HP 12c Owners Manual

							 
181 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 181 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
  Appendix C 
Error Conditions 
Some calculator operations cannot be performed under certain conditions (for 
example, z
 when x = 0). If you attempt such an operation under these conditions, 
the calculator will display the word Error
 followed by a digit, 0
 through 9
. Listed 
below are operations that cannot be performed under the conditions specified. The 
symbols x and y represent the number in the X- and Y-registers, respectively, when 
the operation key is pressed. 
Error 0: Mathematics 
Operation Condition 
z
 
x = 0 
y
 
x = 0 
r
 
x < 0 
°
 
x 
≤ 0 
q
 
y = 0 and x 
≤ 0 
 
y < 0 and x is noninteger. 
à
 
y = 0 
Z
 
y = 0 
?z
(0 through 4) x = 0 
e
 
x is noninteger 
 
x < 0  
						

							182  Appendix C: Error Conditions 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 182 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Error 1: Storage Register Overflow 
Operation Condition 
?+
(0 through 4) 
?-
(0 through 4) 
?§
(0 through 4) 
?z
(0 through 4) 
A
 
 Magnitude of result is greater than 
9.999999999×10
99. 
Error 2: Statistics 
Operation Condition 
Ö
 
n (number in R
1) = 0 

 
Σx = 0 
v
 
n = 0 
n = 1 
n
Σx
2 – (
Σx)2< 0 
n
Σy2 – (
Σy)2< 0 
R
 
n = 0 
n
Σx
2  – (
Σx)2 = 0 
Q
 
n = 0 
n
Σy
2 – (
Σy)2 = 0 
R~ 
Q~
 
 [n
Σx
2 – (
Σx)2][n
Σy2 – (
Σy)2] 
≤ 0 
Error 3: IRR 
Refer to Appendix B. 
Error 4: Memory 
z Attempting to enter more than 99 program lines. 
z Attempting to i to a program line that does not exist. 
z Attempting storage register arithmetic in R5 through R9 or R.0 through R.9.  
						

							  Appendix C: Error Conditions  183   
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 183 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Error 5: Compound Interest 
Operation Condition 
n
 
PMT 
≤ –PV × i 
PMT = FV × i 
i 
≤ –100 
The values in i, PV, and FV are such that no 
solution exists for n. 
¼
 
PMT = 0 and n < 0 
Cash flows all have same sign. 
$
 
i 
≤ –100 
P
 
n = 0 
i = 0 
i 
≤ –100 
M
 
i 
≤ –100 
!
 
x 
≤ 0 
x is noninteger. 
l
 
i 
≤ –100 
V 
Ý 
#
 
 n 
≤ 0 
n > 10
10 
x 
≤ 0 
x is noninteger 
Error 6: Storage Registers 
Operation Condition 
? 
:
 
 Storage register specified does not exist or has 
been converted to program lines. 
K 
a
 
 n specifies a storage register that does not exist 
or has been converted to program lines. 
l 
L
 
 n > 20 
n > r (as defined by N
) 
n < 0 
n is noninteger 
a
 
x > 99 
x < 0 
x is noninteger  
						

							184  Appendix C: Error Conditions 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 184 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Error 7: IRR 
Refer to Appendix B. 
Error 8: Calendar 
Operation Condition 
Ò 
D
 
 Improper date format or illegal date. 
D
 
Attempting to add days beyond calculator’s date 
capacity. 
E 
S
 
 Improper date format or illegal date. 
 
More than 500 years between settlement 
(purchase) date and maturity (redemption) date. 
 
Maturity date earlier than settlement date. 
 
Maturity date has no corresponding coupon date 
(6 months earlier).
* 
Error 9: Service 
Refer to Appendix E. 
Pr Error 
z Continuous Memory has been reset. (Refer to Continuous Memory, page 
70.) 
z You have reset the calculator using the reset hole (see page 194). 
                                                 
*  This is the case for the 31st of March, May, August, October, and December, plus August 29 
(except in a leap year) and 30. For example, there is no September 31, so March 31 has no 
corresponding coupon date 6 months earlier. 
  To correct this problem for all maturity dates except August 29 and 30, add one day to both 
the settlement date and the maturity date in your calculations. For instance, if a bond were 
purchased on June 1, 2004 (the settlement date) with a maturity date of December 31, 2005, 
you should change the dates to June 2, 2004 and January 1, 2006 for your calculations. 
  For August 29 and 30, there is no calculator solution that gives the correct answer.  
						

