line
Adjusted gross income, or AGI, is your gross income after it has been adjusted for certain qualified deductions that are permitted by the Internal Revenue Service (IRS). These qualified deductions reduce an individual’s gross income, thus reducing the taxable income that they will ultimately have to pay taxes on. You can save money come tax season by lowering your AGI, which will lower your taxable income, in turn. However, many of the adjustments allowed for AGI are specific for particular circumstances that may not apply to everyone.
