Projects with Different Lives and Rental Equivalents

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The concept of equivalent annual cost has already been met by you in a 2.39question. The concept comes in use when you are working on problems of how to effectively work with the annuities such.

Comparing annual payments to multiyear contracts

Let us see the first example. Let us assume that all the existing rate interest is that of 10% on a yearly basis. Honestly, would you sign a contractual lease that compels you deliberately to pay up $1000, $650 and the other $650 in the upcoming years and or will you pay a rent that is of $780 on an annual basis?

The normal present value would be,

Projects with Different Lives and Rental Equivalents 46

The more suitable alternative rent being,

Projects with Different Lives and Rental Equivalents 47

A total three year mortgage will be much cheaper if you obtain it. The assumption that you want is to occupy the building for a total of three years. In case if you wanted the entire building that will be for a year, then is one year of the rental contract will be better.

So, can you calculate the annual rent that will be so different between leasing of a property and renting of a house? This is further called (EAC) equivalent annual cost.

This is pretty easy:

Projects with Different Lives and Rental Equivalents 48

This formula tells that the indifference that is felt in between that of ($1,000, $650, $650) is a three year mortgage along with the yearly payments that are of $777.95 which is the first payment that is due immediately. The other version of such a calculation is paying a rent of house at the end range of a year.

In the particular case,

Projects with Different Lives and Rental Equivalents 49

 Therefore, anyone also would be very indifferent to the paying of $855.74 on a 3- year lease with the particular rent on the year end. And not the year start. You can simply multiply the number to particularly arrive on this figure by multiplying the $777.95 by 1.1.

Projects with Different Lives and Rental Equivalents 50

Now, let’s take a look at the formula 3.3, as the left side hand that is of the equation would be annuity.

Projects with Different Lives and Rental Equivalents 51

If you are to prefer the royal yet common version where first payments occur upon the simple discount that is put up, of 10%:

Projects with Different Lives and Rental Equivalents 52

But, you must not get worked over this formula. For the time span of three years, though you do not need to use this annuity formula that is if someone prefers working on the formula that is listed as 3.3 which is long. Though if one has a lot of payments, then the absolute annuity formula is going to quickly become a more convenient one.

Now let’s work on another certain lease example just for practice. Five year lease that is of the house requires a one-time payment of $1600 which will be followed by 4 other payments that are of $500. This interest rate being 10%, what would the annual cost be of? Let us first workout on the total PV that is of all the peculiar lease payments. Which is,

PV = $1,600 + $500/1.1 + $500/1.12 + $500/1.13 + $500/1.14≈ $3,184.93

The solution must be of,

EAC + EAC/1.1 + EAC/1.12 + EAC/1.13 + EAC/1.14 = $3,184.93

That is

EAC * (1 + 0.9091 + 0.8264 + 0.7513 + 0.6830) ≈ $3,184.93

⇒ EAC ≈ $3,184.93/4.1699 ≈ $763.80

When put in differently, the indifferent five year of a lease plan will be such with a payment amount which is $763.80 every month. The total annuity formula using,

Projects with Different Lives and Rental Equivalents 53

The initial payment will be such that the amount at the year’s end.

So, are you ready to move to an example from the true world of righteous market example? This is a real story.  My absolute car lease was quoted as $1500 as a reason to the signing. This was followed by a $500 every month sum for duration of 35 months. The EAC, what would that be for the contract? If the not given interest rate is assumed to be 0.5% every month, the total present value would be,

Projects with Different Lives and Rental Equivalents 54The annual cost would be equivalent, what would the rental be upfront to the payment,

Projects with Different Lives and Rental Equivalents 55

This is payable at only the end of every month significantly.


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