Consumption and investment, finance and production

Financial investment, productive investment and consumption. How are they related?

Introduction

Brealey, Myers and Allen (2011) in his book "Principles of Corporative Finance", shown in Chapter 1 an interesting reflection on the difference between current consumption and future consumption improved by the financial investment (deposit money in a bank) as savings or productive (placing the money in a business). We recognize the validity of the assumptions that indicate the efficiency of the capital market which can act in both markets, financial and productive; also other aspects such as the ability to borrow money from the bank (the inverse operation of savings deposit).

The meaning is clear for discerning readers familiar with the matter, however some calculations may seem complicated, therefore, in this issue we develop in detail this interesting topic.

Suppose that a generous God gives four people an amount of money: $ 100,000. Each is free to use it as you want, but there are certain restrictions. Free use will be in the present moment, within a year or interim periods. Never beyond the first year. For those who prefer to save money, because it's petty and do not want to spend or not to do anything and decides to keep money under the mattress (like pirates on a mysterious island), the punishment is eventually not enjoy that money because the forget where is the treasury or rats devoured money. It is the price to idiocy or laziness.

One of them, ambitious, unscrupulous and greedy for easy results decides to bet in casinos or horse racing; believed to have answers and accurate data to win. He can earn a lot, but most likely lose everything. It is the reward for greed and folly.

The two others are like the grasshopper and the ant fable; Grasshoper prefers to consume everything today and live it up as long as the money. At least no one takes away the dancing, but tomorrow will go hungry. The other is as diligent ant, patient and always thinking ahead. He  can save on the bank (financial investment), earning little but surely receive more than deposited now; another option is to invest in a business. Although there is some risk, knows that business is real, legal and there is a market; therefore he may receive more tomorrow.

The Ant and the Grasshopper can adopt intermediate positions. Do not be too austere nor too wasteful, consume something today and have to consume tomorrow. Eventually they will learn how to make a balanced distribution. The graph shows the available options.

Calculations and explanation of the process

Table 1 shows the extreme and intermediate positions relative to current consumption and savings in the financial system . It consumes everything today (US $ 100,000) or wait a year and receives

F = C * (1 + rate), F = future amount, C = current amount
US $ 110,000 = 100,000 * (1+ i) = 100,000 * (1.10),

where i = 10% is the interest rate paid by the bank (the bank pays the saver to use their money in their own business and get its profit). Figure 1 shows these options

Table 2 shows the choice between saving or investing in a business that has a yield of 21%. The ant invests in business and can receive US 121,000 within a year. Brealey et al (2011, p. 19) added the possibility that the grasshopper can invest in the business and to the security of receiving 121,000, to consume can now apply for a bank loan for the current equivalent. The bank charges 10% interest, therefore, receives

C = F / (1 + rate)
110,000 = 121,000 / (1 + r) = 121,000 / (1.10)

Where r = rate of interest charged by the Bank.

Actually, this rate should be higher than 10% paid to savers because ,where would gain banking? Assume that actually charges 15%, then the grasshopper  receives

105,217 = 121.00 / (1 + 15%) = 121,000 / (1.15)

In Figure 3 the combined two options are presented. As time passes, the difference between what is gained by financial investment (savings banks) and productive investment (business) is greater.

 

In this case, it is possible that the ant and the grasshopper perhaps, can do a combination of activities: consume today a part of wealth, invest some in the bank and the rest in the business. So, would diversify and reduce risk. If the business fails, they lose only the inverted portion but still keep the savings in the bank.

Table 4 shows the choice between current consumption and risky. The potential gain is much higher but there is also increased risk. You can lose everything invested in this dangerous adventure. It is an extreme, not wise and unwise decision.