							 
185 
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Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
  Appendix D
 
Formulas Used 
Percen t ag e  
100) Rate( ) Base(
%x y×
= 
⎟ ⎟
⎠ ⎞
⎜ ⎜
⎝ ⎛
−
= ∆
) Base() Base( ) NewAmount(
100 %yy x 
⎟ ⎟
⎠ ⎞
⎜ ⎜
⎝ ⎛
=
) Total() Amount(
100 %Tyx 
Interest 
n  = number of compounding periods. 
i  = periodic interest rate, expressed as a decimal. 
PV  = present value. 
FV  = future value or balance. 
PMT   = periodic payment. 
S  = payment mode factor (0 or 1) indicating treatment of PMT.  
0 corresponds to End, 1 to Begin. 
I  = interest amount. 
INTG (n)  = integer portion of n. 
FRAC (n)  = fractional portion of n. 
Simple Interest 
i PV n
I× × =
360360 
i PV n
I× × =
365365  
						

							186  Appendix D: Formulas Used 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 186 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Compound Interest 
Without an odd period: 
n ni FV
ii
PMT iS PV− −+ +
⎥ ⎥
⎦ ⎤
⎢ ⎢
⎣ ⎡
+ −
⋅ ⋅ + + =) 1 ( ) 1 ( 1
) 1 ( 0 
With simple interest used for an odd period: 
) ( INTG) INTG() 1 () 1 ( 1
) 1 ( ] ) FRAC( 1 [ 0nni FVi i
PMT iS n i PV−−++
⎥ ⎥
⎦ ⎤
⎢ ⎢
⎣ ⎡
+ −
+ + + =
 
With compound interest used for an odd period: 
) ( INTG) INTG(
) FRAC() 1 () 1 ( 1
) 1 ( ) 1 ( 0nn
ni FVi i
PMT iS i PV−−++
⎥ ⎥
⎦ ⎤
⎢ ⎢
⎣ ⎡
+ −
+ + + =
 
Amortization 
n= number of payment periods to be amortized. 
INT
j= amount of PMT applied to interest in period j. 
PRN
j= amount of PMT applied to principal in period j. 
PV
j= present value (balance) of loan after payment in period j. 
j= period number. 
INT
1= {0 if n = 0 and payment mode is set to Begin. 
|PV
0 × i|RND (sign of PMT) 
PRN
1= PMT – INT1 
PV
1= PV0 + PRN1 
INT
j= |PVj –1 × i|RND × (sign of PMT) for j > 1. 
PRN
j= PMT – INTj 
PV
j= PVj –1 + PRNj 
 
∑ ∑=+ + + = =n
n jINT INT INT INT INT1 j2 1... 
∑ ∑=+ + + = =n
n jPRN PRN PRN PRN PRN1 j2 1... 
∑+ =PRN PV PVn
0  
						

							  Appendix D: Formulas Used  187 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 187 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Discounted Cash Flow Analysis 
Net Present Value 
NPV  = net present value of a discounted cash flow. 
CF
j = cash flow at period j. 
n ni CF
i CF
i CF
CF NPV
) 1 ( ...
) 1 ( ) 1 (2 2
1 1
0+ + +
+ +
+ + = 
Internal Rate of Return 
n  = number of cash flows 
CF
j  = cash flow at period j. 
IRR  = Internal Rate of Return 
0
1) 1 ( ) 1 ( 1
0CF IRR
IRRIRR
CFj q jnq
k
jn
j
+
⎥
⎦ ⎤
⎢
⎣ ⎡
+ ⋅
⎥ ⎥
⎦ ⎤
⎢ ⎢
⎣ ⎡
+ −
⋅ =∑ −
=− 2 
x = INTG (0.4mm + 2.3) 
z = (yyyy) 
INTG = Integer portion. 
Note:
 Additional tests are performed in order to ensure that the century (but 
not millennium) years are not considered leap years. 
30/360 Day Basis 
DAYS = f(DT2) – f(DT1) 
f(DT) = 360 (yyyy) + 30mm + z 
for f(DT
1) 
if dd
1 = 31 then z = 30 
if dd
1 ≠ 31 then z = dd1 for f(DT2) 
if dd
2 = 31 and dd1 = 30 or 31 then z = 30 
if dd
2 = 31 and dd1 < 30 then z = dd2 if dd2 < 31 then z = dd2  
						

