3062 Chapter 53 Details Contents Investments and Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3063 Saving Output to SAS Data Sets . . . . . . . . . . . . . . . . . . . . . . . . 3063 Loading a SAS Data Set into a List . . . . . . . . . . . . . . . . . . . . . . 3065 Saving Data from a List to a SAS Data Set . . . . . . . . . . . . . . . . . . 3065 Right Mouse Button Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3066 Depreciation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3067 Straight Line (SL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3067 Sum-of-Years Digits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3067 Declining Balance (DB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3069 Rate Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3070 The Tools Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3070 Dialog Box Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3071 Minimum Attractive Rate of Return (MARR) . . . . . . . . . . . . . . . . . . . . . 3071 Income Tax Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3072 Inflation Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3073 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3074 Investments and Data Sets Investment Analysis provides tools to assist you in moving data between SAS data sets and lists you can use within Investment Analysis. Saving Output to SAS Data Sets Many investment specifications have a button that reads Save Data As . Clicking that button opens the Save Output Dataset dialog box (see Figure 53.1). This dialog box enables you to save all or part of the area generated by the specification. 3064 ✦ Chapter 53: Details Figure 53.1 Saving to a Dataset The following items are displayed: Dataset Name holds the SAS data set name to which you want to save. Browse opens the standard SAS Open dialog box, which enables you to select an existing SAS data set to overwrite. Dataset Label holds the SAS data set’s label. Dataset Variables organizes variables. The variables listed in the Selected area will be included in the SAS data set. You can select variables one at a time, by clicking the single right-arrow after each selection to move it to the Selected area. If the desired SAS data set has many variables you want to save, it may be simpler to follow these steps: 1. Click the double right-arrow to select all available variables. 2. Remove any unwanted variable by selecting it from the Selected area and clicking the single left-arrow. The double left-arrow removes all selected variables from the proposed SAS data set. The up and down arrows below the Available and Selected boxes enable you to scroll up and down the list of variables in their respective boxes. Save Dataset attempts to save the SAS data set. If the SAS data set name exists, you are asked if you want to replace the existing SAS data set, append to the existing SAS data set, or cancel the current save attempt. You then return to this dialog box ready to create another SAS data set to save. Saving Data from a List to a SAS Data Set ✦ 3065 Return takes you back to the specification dialog box. Loading a SAS Data Set into a List Right-click in the area that you want to load the list and release on Load . This opens the Load Dataset dialog box (see Figure 53.2). Figure 53.2 Load Dataset Dialog Box The following items are displayed: Dataset Name holds the name of the SAS data set that you want to load. Browse opens the standard SAS Open dialog box, which aids in finding a SAS data set to load. If there is a Date variable in the SAS data set, Investment Analysis loads it into the list. If there is no Date variable, it loads the first available time-formatted variable. If an amount or rate variable is needed, Investment Analysis searches the SAS data set for a Amount or Rate variable to use. Otherwise it takes the first numeric variable that is not used by the Date variable. Dataset Label holds a SAS data set label. OK attempts to load the SAS data set specified in Dataset Name . If the specified SAS data set exists, clicking OK returns you to the calling dialog box with the selected SAS data set filling the list. If the specified SAS data set does not exist and you click OK , you receive an error message and no SAS data set is loaded. Cancel returns you to the calling dialog box without loading a SAS data set. Saving Data from a List to a SAS Data Set Right-click in the area you want to hold the list, and release on Save . This opens the Save Dataset dialog box. 3066 ✦ Chapter 53: Details Figure 53.3 Save Dataset Dialog Box The following items are displayed: Dataset Name holds the SAS data set name to which you want to save. Browse opens the standard SAS Save As dialog box, which enables you to find an existing SAS data set to overwrite. Dataset Label holds a user-defined description to be saved as the label of the SAS data set. OK saves the current data to the SAS data set specified in Dataset Name . If the specified SAS data set does not already exist, clicking OK saves the SAS data set and returns you to the calling dialog box. If the specified SAS data set does already exist, clicking OK warns you and enables you to replace the old SAS data set with the new SAS data set or cancel the save attempt. Cancel aborts the save process. Clicking Cancel returns you to the calling dialog box without attempting to save. Right Mouse Button Options A pop-up menu often appears when you right-click within table editors. The menus offer tools to aid in the management of the table’s entries. Most table editors provide the following options. Figure 53.4 Right-Clicking Options Add creates a blank row. Depreciation Methods ✦ 3067 Delete removes any currently selected row. Copy duplicates the currently selected row. Sort arranges the rows in chronological order according to the date variable. Clear empties the table of all rows. Save opens the Save Dataset dialog box where you can save the all rows to a SAS Dataset for later use. Load opens the Load Dataset dialog box where you select a SAS Dataset to fill the rows. If you want to perform one of these actions on a collection of rows, you must select a collection of rows before right-clicking. To select an adjacent list of rows, do the following: click the first pair, hold down SHIFT, and click the final pair. After the list of rows is selected, you may release the SHIFT key. Depreciation Methods Suppose an asset’s price is $20,000 and it has