HP 12c Owners Manual

							 Section 13: Investment Analysis 141 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 141 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
remaining depreciable value. If desired, press 
:$:3=~-:M- to find the total depreciation through the 
current year. 
9. Press t for the amount of depreciation then, if desired, press ~ for the 
remaining depreciable value for the next year. Repeat this step for the 
following years. 
10. For a new case press gi00 and return to step 2. 
Example:
 An electron beam welder which costs $50,000 is purchased 4 months 
before the end of the accounting year. What will the depreciation be during the 
first full accounting year (year 2) if the welder has a 6 year depreciable life, a 
salvage value of $8,000 and is depreciated using the declining-balance 
depreciation method?
 The declining-balance factor is 150%. 
Keystrokes Display  
fCLEARG 
  
50000$ 
50,000.00 Book value. 
8000M 
8,000.00 Salvage value. 
150¼ 
150.00 Declining-balance factor. 
6n 
6.00 Life. 
2\ 
2.00 Year desired. 
4t 
2.00 
11,458.33 Second year: 
depreciation. 
Sum-of-the-Years-Digits Depreciation 
The following hp 12c program calculates the sum-of-the-years-digits depreciation 
for the year desired with the acquisition date occurring at any time during the 
year. 
KEYSTROKES DISPLAY KEYSTROKES DISPLAY 
fs  - 21-    30 
fCLEARÎ 00- n 22-    11 
1 01-     1:0 23-  45   0 
2 02-     2gm 24-  43  35 
z 03-    10gi35 25-43, 33   35 
?1 04-  44   1:2 26-  45   2 
~ 05-    34gu 27-  43  31  
						

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KEYSTROKES DISPLAY KEYSTROKES DISPLAY 
?2 06-  44   2:0 28-  45   0 
1 07-     1fÝ 29-  42  24 
- 08-    30t 30-    31 
?0 09-  44   01 31-     1 
1 10-     1?=0 32-44  40   0 
fÝ 11-  42  24?=2 33-44  40   2 
:1 12-  45   1gi26 34-43, 33   26 
§ 13-    20:2 35-  45   2 
?3 14-  44   3gu 36-  43  31 
:$ 15-  45  13:$ 37-  45  13 
~ 16-    34:M 38-  45  15 
- 17-    30- 39-    30 
$ 18-    13:3 40-  45   3 
:n 19-  45  11gi30 41-43, 33   30 
:1 20-  45   1fs  
 
REGISTERS 
n: Life  i: Unused  PV: Dep. Value  PMT: Unused 
FV: Salvage 
R0: Used  R1: #Mos./12  R2: Counter 
R3: 1st Yr. Dep.  R4–R.4: Unused   
 
1.  Key in the program. 
2. Press fCLEARG. 
3.  Key in the book value then press $. 
4.  Key in the salvage value then press M. 
5.  Key in the life in years (an integer) then press n. 
6.  Key in the year desired then press \.  
						

							 Section 13: Investment Analysis 143 
 
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7.  Key in the number of months in first year* then press t.† The display will 
show the amount of depreciation for the desired year. If desired, press ~ 
to see the remaining depreciable value, then press :$:3= 
~-:M- to find the total depreciation through the current year. 
8. Press t for the amount of depreciation then, if desired, press ~ for the 
remaining depreciable value for the next year. Repeat this step for the 
following years. 
9.  For a new case press gi00 and return to step 2. 
Example:
 A commercial movie camera is purchased for $12,000. If maintained 
properly, the camera has a useful life expectancy of 25 years with $500 salvage 
value. Using the sum-of-the-years-digits method, what is the amount of depreciation 
and the remaining depreciable value for the 4th and 5th years?
 Assume the first 
depreciation year is 11 months long. 
Keystrokes Display  
fCLEARG 
  
12000$ 
12,000.00 Book value. 
500M 
500.00 Salvage value. 
25n 
25.00 Life. 
4\ 
4.00 Year desired. 
11t 
 
~ 
4.00 
781.41 
8,238.71 Fourth year: 
depreciation, 
remaining depreciable value. 
t 
 
~ 
5.00 
746.02 
7,492.69 Fifth year: 
depreciation, 
remaining depreciable value. 
                                                 
* Refer to straight-line depreciation instruction note, page 137.   
† The display will pause showing the year number before showing the amount of depreciation 
for that year.  
						

