# 4a- Easy illustration for MARR, WACC definitions.

## What are MARR, and WACC?

### What is the minimum attractive rate of return?

The first expression is the MARR, which is the Minimum-Attractive Rate of Return If you have the interest to borrow from your cousin to start a new business to open a coffee business.

You must still have a return of more than that 10%, at least 11%, to make business, otherwise, you will lose in the future, so we want the minimum % to safeguard against losing, if you invest with a lower %, then you will lose.

### What is the weighted average cost of capital (WACC)?

WACC is the weighted cost of money from mixed money lenders. This is a mix of money you want to get from others to make your business.

If you borrow from the bank this is called debt if you take from your funds that are called Equity or another person who wants to invest with you, he will get a higher rate than the bank offers.
Remember WACC should be used if you have a mix “between equity lenders ”.=Your cousin ”.The debt is the bank.
If you take from your equity, then the part of the bank will be canceled, and vice versa. If you take money from a bank, then disregard the part of equity as we will see.

There is a sketch as shown. Cost of capital, in simpler words, is the money needed to make your business can be divided into two parts, one part to be borrowed from the bank, which has a cost.

The second part of the funding is by equity through financing and buying bonds, it has a cost of equity, which is defined here as the cost associated with using shareholder’s capital. The cost of capital =percentage of (cost of debit+ cost of equity)/ total cost.

#### WACC with no tax.

Let us have a look at an example. If one-third of the capital of the firm is borrowed – at a rate of 6% and the remainder of the capital is equity earning 12%, then what will be the alleged minimum rate of return? this is a sketch for the capital, if someone borrows from the bank, we call it debit if we take from our own funds, We call it Equity. Each one of these has a cost.

This is the capital in our example 1/3 of the investment is taken from the bank, the rate of the bank is 6%, the remaining investment, which is 2/3 is taken from the Equity, and the cost of

To get the WACC for this case 1/3*of investment from the Bank *0.06+(2/3)*0.12=10%, this is called WACC, then the minimum attractive rate of return must be >10%. The remaining investment, which is 2/3 is taken from Equity, the cost of equity=12%, for that mix.

To get the WACC for this case:(1/3* total investment from the Bank *0.06)+(2/3)*(0.12) =10%. This is called WACC, then the minimum attractive rate of return must be >10%.

This is the equation used in estimation =(E/V)RE+(D/V)(1-Tc)+(D/V)*(1-Tc), Tc the tax rate. The relevant definitions of each item are shown.

#### WACC with tax included.

Solved example, if debt=\$2000, Rate of debt=0.06, if Equity =\$8000, Rate of Equity=0.125, and Tax rate 30%

The WAAC can be found by using the modified equation, due to tax rate Please refer to the next slide.

In the WACC, we take the \$8000 to be multiplied by 12.50%, then the remaining investment, which is =\$2000. 20000.06 (deduction after tax is taken into consideration).

This is the PDF file used for this post.

The next post title is What is the definition of IRR?

For a useful external resource, Engineering Economy this is a link: Applying Theory to Practice.

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