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Time Value Concept
Hello everyone, I welcome you all to the lecture 8 of this course construction methods and equipment management. So, we are going to continue our discussion on the equipment life and the replacement analysis.So, let us have a recap of what we learnt in the last lecture. So, we have discussed about different approaches of replacement analysis based on minimum cost and maximum profit. So, it depends upon how are you going to optimize the production with respect to minimum cost or with respect to maximum profit. So, based upon that we have to make a choice of the particular method.But the demerit of what we discussed in the last class is we did not consider the timing of the cash flows, the illustrations which we have worked out in the last lecture, so that is a major limitation. So, since we did not consider the timing of the cash flows, so the estimate whatever made is only approximate only.So, that is why in this present lecture, we are going to consider the timing of cash flows also and do the equipment replacement analysis. So, let us see what is the outline of the today's presentation. So, we are going to discuss about the replacement analysis using time value concept in this lecture. We will see how to determine the economic life of the machine based on the equivalent annual cost of the machine.So, how to consider the equivalent annual cost? We are going to discuss in this lecture. So, basically we know that the cash flows occur at different time period. So, we need to consider those cash flows which are occurring at different time interval into a particular time period say t = 0. So, we have to convert it into a particular time period and then make the analysis.So, that is what we are going to see, we are going to use the time value concept and do the replacement analysis. So, in this we are going to work on 2 different types of problems one we will determine the economic life of the machine which will help us to determine what is the optimum replacement type of the machine using equivalent annual cost method. Then we will compare the present equipment that is a defender with the proposed equipment that is a challenger.And we will see what is the optimum replacement and whether it is suitable to continue with the defender or it is preferable to replace a defender with a challenger. So, we work out a illustration on comparison between defender and the challenger using time value concept. So, these are the 2 types of problems which we are going to work out in this particular lecture.(Refer Slide time: 02:55)So, let us see what are all the important points which have to be kept in mind in this replacement analysis. So, always this replacement analysis is to be done from the third party approach or the outsider perspective. That means, say for example if you have purchased equipment say 35,00,000 8 years before. So, your purchase this equipment at the cost of 35,00,000, 8 years before.So, now that the current value that is the current market value of the machine say it is 8,00,000. So, what is important to the third party or the outsider is only the current value 8,00,000, he is not bother about at what price you are purchasing the machine 8 years before. So, this 35,00,000 is not relevant to him, relevant to the third party. So, that is why in the replacement analysis you have to always visualize from the third party approach or the outsider perspective.So, your initial cost of a defender or the current equipment is not relevant in the replacement analysis. So, what is relevant is only the current market value of the machine. So, the first cost of the defender will be the estimated market value of the equipment from the perspective of the third party. So, that will be the first cost of the defender, so you have to forget about the initial cost.So, what is the first cost of defender, that is the estimated current market value of the machine from the third party perspective. It is incorrect to use the depreciated book value taken from theaccounting records, like you might have estimated the book value using some depreciation accounting method. Say for example, you have estimated the book value to be 10,00,000. So, using your depreciation accounting method, you have entered in your accounting records that the estimated book value is 10,00,000.But the current market value of machine is only 8,00,000, what is important is only 8,00,000 to the third party. Your estimated book value is not important to the third party. That is why it is incorrect to use the depreciated book value taken from the accounting records. So, what we have to use in the replacement analysis is only the current value of the asset when sold in the market, it is called as the market value or the trading value, that is only important when the replacement analysis. So, you should forget about the initial cost you should forget about the estimated book value.So, you should only consider the current market value of the machine or the trade-in-value of the machine, that is only important for the defender, so that is what is given here. So, these are the important things you should keep in mind while doing the replacement analysis. And similarly the challenger first cost is estimated initial investment necessary for acquiring the particular machine to a project site.