# HOW TO GROSS UP

GROSS UP

In loan documentation, a clause with the effect that if a lender suffers a cost in relation to a tax, for example withholding tax, the borrower should indemnify the lender by increasing the related payments to the lender to a grossed up amount.

The Treasurers Wiki

'Grossing-up' calculations will need to be done at some point in your career, so here are some tips on how to master them.

# THE FIRST THINGS YOU NEED TO KNOW

1. how to do a ‘grossing-up’ calculation; and
2. recognising that one was needed.

Let’s take a look at what a grossing-up calculation involves, and what it doesn’t. Then we’ll apply it to some examples.

# HOW TO GROSS UP

Grossing up means increasing a net amount using the following relationship:

 GROSS AMOUNT = Net amount divided by (1-grossing-up rate)

A common example is grossing up interest for income tax or withholding tax.

# EXAMPLE

Net interest is £100 and the tax rate is 20% (= 0.20).
In this case:

 GROSS INTEREST = Net interest £100 divided by (1-0.20 = 0.80)

The tax is charged on the gross amount of £125 (x 20% = £25 tax).
This is why the calculation is to DIVIDE BY (1 – tax rate) to give the right answer of £100/(1 – 0.20) = £125.
The calculation is not to multiply by (1 + tax rate). This would give a wrong answer of £100 x (1 + 0.20) = £120, which is too small.
(Because tax payable at 20% on £120 = £24; and when £24 tax is deducted from £120, only £96 remains, not the required £100.)

# GROSS INTEREST CALCULATION

 20% tax GROSS INTEREST = £100 divided by (1-0.20 = 0.80) = £125 Net interest £100

Now, let’s prove that our answer is right.

# CHECK GROSS INTEREST

 20% tax X £125 = £25 = Gross interest £125 + Net interest £100

# GROSSING UP A LOAN (EASY)

The treasurer of Party Pretzel plc wishes to raise a net amount of at least EUR 20m and is considering:

A line of credit from the company’s bankers at an interest rate of 5.5% per annum, with an accompanying requirement that, for the duration of the loan, a minimum balance of 20% of the loan amount should be maintained in the company’s non-interest-bearing current account with the bank.

## HOW TO GROSS UP THE LOAN

Interest will be charged (at 5.5%) on the gross loan amount, not the net.

So the first step is to calculate the gross loan amount.
The 20% balance to be maintained in the current account is not available for the borrower during the life of the loan. It is locked away (like the 20% tax that was payable in our earlier example).

So this grossing-up calculation will be very similar to the gross interest calculation that we did earlier.

 20% in current a/c Gross loan amount EUR 20m divided by (1-0.20=0.80)   = EUR 25m Net loan amount EUR 20m

Now, prove the answer.

 20% x 25m = EUR 5m = Gross loan amount EUR 25m + Net loan amount EUR 20m

EUR 25m is the amount on which interest will be calculated and charged by the bank. Even though only EUR 20m will be available to the borrower (EUR 5m = 20% being locked in the current account). In life, loans are always more expensive than they appear to be...

## A COMMON MISTAKE

Many professionals make errors at the first step of estimating the gross value of share issue required to raise a net amount of £24m after issue costs amounting to 4% of the gross proceeds.

# HOW TO GROSS UP ISSUE RECEIPTS

Party Pretzel plc proposes to obtain a quotation on the London Stock Exchange and raise additional share capital for a net amount of £24m. Administration and issue costs are expected to be 4% of the gross receipts.
How would you go about calculating the gross receipts?

The share issue is good news for the advisers because of the fees they will earn.
The 4% total costs paid to the administrators and advisers are not available for Party Pretzel plc. But they will be part of the total subscription price paid by the investors.
So the shape of this grossing-up calculation is similar to the previous one.

 4% costs Gross issue proceeds £24m divided by (1-0.04=0.96)   = £25m Net issue proceeds  = £24m

Now, proving it.

 4% x 25m = £1m = Gross issue proceeds £25m + Net loan amount EUR 20m

So £25m is the total amount that Party Pretzel plc needs to attract from its investors.

# BETA CALCULATION (HARD)

For Party Pretzel plc share issue to be successful, the company has been advised that it should make the issue by means of a comparison with an appropriate quoted company. The most appropriate company for this purpose is considered to be Wik plc.
The beta of the market is 37.5% less than the beta of Wik plc.

# HOW TO GROSS UP THE MARKET BETA

For this, we need to know:

1. How to do a grossing-up calculation as practised above; and
2. That the beta of the market (to gross up) is always 1 by definition.

There is a difference of 37.5% between the beta of Wik plc and the beta of the market, defined as a proportion of the beta of Wik plc (to be calculated).

## BETA GROSSING-UP CALCULATION

 37.5% difference Beta of Wik plc 1.0 divided by (1-0.375 = 0.625)  = £1.6 Beta of the market 1.0

Let’s prove the calculated beta.

 37.5% x 1.6m = 0.6 = Beta of Wik plc 1.6 + Beta of the market 1.0

The market beta of 1.0 is indeed smaller than Wik plc’s beta of 1.6 by 0.6/1.6 = 37.5%.
Note that it is not right to add the 37.5% to 1.0 to calculate a beta of 1.375.
This would be too small because the market beta of 1.0 would only be smaller than it by 0.375/1.375 = 27% (rather than the 37.5% we need).

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Author: Doug Williamson

Source: The Treasurer magazine