How to Calculate Nominal After-Tax Rate of Return?

The nominal after-tax rate is the base rate of return on an investment adjusted for taxes. It provides an alternative approach to investors for comparing different investment options adjusted for different tax rates.

Let’s understand what the nominal post-tax rate of return is and how it is calculated.

What is the Nominal Rate of Return?

The nominal rate of return refers to the return achieved by an investment before adjusting any discounts, premiums, and expenses.

In simple words, it is the gross rate of return earned on an investment. It is simply the percentage term used for investment appreciation over a specific period.

Therefore, it expresses the gain or loss on an investment in a percentage term for a specified period. Since it does not adjust for any expenses or premiums, it is also called the face or book amount of a return.

The nominal rate of return can be contrasted with the real rate of return. It will include adjustments for inflation, taxes, premiums, commissions, and other expenses.

What is the Nominal After-Tax Rate of Return?

The nominal after-tax rate of return refers to the nominal rate adjusted for the tax effect on investment. It is simply a variation of the nominal rate of return used by investors to analyze the impact of taxation.

The nominal post-tax rate of return can be considered an intermediary rate between the nominal and real rate of return. The real rate of return adjusts for other factors including inflation, premiums, and management costs as well.

So, when investors only consider the tax expenses, it will give us the nominal post-tax rate of return. Since the inflation rate is hardly zero for any investment, it can’t be classified as the real rate of return.

How to Calculate Nominal After-Tax Rate of Return?

Let’s first list the formulas for a nominal and post-tax nominal rate of returns and then elaborate on the process to calculate these rates.

Nominal Rate of Return = [(Current Market Value – Original Market Value)/Original Market Value]*100

The formula can also be rearranged like this:

The nominal after-tax rate of return can be calculated by adjusting the tax factor:

Nominal After-Tax Rate of Return = Nominal Rate of Return × (1 – Effective Tax Rate)

You can follow these simple steps to calculate both these rates.

Step 01:

The first step is to arrange the investment’s original and current market values. For the second part, you’ll also need the effective tax rate applicable to the investor.

Step 02:

Subtract the original value of the investment from the current market value of the investment. Then, divide the result by the actual value of the investment.

Step 03:

Simply multiply the result by 100 to convert the figure into a percentage value.

Step 04:

Now, you can use the formula listed above to account for the tax rate. In this step, you can also directly deduct the inflation rate from the nominal rate to calculate the after-tax rate of return.

Example

Suppose an investor purchased 1,500 stocks at \$37 per share worth \$ 55,500. The investor holds these stocks for one year and the stock prices increase to \$ 43.7 per share or \$ 65,550

Nominal Rate of Return = (65,550 – 55,500)/55,500 × 100

Nominal Rate of Return = 18.10%

Suppose the investors pay capital gains taxes at the rate of 16%.

Then, the nominal after-tax rate will be:

Nominal After-Tax Rate of Return = Nominal Return × (1- Effective Tax Rate)

Nominal After-Tax Rate of Return = 18.10% × (1 – 16%)

Nominal After-Tax Rate of Return = 15.20%

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We can also use the same approach to calculate the nominal rate of return using the share price.

Nominal Rate of Return = [ (43.7 – 37.0)/37.0] × 100

Nominal Rate of Return = 18.10%

Nominal After-Tax Rate of Return = 18.10% × (1- 16%) = 15.20%

Importance of Nominal After-Tax Rate of Return

The nominal rate of return forms the basis of investment analysis for investors. It helps investors compare similar investment options before making any adjustments.

Tax rates can vary by jurisdiction and by taxpayer depending on the income level, investment holding period, amount of profit, and tax rates.

Also, the inflation rate may vary by state or country while the gross return on an investment may be the same. Thus, comparing investments at a nominal rate makes sense before adjusting results for different factors.

Investors take a step further to analyze the impact of taxation by using the nominal after-tax rate of return. This rate considers the tax deductions and provides another perspective on a potential investment opportunity.

If the investor does not need to pay income taxes, then the nominal and nominal post-tax rates of returns will be the same.

Advantages of Nominal After-Tax Rate of Return

Using the nominal after-tax rate of return provides some good benefits to analysts:

• It forms the basis of investment analysis and can be considered a starting point.
• The nominal rate can be adjusted for taxes and inflation to calculate the real rate of return.
• Adjusting for tax provides another perspective on investment analysis while using the simplistic nominal rate.
• It helps compare similar investment options where tax rates vary or investors have different tax slabs.
• It is useful in comparing tax-free investments like municipal bonds.
• It is simple to calculate and it is widely advertised by banks and other financial institutions.

Limitations of Nominal After-Tax Rate of Return

The nominal after-tax rate of return has its limitations as well:

• Investors primarily rely on the real rate of return by adjusting for taxes, inflation, premiums, and other expenses related to an investment.
• It cannot be considered an accurate or actual rate of return for an investor as different types of expenses/premiums can change the returns significantly.
• It can be misleading at times since it does not consider inflation which could otherwise give a negative rate of return in high-inflation economies.
• Relying only on the nominal rate of return can result in miscalculations for tax-free investments like municipal bonds and investment trusts.

Nominal Vs. Real Rate of Return

The real rate of return refers to the actual return received by an investor after adjusting for taxes and inflation effects.

Investors pay income taxes on their returns and also brokerage fees, commissions, and other costs. Then, inflation can impact an investment significantly when held for a longer period.

Thus, an investor must consider all these costs of holding an investment and calculate an actual rate of return received. It can be calculated from the nominal rate of return.

We can use Fisher’s equation to describe the relationship between the nominal, real, and inflation rates.

Real Rate of Return = [(1 + Rn) / (1 + Ri)] – 1

Here Rn refers to the nominal rate of return and Ri refers to the inflation rate. Then, the real rate can be converted into an after-tax rate as well.

After-Tax Real Rate of Return = Real Rate of Return × (1- Effective Tax Rate)

We can see the relationship between the nominal and real rates is mainly for adjusting inflation and tax costs.