Time Value of Money

Time value of money is similar to opportunity cost. I have some money that i can invest in some project, but what is my next best opportunity. If i can see the difference, then okay but if not then search for another opportunity given the resources that you have.

Value is relative, compare with next best investment, if it does then it generates value for you.
Every instrument can be thought of as a series of cash flows. The diagram that we draw is called the time line. Divide future in periods. Give them a time subscript. you make an investment at time=0 to buy something and after that you hope to operate this or get some positive returns from the business. Forever perhaps or for a limited time period. The ideas is to figure out when cash flows occur. Using this diagram is extremely simple. Do use the time line even if the problem looks trivial. Donot hesitate to use the time line in order to note the time value of money.

We talk about two values, present value and future value.what would my cash flows be worth, if i kept investing these cash flows in the next best opportunity. Cash flows earn interest on interest as cash flows are invested year after year or period after period.

How much of the next-best investment would i buy to get these cash flows

PV and FV are additive in nature, that i can break up.

For loans
PV of payments = principal that you borrow
At any time at balance = FV of principal - FV of payments made

Interest Rates
APR (Annual Percentage Return ) is Bull shit. It is less than informative.
We need information on the following things
Time period covered by the Rate
Compounding Frequency
Rate

THree ways to quote rates or return of rates
Periodic Rate, Rp. The r that we use in FV and PV is a periodic rate. so first figure out what the periodic rate is.

Second way) Stated annual rate RA.
THird way )Very Handy tool as it is very informative = 1 year periodic rate =simple annual rate =annual rate compounded 1 per year.

(1+annual rate ) = (1+rp)^n
rp=ra/m

Why is the depreciation added back ?

The depreciation is added back as it is a non-cash expense or in other words it can be understood as follows

When the company purchases an asset, it is spending the entire amount to buy it at a single point of time, but in accounting it only takes the depreciation into account, therefore while calculating the FCFE we subtract the capex of the company and also depreciation. In order to account for that depreciation which was subtracted above add it back.

Why are other non-cash expenses like bad debts not added back

They are not added back because they are already accounted for in the working capital. Whenever we have bad debts, we treat them as expenses and reduce an equivalent amount from the accounts recievable, thereby netting the whole thing. Therefore there is no need to add back these expenses.

Working

Operating Income	20 cr
Operating expenses(Inclusive of losses due to bad debts and depreciation):	16cr
Net operating Income (EBIT)	4cr
Interest expense	50lkh
PBT	3.5cr
Tax rate	40% (Marginal tax rate)
PAT	2.1cr
Less:Changes in working capital(Current assets - current liabilities) = Debtors+Inventory-Bad debts-current liabilites)	30lk
Less:Net Capex	50lkh (Capex-depreciation)
Therefore the FCFE becomes	1.3cr

There are two things that we must note here:

• Depreciation has not been added back explicitly because, it was present in the net capex already and when we subtracted net capex deprecation was effectively added back


• The same is the case with bad debts, when we subtracted working capital changes, the bad debt effectively was added back

My Doubts

While calculating the cost of capital, we take the D/E ratio, while calculating the Cost of equity we use beta which is a function of D/E so are we not double counting the entire thing.?

Should Cash be considered a part of Working Capital

This question can be looked in two different ways

The first view is that the cash that is present with the companies is generally invested in treasury bills, short term government securities and commerical papers.Moreover they are riskless investments so while discounting we do not us a risk free rate. Therefore there comes a logical inconsistency

The second view is that, there are industries which are working capital intensive and hence require a large amount of cash for their day to day operations, for such companies it makes sense to assume that 5% of the cash would to be a part of the working capital cycle

Should short term debt and part of long term retiring be considered a part of current liabilities ?

They should not be considered a part of the working capital and should be considered while calculating the cost of capital. There is no sense in double counting it. But if you use the FCFE method then it makes sense to include the short term debt to be a part of the working capital as it will not be taken into account during the Cost of equity calculation

Effect of Net operating Losses

For firms which have huge net operating losses carried forward there is tremendous potential for savings in the first few years, till they generate positive earnings.
Till the time there is Non operating losses accumulated with the firm, the firm would not be paying any tax, as the profits start flowing in, first the NOL will be covered and after than any taxable income that remains would be taxed. The tax rate would be calculated on the taxrate*taxable income/Total Income. Therefore the tax rate can build up over a period of time to 35% in the end

IS FCFE correct ?

This question once came to my mind, is the FCFE method correct because drawing an analogy from the bond markets, the value of the bond is the PV of all the future cash flows from the bond. Hence the PV of a share should be the PV of all the cash flows that would be received by the shareholder. So in that sense the DDM becomes the best method, but still people do not use it. It is shunned by the investor community. Then i looked up the internet to find the answer that i needed

A. Damodaran has put this answer very beautifully in his book, he says that FCFE assumes that all the potential cash that is left after payment of debt holders, taxes and operating expenses is assumed to be paid to the equity holders. Therefore we can say that the investors get the FCFE. It assumes that there is no cash build up in the company and all the cash available is distributed to the shareholders. Therefore we would have seen that the cash component of the present year is added separately to the equity value.

Also the reason for the firm not giving out Dividends =FCFE are as follows

The company might have future needs for huge capex. Therefore in order to account for that requirement the company doesnot pay out in full

Companies, in good time generally do not tend to increase the dividends becuase if in the future time periods they were to decrease the dividend, the market takes it as a bad signal and beats the stock price. Therefore we often see a lag between the increase in dividend distributed and the increase in earnings

The management might want to build an empire of its own, and hence wants to increase the cash present with it

What does a reduction in Risk premium IN CAPM mean

It means that the country has matured, the economy has matured, the risk associated with investing has decreased. Or if the investment is in emerging markets it means the markets will emerge over time and the investors will ask for a lesser premium to invest in these countries.