a salvage value of $5,000 in five years. The following sections describe various methods to quantify the depreciation. Straight Line (SL) This method assumes a constant depreciation value per year. Assuming that the price of a depreciating asset is P and its salvage value after N years is S , the annual depreciation is: P S N For our example, the annual depreciation would be $20; 000 $5; 000 5 D $3; 000 Sum-of-Years Digits An asset often loses more of its value early in its lifetime. A method that exhibits this dynamic is desirable. Assume an asset depreciates from price P to salvage value S in N years. First compute the sum-of-years as T D 1 C 2 C CN . The depreciation for the years after the asset’s purchase is: 3068 ✦ Chapter 53: Details Table 53.1 Sum-of-Years General Example Year Number Annual Depreciation first N T .P S/ second N 1 T .P S/ third N 2 T .P S/ : : : : : : final 1 T .P S/ For the ith year of the asset’s use, the annual depreciation is: N C1 i T .P S/ For our example, N D 5 and the sum of years is T D 1 C 2 C 3 C 4 C 5 D 15 . The depreciation during the first year is .$20; 000 $5; 000/ 5 15 D $5; 000 Table 53.2 describes how Declining Balance would depreciate the asset. Table 53.2 Sum-of-Years Example Year Depreciation Year-End Value 1 .$20; 000 $5; 000/ 5 15 D $5; 000 $15; 000:00 2 .$20; 000 $5; 000/ 4 15 D $4; 000 $11; 000:00 3 .$20; 000 $5; 000/ 3 15 D $3; 000 $8; 000:00 4 .$20; 000 $5; 000/ 2 15 D $2; 000 $6; 000:00 5 .$20; 000 $5; 000/ 1 15 D $1; 000 $5; 000:00 As expected, the value after N years is S. S D P .5 years’ depreciation/ D P Â 5 10 .P S/ C 4 10 .P S/ C 3 10 .P S/ C 2 10 .P S/ C 1 10 .P S/ Ã D P .P S/ Declining Balance (DB) ✦ 3069 Declining Balance (DB) Recall that the straight line method assumes a constant depreciation value. Conversely, the declining balance method assumes a constant depreciation rate per year. And like the sum-of-years method, more depreciation tends to occur earlier in the asset’s life. Assume the price of a depreciating asset is P and its salvage value after N years is S . You could assume the asset depreciates by a factor of 1 N (or a rate of 100 N %). This method is known as single declining balance. The annual depreciation is: 1 N .previous year’s value/ So for our example, the depreciation during the first year is $20;000 5 D $ 4; 000 . Table 53.3 describes how declining balance would depreciate the asset. Table 53.3 Declining Balance Example Year Depreciation Year-End Value 1 $20;000:00 5 D $4; 000:00 $16; 000:00 2 $16;000:00 5 D $3; 200:00 $12; 800:00 3 $12;800:00 5 D $2; 560:00 $10; 240:00 4 $10;240:00 5 D $2; 048:00 $8; 192:00 5 $12;800:00 5 D $1; 638:40 $6; 553:60 DB Factor You could also accelerate the depreciation by increasing the factor (and hence the rate) at which depreciation occurs. Other commonly accepted depreciation rates are 200 N % (called double declining balance as the depreciation factor becomes 2 N ) and 150 N %. Investment Analysis enables you to choose between these three types for declining balance: 2 (with 200 N % depreciation), 1.5 (with 150 N %), and 1 (with 100 N %). Declining Balance and the Salvage Value The declining balance method assumes that depreciation is faster earlier in an asset’s life; this is what you wanted. But notice the final value is greater than the salvage value. Even if the salvage value were greater than $6,553.60, the final year-end value would not change. The salvage value never enters the calculation, so there is no way for the salvage value to force the depreciation to assume its value. Newnan and Lavelle (1998) describe two ways to adapt the declining balance method to assume the salvage value at the final time. One way is as follows: Suppose you call the depreciated value after i years V .i/. This sets V .0/ D P and V .N / D S. 3070 ✦ Chapter 53: Details If V .N / > S according to the usual calculation for V .N /, redefine V .N / to equal S. If V .i/ < S according to the usual calculation for V .i/ for some i (and hence for all subsequent V .i/ values), you can redefine all such V .i/ to equal S. This alteration to declining balance forces the depreciated value of the asset after N years to be S and keeps V .i/ no less than S. Conversion to SL The second (and preferred) way to force declining balance to assume the salvage value is by conversion to straight line. If V .N / > S , the first way redefines V .N / to equal S; you can think of this as converting to the straight line method for the last timestep. If the V .N / value supplied by DB is appreciably larger than S , then the depreciation in the final year would be unrealistically large. An alternate way is to compute the DB and SL step at each timestep and take whichever step gives a larger depreciation (unless DB drops below the salvage value). After SL assumes a larger depreciation, it continues to be larger over the life of the asset. SL forces the value at the final time to equal the salvage value. As an algorithm, this looks like the following statements: V(0) = P; for i=1 to N if DB step > SL step from (i,V(i)) take a DB step to make V(i); else break; for j = i to N take a SL step to make V(j); The MACRS, which is discussed in the section that describes the Depreciation Table window, is actually a variation on the declining balance method with conversion to the straight line method. Rate Information The Tools Menu Figure 53.5 shows the Tools menu. Dialog Box Guide ✦ 3071 Figure 53.5 The Tools Menu The Tools ! Define Rates menu offers the following options. MARR opens the Minumum Attractive Rate of Return (MARR) dialog box. Income Tax Rate opens the Income Tax Specification dialog box. Inflation opens the Inflation Specification dialog box. Dialog Box Guide Minimum Attractive Rate of Return (MARR) Selecting Tools ! Define Rates ! MARR from the Investment Analysis dialog box menu bar opens the MARR dialog box that is displayed in Figure 53.6. . 30 69 Rate Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3070 The Tools Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3070 Dialog Box Guide. no way for the salvage value to force the depreciation to assume its value. Newnan and Lavelle ( 199 8) describe two ways to adapt the declining balance method to assume the salvage value at the. $3; 200:00 $12; 800:00 3 $12;800:00 5 D $2; 560:00 $10; 240:00 4 $10;240:00 5 D $2; 048:00 $8; 192 :00 5 $12;800:00 5 D $1; 638:40 $6; 553:60 DB Factor You could also accelerate the depreciation