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Full- and Partial-Year Depreciation with Crossover   
When calculating declining-balance depreciation it is often advantageous for tax 
purposes to switch from declining balance to straight-line depreciation at some 
point. This hp 12c program calculates the optimum crossover point and 
automatically switches to straight-line depreciation at the appropriate time. The 
crossover point is the end of the year in which the declining-balance depreciation 
last exceeds or equals the amount of straight-line depreciation. The straight-line 
depreciation is determined by dividing the remaining depreciable value by the 
remaining useful life. 
Given the desired year and the number of months in the first year, this program 
calculates the depreciation for the desired year, the remaining depreciable value, 
and the total depreciation through the current year. 
KEYSTROKES DISPLAY  KEYSTROKES DISPLAY 
fs  :4 48-  45   4 
fCLEARÎ 00- z 49-    10 
1 01-     1go 50-  43  34 
2 02-     2gi53 51-43, 33   53 
z 03-    10gi65 52-43, 33   65 
?6 04-  44   6d 53-    33 
:n 05-  45  110 54-     0 
~ 06-    34:0 55-  45   0 
- 07-    30go 56-  43  34 
?4 08-  44   4gi86 57-43, 33   86 
d 09-    33:$ 58-  45  13 
?0 10-  44   0:5 59-  45   5 
1 11-     1- 60-    30 
?-0 12-44  30   0$ 61-    13 
?2 13-  44   21 62-     1 
?3 14-  44   3?-4 63-44  30   4 
f# 15-  42  25gi40 64-43, 33   40 
:6 16-  45   6:4 65-  45   4  
						

							 Section 13: Investment Analysis 145 
 
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Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
KEYSTROKES DISPLAY  KEYSTROKES DISPLAY 
§ 17-    20n 66-    11 
?1 18-  44   10 67-     0 
:$ 19-  45  13?6 68-  44   6 
~ 20-    341 69-     1 
- 21-    30?-2 70-44  30   2 
$ 22-    13?=0 71-44  40   0 
\ 23-    36:5 72-  45   5 
gF 24-  43  36?-1 73-44  30   1 
~ 25-    34:3 74-  45   3 
:M 26-  45  15fV 75-  42  23 
- 27-    30?+1 76-44  40   1 
~ 28-    341 77-     1 
:0 29-  45   0?-0 78-44  30   0 
1 30-     1?+2 79-44  40   2 
go 31-  43  34?+3 80-44  40   3 
gi39 32-43, 33   39d 81-    33 
d 33-    33:0 82-  45   0 
d 34-    331 83-     1 
1 35-     1go 84-  43  34 
gu 36-  43  31gi74 85-43, 33   74 
d 37-    33d 86-    33 
t 38-    31d 87-    33 
1 39-     1:2 88-  45   2 
?+2 40-44  40   2gu 89-  43  31 
?-0 41-44  30   0d 90-    33 
f# 42-  42  25t 91-    31  
						

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KEYSTROKES DISPLAY  KEYSTROKES DISPLAY 
?+1 43-44  40   1:6 92-  45   6 
?5 44-  44   5gm 93-  43  35 
:$ 45-  45  13gi74 94-43, 33   74 
:M 46-  45  15gi58 95-43, 33   58 
- 47-    30fs  
 
REGISTERS 
n: Life  i: Factor  PV: Dep. Value  PMT: Unused 
FV: Salvage 
R0: Used  R1: Dep.  R2: Counter 
R3: Used  R4: Used  R5: Used  R6: Used 
 
1.  Key in the program. 
2. Press fCLEARH. 
3.  Key in the book value then press $. 
4.  Key in the salvage value then press M. 
5.  Key in the life in years (an integer) then press n. 
6.  Key in the declining-balance factor as a percentage then press ¼. 
7.  Key in the desired year and press \. 
8.  Key in the number of months in the first year
* then press t† to calculate 
the amount of depreciation for the desired year. 
9.  If desired, press ~ to see the remaining depreciable value. 
10. If desired, press :1 to see the total depreciation through the current year. 
11. Continue  pressing t* to find the amount of depreciation for the successive 
years. Steps 9 and 10 may be repeated for each year. 
12. For a new case press gi00 and return to step 2. 
                                                 
*  Refer to straight-line depreciation note page 137.   
†  The display will pause with the year number before displaying the amount of depreciation for 
that year.  
						

							 Section 13: Investment Analysis 147 
 
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Example: 
An electronic instrument is purchased for $11,000, with 6 months 
remaining in the current fiscal year. The instrument’s useful life is 8 years and the 
salvage value is expected to be $500. Using a 200% declining-balance factor, 
generate a depreciation schedule for the instrument’s complete life. What is the 
remaining depreciable value after the first year?
 What is the total depreciation 
after the 7th year?
 
