Value of something after n-years is calculated with the formula below. This concerns about savings when the value of the capital increases each year.
- i = interest
- n = years
When we calculate value for the money that we will receive after the years we have to discount it in to current value. Respectively to the formula above if money increases it’s value every year, the money we receive later is valued lower today.
In investment calculations the yearly savings is normally converted into the form of current value and that is compared to the investments acquisition cost. All coming money are discounted to current value so that they are comparable.
If investment saves every year same amount we can easily calculate its whole holding time savings in current value.
Example our investment saves every year 50 000 € on work and material costs. Holding time of the investment is 10 years and our company uses 12 % interest in all calculations. From the formula above we can calculate that our periodical payment factor is 5,6502. So the investments savings in 10 years is:
50 000 € * 5,6502 = 282 510 €.
If it costs more than 282 510 € to invest, it is not profitable investment.
If our savings are not equal every year we have to calculate each years savings independently.
This formula can and is used to calculate also the current value of the residual value. In our example if investment is after 10 years worth of 25 000 € we must convert it in to current value. We can calculate the single payment factor to be 0,3220. This means that we will have 8 050 € in current value.
Summarized our savings and residual value are 290 560 €. This means that our investment can cost this much to break even.
Notice that the residual value can also be negative. If no one doesn’t want to buy it or it costs more to unload than its selling price is, we can end up paying to get rid of it. It will increase our investment value.
In annuity method the investment cost is divided into whole holding period as in yearly cost. Yearly cost is investment value * annuity factor.
Now lets imagine that the investment in our previous example costs 290 000 € which is barely profitable after the yearly savings and residual value calculated before.
Annuity factor is 0,1770 and the yearly cost is 290 000 € * 0,1770 = 51 330 €.
Because we can generate only 50 000 € each year, this investment is not profitable.
If we want to notice also the residual value it must be discounted with single payment factor and then removed from the investment. Then this investment cost is divided to yearly cost with annuity factor.
[ 290 000€ – (25 000 € * 0,3220) ] * 0,1770 = 49 905,15 €
This way yearly profit of the investment is 94,85 € which is barely profitable.
Payback period is very simple way to calculate investments. In its simplest way it is just investment value / yearly savings = payback period.
Payback time in our example is 5,8 years so our 10 year holding time is highly profitable.
Notice that this doesn’t include any discounting of the yearly savings. If we want to do this correctly we must discount every years savings with the single payment factor and calculate how many years it takes to pay back the investment.
Below is my Excel-calculation of this example. Investment generates only 282 511 € in 10 years. If we add residual value 8 050 € we end up in the same 290 560 € that we calculated before.
Notice that the average annual saving is 28 251 € which is one-tenth of the result we had in the periodical payment method.
When computing your investment you must pay attention for maintenance and repairs costs. If your investment needs steady maintenance each year it is easy to calculate with the periodical payment method. But if it needs bigger repairs in the end of the holding period you must use the single payment method to compute the sum of your yearly net savings.
If repair increases holding time the rationality of the repair can be calculated as in the original investment. Consider repair costs as an investment cost.
Now you can try these investment calculations here.