Discounted cash flow

Discounted cash flow seems like a very difficult concept but it is not so in reality. However, it has a few common sense implications. For people who want to understand and make financial plans, it is necessary to understand its basic concepts. The advanced working can be done in excel.

Basic ideas

1. Time has value - one rupee today is more valuable than one rupee a year later.
2. Time value of money depends on risk taken (for future income) or opportunity cost (for future cost).
• Thus, one rupee a year later in FDs is MORE valuable than one rupee a year later in equity.
• Similarly, one lakh rupee today are more valuable than one year later if you have an outstanding personal loan (with high interest that you can prepay) vis-a-vis if you are going to invest the money in FDs and pay 30% tax on the interest.
3. To make decisions, simply calculate that impact in terms of today's money that they are worth. This will level differences in the time value AND risk.
4. Discounting - to find the present value of some money that you would get 1 year from now, just divide the amount by (1 + discount rate). So if the amount is Rs 55,000 and the discount rate is 10%, the present value will be 55,000 / (1 + 0.1) = 50,000.

Example 1

Arun is buying a car. The dealer has two schemes, one in which Arun gets a discount of 50,000 and the other in which the dealer gives an interest free loan of Rs 6,00,000 for 1 year.

The present cost in first case is clearly 5,50,000 since Arun just pays 5,50,000 today. In the second case, he does not pay anything today but pays Rs 6,00,000 1 year from now.

If he has an outstanding personal loan of say 10,00,000 at 14%, then the present cost of 6,00,000 (which he has to repay) is 5,26,315. So it is better to take the interest free loan.

On the other hand, if Arun will put the money in FDs with 10% interest rate, on which he will pay 30% tax then the net return is just 7%. So the present cost is 5,60,747. So in this case, it is better to take the discount.

Example 2

Arun is investing in a house worth 1,00,00,000 by paying Rs 30,00,000 today and taking a home loan. The builder will pay all the interest till the house is ready 3 years later and the builder assures him that the house will appreciate by 25%. Arun expects the stock market to increase by 50% in three years and he believes that the risk in stock market is equivalent to the risk in purchasing a house.

For the house, the cash flow is -30,00,000 today and 55,00,000 three years from now. On the face of it, it seems like 80%+ returns. On the other hand, the cash flow in stock market is -30,00,000 today and 45,00,000 three years from now. So it seems that it is better to invest in the house.

However, that is not the case. Even if the risk of house appreciation and risk of stock market by itself is the same, things change because of the way the deal is structured. In the house case, Arun is borrowing 70,00,000 Rs from the bank to fetch higher returns. This leads to a higher risk. Thus, even though the house appreciates by just 25%, Arun fetches a return of 83%. However, if the house had depreciated by 10%, then Arun would have faced a return of -33% (the house would be worth 90,00,000 so after reducing the loan, Arun would be faced with a loss on 10,00,000 on a capital of 30,00,000). In other words, with leverage (i.e. taking loans), good days are better and bad days worse. So risk is higher.

Calculating the discount rate is difficult here. If the risk free rate (the so called repo rate) over the three years is 25%, than we can say that 25% is time value of money and remaining 25% (in stock market) is risk value. In the property purchase case, since the leverage is 3.33 (1,00,00,000 / 30,00,000) so the risk value should be 3.33 * 25% and total discount rate should be 108.25%. So the present value of the house is -3,58,900 while the present value in the stock market case is 0. In other words, it is better to invest in the stock market than in the house.

Summary

While evaluating returns, never simply add up cash flows at different points of time but discount them by an appropriate interest rate. For non risky instruments, the FD or repo rate (usually 5%-9%) is a good discounting rate and for equity or stocks, the stock market return (usually 12%-14%) is a good discount rate.

Also keep a look out for what the risk factors are. Anything that implicitly has higher risks (due to loans, uncertainty etc) needs higher returns to justify it.