Syndicate
Selecting an Investment Examples
Example A
Initial investment 5,000,000. Sum to collect at the end of the first year of 3,000,000 and of 3,000,000 at the end of the second year, because the sums to collect are received at the en of each year. The pay vback term is of two years.
Initial investment 5,000,000. Sum to collect at the end of the first year of 3,000,000 and of 3,000,000 at the end of the second year, because the sums to collect are received at the en of each year. The pay vback term is of two years.
Example B
The first investment is recovered after three years and the second investment after one year, so according to the payback criterion the second investment is more convenient than the first.
Sums to Collect
1st Investment 2nd Investment
Initial investment 4,000,000 4,000,000
End of the first year 0 5,000,000
End of the second year 0 0
End of the third year 5,000,000 0
Dynamic methods
The dynamic methods take into account the moment in which the payments and sums to collect are produced. In consequence, a determined payment or sum to collect will have a different valuation according to the moment in which it is produced.
The most used dynamic methods are:
- the actual net value method (ANV)
- the internal profit rate (IPR)
- Before trying the dynamic methods, it is necessary to introduce the concept of the present value.
- calculation of the present value of a sum to collect or to pay in the future
- The current value of an amount to collect or to pay in the future is the conversion of money units of today into future money units. The current value is obtained by transforming the money units of today into a future value. To make the conversion of future money unit into money units of today, you have to take into account the updated rate.
- For example, if you have to collect 100 money units after one year, and the annual updated rate is 10%, you will receive an amount which current value is 100 m.u.. To obtain the current value of the 110 m.u, you have to divide such sum by one plus the updated rate.
Current value = future value = 110 = 110 = 100
1 + annual updated rate 1 + 0.10 1.10
- With the previous example, what you are affirming is that it is the same to collect 110 m.u. after one year than to receive 100 m.u. today. If you have to update an amount that has to be collected or paid after more than one year the formula to use is the following:
- Current value = future value
- (1 + annual updated rate)n.
- Observe that the denominator is elevated to the number of years (n) that are going to pass before the collection or payment is done.
For example, if you have to collect 121 m.u. after two years and you know that the annual updated rate is 10%, then the current value would be:
- Current value = future value = 121 = 121 = 100 m.u
- 1 + annual updated rate (1 + 0.10)2 1.21
Net Current Value (NAV)
- The net current value of an investment is the updated value of all the sums collected, minus the updated value of all the payments.
NAV = Current value of all sums collected - current value of all payments
An investment will be advisable if the NAV is positive and not advisable if the NAV is negative. If the NAV is equal to 0, the investment will be indifferent.
From among several alternatives, the most tangible investment would be that in which the NAV is more positive.
The following are the calculations of the NAV?s from the previous examples that we have studied:
Example A
Initial investment = 5,000,000
Sum to collect = 3,000,000 (end of the first year)
Sum to collect = 3,000,000 (end of the second year)
Updated rate = 10%
NAV = -5,000,000 + 3,000,000 + 3,000,000 =
1 + 0.10 (1 + 1.10)2
= -5,000,000 + 3,000,000 + 3,000,000 =
1 + 0.10 1.21
= -5,000,000 + 2,727,272 + 2,479,338 = 206,610
The investment is advisable, due that the NAV is positive
Example B
Sums to Collect
1st Investment 2nd Investment
Initial investment 4,000,000 4,000,000
End of the first year 0 5,000,000
End of the second year 0 0
End of the third year 5,000,000 0
The NAV from the first investment is:
NAV = -4,000,000 + 5,000,000 =
(1 + 0.10)3
= -4,000,000 + 5,000,000 =
1.331
= -4,000,000 + 3,756,574 = -243,426
The NAV from the second investment is:
VAN = -4,000,000 + 5,000,000 =
(1 + 0.10)
= -4,000,000 + 4,545,454 = 545,454
Due that the second investment has a positive NAV, it is preferable to the first.
- internal Profit Rate (IPR)
- The internal profit rate (IPR) is that updated rate that makes that the net value of an investment is equal to zero.
- NAV = 0 = current value of all the sums collected – current value of all
payments
According to this method, an investment is advisable if its IPR is equal or higher than the minimum interest rate that you wish to obtain. The best alternative, when choosing among several investments, would be of that which has a greater IPR.
The calculation of the IPR is sometimes very complex and unless you have a programming calculator, we recommend for you to use the proof and error system. In this way, you calculate the NAV of the investment for any type of rate. According to the results of the value of the NAV, we will calculate new Nav?s for different rates until we can find with enough exactness the interval in which the IPR is found.
For example, let?s suppose that + (updated rate) = 7%, NAV = -800, and for + = 4%, NAV = +50. Then, the IPR is between 4% and 7%. You would then calculate the NAV for + = 5%. If the NAV would be of –26 for + = 5%, it would indicate that the IPR is between 4 and 5%. If this interval is considered too ample, you would shorten it by calculating the NAV for 4.75 and 4.25%, and so on.
Observe that while the NAV quantifies the absolute earnings in money units that the investment will produce, the IPR informs of the percentage of the profits of an investment.
The following are two examples that we will study and that have been used before.
Example A
Calculate the IPR of an initial investment of 5,000,000 from which you will obtain 3,000,000 after one year and 3,000,000 after two years. The IPR will be that rate which will make the NAV to equal zero:
NAV = -5,000,000 + 3,000,000 + 3,000,000 = 0
1 + IPR (1 + IPR)2
If you calculated by using the proof and error method, it will be:
- for + = 12%, the NAV is equal to +70 – 152;
- for + = 13%, the NAV is equal to +4 – 307;
- for + = 14%, the NAV is equal to –60,020
So the IPR will be comprehended between 13% and 14%
Example B
Sums to Collect
1st Investment 2nd Investment
Initial investment 4,000,000 4,000,000
End of the first year 0 5,000,000
End of the second year 0 0
End of the third year 5,000,000 0
The IPR of the first investment is:
- NAV = -4,000,000 + 5,000,000 = 0
- ( 1 + IPR)3
The IPR of the second investment is:
- NAV = -4,000,000 + 5,000,000 = 0
- ( 1 + IPR)
IPR = 25%
The second investment is preferable than the first one because it has a higher IPR.