(Refer Slide Time: 05:47)So, what are the other points to be kept in mind? So, as I told you all the other past estimates like your initial cost, your estimated salvage value when you purchase equipment, you might have made some estimate of it is useful life, estimate of the salvage value, all those are past estimates. Estimate of salvage value, estimate of useful life and the sunk cost, I will tell you what is sunk cost?All these are not considered in the replacement analysis, these are irrelevant in the replacement analysis. So, what is this sunk cost? Say as I told you earlier, like your current market value of the machine say it is 8,00,000, the current market value of the machine is 8,00,000. Now but you have estimated the book value of the machine as 10,00,000 using your own accounting method, depreciation accounting method.You have estimated the book value entering the account in records, it is supposed to be 10,00,000, but your current market value now is only 8,00,000. So, the difference between these 2 is your sunk cost. This is the amount of money which is spent in the past or it cannot be recovered, the cost which cannot be recovered, that is called the sunk cost. So, you might have estimated the book value to be 10,00,000 but even though your estimated book value is 1000000, your current market value is only 8,00,000.What is important to me is only this 8,00,000. So, this difference of money is called as a sunk cost which cannot be recovered. Sunk costs is the cost, the amount of money that is spent in the past and cannot be recovered now or in the future, that is called as the sunk cost. So, this sunk cost occurs when the estimated book value of the equipment using depreciation accounting method is greater than the current market value of the machine.So, when your estimated book value is going to be greater than the current market value, the difference is called as the sunk cost. That sunk costs also should not be considered in the replacement analysis. So, what you should bother about is only the current estimate, so the current estimate is your current market value of the machine. That is only relevant in the replacement analysis with respect to the defender.(Refer Slide Time: 07:54)So, I hope you remember this pictorial representation of the variation of the cost of the equipment with the age of the machine. So, you can see that the operating and the maintenance cost you can see it increases, with increase in the life of the machine. As the machine becomes older, your operating in the maintenance cost increases you can see that. And similarly your capital recovery the ownership cost component, you can see that it reduces with increase in duration of the machine.As I told you, as the ownership cost it is getting distributed over a larger period it is cost reduces the time. So, when you add both you can see what is happening to the total cost, total cost reduces, reaches a minimum and then again starts increasing. It reaches the minimum and then again starts increasing, why it starts increasing again? Because as the machine becomes older, there will be a significant increase in the repair cost and the maintenance cost and the operating cost, that is why it start in increasing.So, we are supposed to replace the equipment when the total cost associated with the machine is minimum. So, this time period is called as a economic life of the machine. So, this is the optimum replacement time of the machine. So, any equipment owner, he would like to replace the machine before the cost associated with the machine increases significantly.So, he has to determine the economic life of the machine and after economic life he has to replace the machine immediately. So, in this we are going to consider the time value concept and we are going to calculate the equivalent annual cost. So, we are going to calculate the equivalent annual cost of all the cost components.(Refer Slide Time: 09:38)So, economic life using EAC that means equivalent annual cost. So, now how to calculate the equivalent annual cost of the operating and the maintenance cost.(Refer Slide Time: 09:50)Let us see how to calculate. So, to calculate the equivalent annual cost of the operating and maintenance cost, see we have to find it is present worth first. Say for example let us draw a cashflow diagram. So, this is the purchase price of the machine made a time t = 0. So, these are the operating and maintenance cost which are happening at a particular time period. Say at the end of the year 1, this is your operating and maintenance cost at the end of year 2, this is your operating and maintenance cost at the end of year 3.At the end of year 3 say you are going to sell this old machine at the particular salvage value say the salvage value is S. So, now, so we have drawn the cash flow diagram, now let us see how to find the equivalent annual cost of the operating and the maintenance cost. So, this operating and maintenance cost are occurring at different time periods. Now the first thing you are going to do is, you have to convert these cash flows occur in a different time period to a particular time say t = 0.We have to convert all these cash flows to time t = 0, that means you are going to find the present worth of the operating and the maintenance cost. Find the present worth of the operating and maintenance cost, how to find the present worth? You have to use the present work factor, so how to find the present worth factor? So, you need to find P for the given F, i, n, so for the known future value, known interest rate i for the known period you are going to find the present value, that is the present worth of the machine.So, the factor is 1 divided by 1 + i power n, so this is your present worth factor. So, this present worth factor, so you have to multiply your operating and maintenance cost with the present worth factor, multiplied by the present worth factor. We will get the present worth of the operating and maintenance cost. The first thing is to determine the present worth of the each operating and the maintenance cost value.So, with the help of P by F, i, n factor that is present worth factor. Now what you do is after converting the cash flows to time = 0, you redistribute the present value using the uniform series capital recovery factor. So, that means we are going to convert the present value into equivalent annual cost using uniform series capital recovery factor.