							188  Appendix D: Formulas Used 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 188 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Bonds 
Reference: 
Spence, Graudenz, and Lynch, Standard Securities Calculation Methods, 
Securities Industry Association, New York, 1973. 
DIM= days between issue date and maturity date. 
DSM= days between settlement date and maturity date. 
DCS= days between beginning of current coupon period and 
settlement date. 
E= number of days in coupon period where settlement occurs. 
DSC= E – DCS = days from settlement date to next 6–month coupon 
date. 
N= number of semiannual coupons payable between settlement 
date and maturity date. 
CPN= annual coupon rate (as a percentage). 
YIELD= annual yield (as a percentage). 
PRICE= dollar price per $100 par value. 
RDV= redemption value. 
For semiannual coupon with 6 months or less to maturity: 
⎥
⎦ ⎤
⎢
⎣ ⎡
× −
⎥ ⎥ ⎥
⎥
⎦ ⎤
⎢ ⎢ ⎢
⎢
⎣ ⎡
× ++
=
2
)
2 ( 100)
2 ( 100
CPN
E DCS
YIELD
E DSMCPN
RDV
PRICE 
For semiannual coupon with more than 6 months to maturity: 
⎥
⎦ ⎤
⎢
⎣ ⎡
× −
⎥ ⎥ ⎥ ⎥ ⎥ ⎥
⎦ ⎤
⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎣ ⎡
⎟
⎠ ⎞
⎜
⎝ ⎛
+ +⎥ ⎥ ⎥ ⎥
⎥
⎦ ⎤
⎢ ⎢ ⎢ ⎢
⎢
⎣ ⎡
⎟
⎠ ⎞
⎜
⎝ ⎛
+ =∑=+ − + −E DCS CPN
YIELDCPN YIELDRDV
PRICE
N
K
E DSC
KE DSC
N
2
200 12 200 111 1
  
						

							  Appendix D: Formulas Used  189 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 189 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Depreciation 
L  = asset’s useful life expectancy. 
SBV  = starting book value. 
SAL  = salvage value. 
FACT  = declining-balance factor expressed as a percentage. 
j = period number. 
DPN
j  = depreciation expense during period j. 
RDV
j  = remaining depreciable value at end of period j  
= RDV
j–1 – DPNj where RDV0 = SBV – SAL 
RBV
j  = remaining book value = RBVj–1 – DPNj where RBV0 = SBV 
Y
1  = number of months in partial first year. 
 
Straight-Line Depreciation 
Keyboard function: 
LSAL SBV
DPNJ−
= for j = 1, 2, …, L 
Program for partial first year: 
12
1
1Y
LSAL SBV
DPN⋅ −
= 
LSAL SBV
DPNJ−
= for j = 2, 3, …, L 
DPN
L + 1 = RDVL 
Sum-of-the-Years-Digits Depreciation 
2) 2 )( 1 (
FWWSOYDk++
= 
where W = integer part of k 
  F = fractional part of k. 
(i.e., for k = 12.25 years, W = 12 and F = 0.25). 
Keyboard function: 
) ( ) 1 (SAL SBV
SOYDj L
DPN
L J
− ⋅ + −
=  
						

							190  Appendix D: Formulas Used 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 190 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Program for partial year: 
) (
121
1SAL SBV Y
SOYDL
DPN− ⋅
⎟
⎠ ⎞
⎜
⎝ ⎛
⋅
⎟
⎠ ⎞
⎜
⎝ ⎛
= 
) ( 21SAL D SBV
SOYDj LADJ
DPN
LADJ j
− − ⋅
⎟ ⎟
⎠ ⎞
⎜ ⎜
⎝ ⎛
+ −
= for j ≠ 1 
where 
⎟
⎠ ⎞
⎜
⎝ ⎛
− =
121Y
L LADJ 
Declining-Balance Depreciation 
Keyboard function: 
L FACT
RBV DPNj j1001⋅ =− for j = 1, 2, …, L 
Program for partial first year: 
12 100
1
1Y
L FACT
SBV DPN⋅ ⋅ = 
L FACT
RBV DPNj j1001⋅ =− for j ≠ 1 
Modified Internal Rate of Return 
n= number of compounding periods. 
NFV
P= Net future value of the positive cash flows.   
NPV
N= Net present value of the negative cash flows. 
⎥ ⎥ ⎥
⎦ ⎤
⎢ ⎢ ⎢
⎣ ⎡
−
⎟ ⎟
⎠ ⎞
⎜ ⎜
⎝ ⎛
− =1 100
1
n
N P
NPV NFV
MIRR 
Advance Payments 
A= number of payments made in advance. 
⎥ ⎥
⎦ ⎤
⎢ ⎢
⎣ ⎡
+ + −+ −
=
− −−
A
iii FV PV
PMT
A nn
) () 1 ( 1) 1 (