Keystrokes Display  
fCLEARH 
0.00  
11000$ 
11,000.00 Book value. 
500M 
500.00 Salvage value. 
8n 
8.00 Life. 
200¼ 
200.00 Declining-balance factor. 
1\ 
1.00 First year depreciation desired. 
6t 
 
~ 
1.00 
1,375.00 
9,125.00 First year: 
depreciation, 
remaining depreciable value. 
t 
2.00 
2,406.25 Second year: 
depreciation. 
t 
3.00 
1,804.69 Third year: 
depreciation. 
t 
4.00 
1,353.51 Fourth year: 
depreciation. 
t 
5.00 
1,015.14 Fifth year: 
depreciation. 
t 
6.00 
761.35 Sixth year: 
depreciation.
* 
t 
7.00 
713.62 Seventh year: 
depreciation.  
:1 
9,429.56 Total depreciation through the 
seventh year. 
t 
8.00 
713.63 Eight year: 
depreciation 
t 
9.00 
356.81 Ninth year: 
depreciation. 
                                                 
* By observation the crossover was year 6. Years 7, 8, and 9 use straight-line depreciation.  
						

							148  Section 13: Investment Analysis 
 
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Excess Depreciation 
When accelerated depreciation is used, the difference between total depreciation 
charged over a given period of time and the total amount that would have been 
charged under straight-line depreciation is called excess depreciation. To obtain 
excess depreciation: 
1.  Calculate the total depreciation then press \. 
2.  Key in the depreciable amount (cost less salvage) then press \. Key in the 
useful life of the asset in years then press z. Key in the number of years in 
the income projection period then press § to get the total straight-line 
depreciation charge. 
3. Press - to get the excess depreciation. 
Example: 
What is the excess depreciation in the previous example over 7 
calendar years?
 (Because of the partial first year, there are 6
1/2 years 
depreciation in the first 7 calendar years.) 
Keystrokes Display  
9429.56\ 
9,429.56 Total depreciation through seventh 
year. 
10500\ 
10,500.00 Depreciable amount. 
8z 
1,312.50 Yearly straight-line depreciation. 
6.5§ 
8,531.25 Total straight-line depreciation. 
- 
898.31 Excess depreciation 
Modified Internal Rate of Return 
The traditional Internal Rate of Return (IRR) technique has several drawbacks which 
hamper its usefulness in some investment applications. The technique implicitly 
assumes that all cash flows are either reinvested or discounted at the computed 
yield rate. This assumption is financially reasonable as long as the rate is within a 
realistic borrowing and lending range (for example, 10% to 20%). When the IRR 
becomes significantly greater or smaller, the assumption becomes less valid and 
the resulting value less sound as an investment measure. 
IRR also is limited by the number of times the sign of the cash flow changes 
(positive to negative or vice versa). For every change of sign, the IRR solution has 
the potential for an additional answer. The cash flow sequence in the example that 
follows has three sign changes and hence up to three potential internal rates of 
return. This particular example has three positive real answers: 1.86, 14.35, and 
29. Although mathematically sound, multiple answers probably are meaningless 
as an investment measure.  
						

							 Section 13: Investment Analysis 149 
 
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This Modified Internal Rate of Return procedure (MIRR) is one of several IRR 
alternatives which avoids the drawbacks of the traditional IRR technique. The 
procedure eliminates the sign change problem and the reinvestment (or 
discounting) assumption by utilizing user stipulated reinvestment and borrowing 
rates. 
Negative cash flows are discounted at a safe rate that reflects the return on an 
investment in a liquid account. The figure generally used is a short-term security 
(T-Bill) or bank passbook rate. 
Positive cash flows are reinvested at a reinvestment rate which reflects the return on 
an investment of comparable risk. An average return rate on recent market 
investments might be used. 
The steps in the procedure are: 
1.  Calculate the future value of the positive cash flows (NFV) at the reinvestment 
rate. 
2.  Calculate the present value of the negative cash flows (NPV) at the safe rate. 
3. Knowing n, PV, and FV, solve for i. 
Example:
 An investor has the following unconventional investment opportunity. 
The cash flows are: 
Group  # of Months  Cash Flow ($) 
0 1 –180,000 
1 5 100,000 
2 5 –100,000 
3 9  0 
4 1 200,000 
Calculate the MIRR using a safe rate of 6% and a reinvestment (risk) rate of 10%. 
Keystrokes Display  
fCLEARH 
0.00  
0gJ 
0.00 First cash flow. 
100000gK 
  
5ga 
5.00 Second through sixth cash flows. 
0gK5ga 
5.00 Next five cash flows. 
0gK9ga 
9.00 Next nine cash flows. 
200000gK 
200,000.00 Last cash flow.  
						

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Keystrokes Display  
10gCfl 
657,152.37 NPV of positive cash flows. 
Þ$ 
  
20nM 
775,797.83 NFV of positive cash flows. 
180000ÞgJ 
  
0gK5ga 
  
100000ÞK 
  
5ga 
  
6gCfl 
-660,454.55 NPV of negative cash flows. 
20n¼ 
0.81 Monthly MIRR 
12§ 
9.70 Annual MIRR.