  The calculation of the quantities consumed in the present and the future is easy. Since the P-value (present) consumption in the future will be equal to

F = (Wealth -P) * (1 + interest rate) if saving is selected or

F = (Wealth -P) * (1 + return) if  is selected the investment in the business

One question in reading is about how much place in both periods if you want the amount available in both cases is the same. The solution lies in the formula:

P = F, ie  P = (Wealth -P) * (1 + rate of profit)

Why business performance rate is higher than the rate of interest earned by savings in banks? By the risk, uncertainty, effort that involves being in a business. It is compensation for that. If business performance is equal to the interest rate paid by the bank, it is better to do nothing and without effort, expect the interest paid by the bank. Note that the return on risky bet is higher because the risk is higher. It is the general rule.

Where are you located?

Reference

Brealey, Richard A .; Myers, Stewart C .; Franklin Allen (2011) Principles of Corporate Finance, 10th Edition. McGraw Hill / Irwin, New York

Valuation of Bonds -Price and performance

How to value  a Bonus at primary and secondary market

Introduction

Suppose that a company needs money to finance its operations, so it goes to funding sources. A bank may be the best alternative if the company is large and has access to preferential rates and terms; shareholders can have very high expectations in terms of performance required; A third source is the issuance of bonds under certain conditions. Suppose the firm has good performance, is known and therefore will have no difficulty placing bonds.

Calculations

Initial data: = $ 1,000 par value, term = five years, at a nominal annual coupon rate of 10% voids, bond type = bullet.

First, we calculate the annual cash flow considering coupons. It is observed that the discounted 10%, the interest rate paid by the issuer for financial equivalence, the value should be 1000, the nominal value. 

If the coupon is semiannual, the calculation is similar except that the number of periods, fees doubles and the discount rate is half the annual rate since this nominal fee. The calculations are shown in the table below 

Now we consider the initial investor who buys the bond issuer. Money certainly has an opportunity cost, that defines the rate of return. If you think that the performance of 6% is suitable, it would pay US $ 1168.5, i.e. greater than the face value of the bond (price above the par or premium price) wreck; on the contrary, if you think the performance should be 12%, the price you pay will be $ 927.9, lower than the nominal value of the bond (below the par or discounted price). It is important to note that when paying above the par, the initial investor does not lose, simply the gain keeps financial equivalence. That is, does not care to pay the sender $ 1168.5 now to receive the cash flows shown for 5 years because 6% is its opportunity cost. 

Note that whatever the rate set by the investor, the interest rate and thus the amount of the coupon, do not vary. They are two separate fees that may or may not be equal,

Suppose now that the initial investor needs liquidity and cannot demand the return to sender, go to the secondary market, which is the secondary investor who has money and an opportunity cost. This time, the bond is valued at a market price that depends on the rate of return required by the investor side.
In the table below, it is observed that if the investor believes that its opportunity cost is 14% require this fee as a financial return on their investment in the purchase of the bond. The price of $ 862.7 is undoubtedly lower than the nominal value (under the par or at a discount). 

Like the primary investor, the secondary investor can pay more than the face value (above the par), because his opportunity cost is low or for other reasons; if anything, pay more than the nominal value does not mean loss.

The secondary investor has two options trading: market information may have on the price of bonds with similar characteristics so decides to negotiate the price setting, so it is necessary to calculate the rate of return associated; moreover, you can set the rate of return and discount cash flows at this rate, to determine the price you pay.

In conclusion, it appears that for the issuer, the cash flow consists of initial income, coupons and final payment (redemption of the bond); the interest rate to calculate the coupon and the discount rate are the same. 

In the case of the primary investor, the values ​​are the same except the initial value can be lower, equal or greater than the initial value of the issuer (nominal value). The interest rate or yield determined by the investor  is i1.

For the secondary investor, also flows are similar except that the initial value is the price paid for the bond. The discount rate r determines the price paid. 

In summary, the issuer is willing to pay an interest rate i (coupon rate), the initial investor can accept that rate or different (i1 = i, i1 <i, i1> i); secondary investor has a rate of return that can be also equal, higher or lower than the initial interest rate (r=i, r<i, r>i).