(Refer Slide Time: 12:34)So, let me find what is A for the given P, i, n. So, that means we are going to find the equivalent annual cost of the present value of your operating and the maintenance cost. So, this is your present value of your operating and the maintenance cost, we have already calculated the present worth of the operating and maintenance cost using present worth factor. Now we are going to find the equivalent annual cost using uniform series capital recovery factor.This is nothing but uniform series capital recovery factor. So, how to find it, i into 1 + i whole power n divided by 1 + i whole power n - 1, this is your uniform series capital recovery factor. So, you multiply this factor with the present worth of your operating and the maintenance cost. So, this will give me the equivalent annual cost of the operating and maintenance cost. So, first thing what we are going to do is, you find the present worth of operating and maintenance cost using present worth factor.Now you find the equivalent annual cost of this present operating and maintenance cost using uniform series capital recovery factor. So, this is how we are going to convert the operating and maintenance cost into equivalent annual cost. Now similarly let us see how to find the equivalent cost of the purchase price and how to find the equivalent cost of the salvage value.(Refer Slide Time: 14:15)So, this purchase price which is made at time 0, your purchase price, you are going to convert it into equivalent annual cost. So, now let us calculate the equivalent annual cost of the purchase price of the machine. So, how to calculate the equivalent annual cost of the purchase price of the machine? You know the purchase price of the machine multiplied by the uniform series capital recovery factor.That is nothing but P into, so you are going to find the A for the known P, i, n, this is your uniform serious capital recovery factor. So, you are going to find the annual cost for the known P, i, n.. So, the uniform series capital recovery factor is nothing but i into 1 + i power n divided by 1 + i whole power n - 1. You multiply it by the purchase price, we will get the equivalent annual cost of the purchase price.Similarly the salvage value, you have to convert the salvage value which is occurring at the future date into equivalent annual cost. So, for that you can make use of the uniform series sinking fund factor. So, how to use the uniform series sinking fund factor?(Refer Slide Time: 15:35)So, you know the salvage value S multiply by, so you are going to find the equivalent annual cost of the salvage value A. For the known future value interest rate i and n, so this is your uniform series sinking fund factor. So, we have discussed about all these factors in the earlier lecture on time value method. So, you can recollect the topic by going through this particular lecture.So, we are going to multiply the salvage value with the uniform series sinking fund factor, we will get the equivalent annual cost of the salvage value. Now the equivalent annual cost of purchase price minus the salvage value gives you the capital recovery. So, when we work out the problem we will understand better.(Refer Slide Time: 16:17)So, basically economic life is the number of years at which the equivalent annual cost, uniform annual cost is minimum. So, we are going to calculate the equivalent uniform annual cost. So, at which a particular time period it is minimum, we are going to find, that is your economic life of the machine. So, you have to consider the most current cost estimates over all the possible years over which your asset may provide you desired service. So, consider all the possible current estimates to get the accurate picture of the replacement time.(Refer Slide Time: 16:50)So, now, let us workout a problem. So, we are going to determine the economic life of a particular machine using the equivalent annual cost method. So, here we are going to consider the equipment track mounted front shovel. So, this machine was purchased for a purchase priceof 35,00,000. So, the machine is expected to last for 8 useful years, so the duration the useful life of the machine is expected to be 8 years.So, now the first cost of the defender is the current, this is nothing but your current trading value of your machine, that is nothing but 22,50,000. Every year the operating cost is going to be same and it is found to be 1,35,000, so the remaining life of the machine estimated is 5 years, you can see 5 years. At the end of 5th year, when you sell it you are going to get a cash inflow of 6,00,000.So, this is nothing but your salvage value of your machine. Now, so based upon this you can estimate the equivalent annual cost. So, how to estimate the equivalent annual cost? You are going to convert this values all this values to time period of t = 0. So, now what you do is, your initial cost of the defender, initial cost of the defender is 22,50,000. So, this one you are going to converted into equivalent annual cost, this is already at t = 0 only.This present value, I am going to convert it into equivalent annual cost, so how to do that? Equivalent annual cost of 22,50,000, so you need to calculate A for know P, i and n. So, what isP? P here is present value 22,50,000, interest rate is 10% 0.1 and number of years is 5. So, it is nothing but you have to use your uniform series capital recovery factor to find this, so it is nothing but i into 1 + i power n divided by 1 + i power n - 1 that is nothing but 0.1 into 1+ 0.1 is 1.1 power 5 divided by 1.1 power 5 - 1. So, what will be this value?(Refer Slide Time: 56:58)This value is found to be 0.2638. Now to find the equivalent annual cost of 22,50,000 you have to multiply this 0.2638 into 22,50,000. So, this gives me the equivalent annual cost as 5,93,550. So, this is the equivalent annual cost of your initial cost of defender, so we have estimated it. Already the operating and the maintenance cost already annual cost and they are equal, they are already annualized cost, so you need not convert them.Now let us go to the salvage value, I need to convert this salvage value into equivalent annual cost. So, you can do it by 2 approaches as I told you can use the uniform series sinking fund factor. You can use uniform series sinking fund factor and convert it into equivalent annual cost or you can find the present worth of this future salvage value using present worth factor and then convert it into a equivalent annual cost using uniform series capital recovery factor.So, both these approaches you can use any one of these approaches you can use. Now let us calculate using uniform series sinking fund factor approach, so let us see how to do that.(Refer Slide Time: 58:34)So, now you need to find the equivalent annual cost of 6,00,000, that is your salvage value. So, you need to find A for the known F, i and n, F is nothing but your future value, the future salvage value. So, what is the salvage value, F is nothing but 6,00,000 and the interest rate is 0.1 number of years is 5, you are going to use this formula, this is nothing but your uniform series sinking fund factor.So, using this we are going to calculate this, this is uniform series capital recovery factor, hope you remember. So, now we are going to use this uniform series sinking fund factor to find the equivalent annual cost, it is nothing that i divided by 1 + i power n – 1, so i is 0.1 divided by 1.1 number of years is 5 – 1, so he will get the factor value as 0.1638. Now to find the equivalent annual cost multiply this 0.1638 by 6,00,000.So, this gives me the equivalent annual cost as 98,280. So, this is the equivalent annual cost of your salvage value 98,280. So, now let us see how it is done? Let me summarize whatever I have discussed so far. So, you are finding the annual worth or the equivalent annual cost of your defender. So, first you are converting the initial cost of the defender, it is 22,50,000 into equivalent annual cost using uniform series capital recovery factor.Your operating cost is already in the annualize form, no need to convert. Then you convert your salvage value 6,00,000 into equivalent annual cost using uniform series sinking fund factor. Thatis what is done here 22,50,000 to the factory is A, for known P, i and n, + 1,35,000 - salvage value you have to multiply with the uniform series sinking fund factor which is nothing but you are going to find A for the given F, interest rate 10% and n = 5.So, now you substituted we will get it, the factor is corresponding to 0.2638, here the factor is corresponding to 0.1638, so when you simplify you will get this value. So, the annualize initial cost of the defender is 5,93,550, this is your outflow. Your operating cost is your cash outflow 1,35,000 add both the cash outflows, you will get the total outflow, then what is your inflow? Your inflow is nothing but your salvage value 98,280 you subtract it from the added value.You will get the final equivalent annual cost of the defender or the annual worth of the defender as 6,30,270. So, this is the cost liability of holding the defender with you, so this is the cost implication or the equivalent annual cost associated with the defender. If you are going to hold this machine for 5 years. So, what is the equivalent annual cost associated is 6,30,270. A similar manner you are going to find the equivalent annual cost for your challenger machine, that is a proposed equipment.(Refer Slide Time: 01:02:18)So, for the new equipment challenger, the initial cost is given as 27,50,000. So, this is a cost for the acquisition of the machine to your project site. Then the salvage value is given as 12,00,000, after 5 years, so after 5 years it is going to be 12,00,000. So, here the life of the machine we areconsidering is 5 years. So, the annual operating and maintenance cost is 90,000, now you are going to find the equivalent annual cost of the proposed asset, that is a challenger, in the same manner, you can find it.(Refer Slide Time: 01:02:51)Let us draw the cash flow diagram first. Now the initial cost of the challenger is 27,50,000, the operating cost is same for every year. For the 5 years it is found to be 90,000, at the end of the 5th year if you are going to sell it your salvage value is 12,00,000. Now, find the equivalent annual cost of your initial cost of a challenger that is 27,50,000, so how to find this? So, you need to find the A for the known P, i, n what is P here?P is the initial cost of your challenger, it is 27,50,000, it is a present value, interest rate is 0.1, number of years is 5. So, now you need to use uniform series capital recovery factor, you have already estimated but let me explain again. So, that you will understand better i into 1 + i power n divided by 1 + i power n - 1. So, 0.1 into 1.1 power 5 divided by 1.1 power 5 - 1. So, what is the value of the factor 0.2638, we simplify we will get 0.2638.To find the equivalent annual cost, to multiply this value by 0.2638 if we multiply both we will get the equivalent annual cost as 7,25,450.(Refer Slide Time: 1:04:13)You can see, so this is what their estimated. Now already the operating cost is annualized, you need to convert that, into equivalent annual cost, it is already equivalent annual cost. Now we are going to calculate the equivalent annual cost associated with the salvage value of the machine. So, let me now estimate the equivalent annual cost of the salvage value 1200000.(Refer Slide Time: 1:04:45)So, you are going to use the uniform series sinking fund factor, using this you can convert it. You need to find the A for the known future value i and n, the future value is nothing but your salvage value 12,00,000, interest rate is 0.1, number of years is 5. So, you are going to use this factor sinking fund factor i divided by 1 + i power n – 1, i is nothing but 0.1 divided by 1.1 power 5 - 1.So, this gives me the answer as 0.1638 we simplify you will get 0.1638 multiply this by 1200000, this is 12,00,000 multiply this by 1200000 you will get the equivalent annual cost as 1,96,560. So, this is the equivalent annual cost of your salvage value 1200000. So, let me know summarize, we are finding the annual worth of the challenger. So, here we are finding the equivalent annual cost of the initial cost of a challenger plus the operating cost minus your salvage value, equivalent annual cost of the salvage value.To find the equivalent annual cost of the initial cost you have to multiply by uniform series capital recovery factor, then add it with the operating cost. Then you have salvage value, you multiply it with the uniform series sinking fund factor and then subtract it from the cash outflow. This is the cash inflow, so these 2 are cash outflows. So, the 7,25,450 is your equivalent annual cost of your initial cost of machine, 90,000 is your operating cost of the machine.So, both are cash outflows, you have to add both. Now your cash inflow is the salvage value - 196560, so you will get the final resultant as 6,18,890. So, this is the cost liability of holding the challenger with you. So, the cost implication of holding the challenger for 5 years the equivalent annual cost will be 6,18,890(Refer Slide Time: 01:07:12)Now let us compare, from the above calculations you confine that the equivalent uniform annual cost of the defender is 630270. So, it is more than that of the equivalent annual cost of challenger which is 6,18,890. Hence it is advisable to replace your defender with a challenger. So, the construction company should replace the defender with the challenger, so this is a decision made.So, in this approach we are comparing 2 different machines, your current existing machine defender and the proposed machine where estimating the equivalent annual cost for both things, and we are finding for which one the cost liability is minimum. So, whichever equipment the cost liability is minimum we will recommend that. In this case, the challenger cost liability is minimum, so it is preferable to replace a defender with the challenger.(Refer Slide Time: 01:08:02)So, we are come to the end of this lecture 8. So, let me summarize whatever we have discussed so far. So, as I told you earlier, the replacement analysis is to be done from outsider perspective or the third party approach. So, the outsider is not concerned about your initial purchase price. For him for the current equipment, he is concerned only about the current trading value of the machine in the market.So, all your past estimates of your initial cost, your estimate of your useful life there, yearly estimates, the yearly estimates of salvage value of the defender and the sunk cost all are irrelevant in the replacement analysis. They should not be considered in the replacementanalysis. You are supposed to consider only the current trading value of your machine, current trading value of your current asset that is only important for an outsider.And I explained to you what is the sunk cost, sunk cost is the cost which cannot be recovered. Say for example, your estimated book value of the machine is going to be higher than the current trading value of the machine, that difference is your sunk cost. The difference between the asset book value and the current market value, this cost cannot be recovered. So, that is a sunk cost, and this cost should not be considered in the replacement analysis.So, basically the economic life of the machine is a time period at which the equivalent uniform annual cost is a minimum. So, we have discussed 2 different types of problems, in one problem we have estimated the economic life of the machine using the equivalent annual cost of the machine. In another problem we have compared the defender and challenger and we have estimated the equivalent annual cost for both the defender and the challenger.And compare both the values for whichever equipment the cost liabilities minimum, we recommend that particular equipment. So, we have discussed 2 different types of approaches using this time value method. So, basically we have dedicated 3 different lectures, lecture 6, 7 and 8 for the equipment life and the replacement analysis. So, as I told you when you do the replacement analysis, we have to consider all the components of the equipment cost.Then only you can get a accurate picture, all the cost including your downtime cost, obsolescence cost, your cost of inflation, everything should be considered in the cost estimation to get the accurate replacement decision. Also you should consider the timing of the cash flows, time value factor you should consider. So, that you can get an accurate replacement decision. So, with this let me conclude with the lecture 8.(Refer Slide Time: 01:10:43)So, these are the reference textbooks which I have used for the preparation of this lecture. I recommend you to procure some of these books for the preparation of topics later. In the next lecture we will be discussing about engineering fundamentals of the earthmoving operation. Like we will be discussing what are all the important fundamental terminologies related to earthmoving operation, I will introduce those terms.And we will also discuss about different types of machines earth moving machines, their mode of operation, how to estimate the productivity of those machines? All those things will be discussed in the upcoming lectures, thank you.