HP 12c Owners Manual

							 
151 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 151 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
  Section 14 
Leasing 
Advance Payments 
Situations may exist where payments are made in advance (leasing is a good 
example). These agreements call for extra payments to be made when the 
transaction is closed. 
This first procedure finds the periodic payment amount necessary to achieve a 
desired yield when a number of payments are made in advance. And, given the 
periodic payment, the second procedure calculates the periodic yield. 
Solving For Payment 
To calculate the payment, information is entered as follows: 
1. Press g and fCLEARG. 
2.  Key in the total number of payments in the lease then press \. 
3.  Key in the total number of payments made in advance then press 
?0-n. 
4.  Key in or calculate the periodic interest rate as a percentage then press ¼. 
5. Press 1Þ$:0+. 
6.  Key in the initial loan amount then press ~z, to obtain the periodic 
payment to be received by the lessor. 
Example 1:
 Equipment worth $750 is leased for 12 months. The equipment is 
assumed to have no salvage value at the end of the lease. The lessee has agreed 
to make three payments at the time of closing. What monthly payment is necessary 
to yield the lessor 10% annually?
 
Keystrokes Display  
g 
  
fCLEARG 
  
12\ 
12.00 Duration of lease. 
3?0-n 
9.00 Number of periodic payments. 
10gC 
0.83  
1ÞP 
–1.00  
$:0+ 
11.64  
750~z 
64.45 Monthly payment to be received.  
						

							152 Section 14: Leasing 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 152 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
If solving for the payment amount will be done repetitively, key in the following hp 
12c program. 
KEYSTROKES DISPLAY  KEYSTROKES DISPLAY 
fs  1 09-     1 
fCLEARÎ 00- Þ 10-    16 
g 01-  43   8P 11-    14 
fCLEARG 02-  42  34$ 12-    13 
:0 03-  45   0:1 13-  45   1 
:1 04-  45   1+ 14-    40 
- 05-    30:3 15-  45   3 
n 06-    11~ 16-    34 
:2 07-  45   2z 17-    10 
¼ 08-    12fs  
 
REGISTERS 
n: n–#Adv. Pmt.  i: i  PV: Used  PMT: –1 
FV: 0 
R0: n  R1: #Adv. Pmt.  R2: i 
R3: Loan  R4–R.7: Unused   
 
1.  Key in the program. 
2.  Key in the total number of payments in the lease then press ?0. 
3.  Key in the total number of payments made in advance then press ?1. 
4.  Key in the periodic interest rate as a percentage then press ?2. 
5.  Key in the loan amount and press ?3; then press t to obtain the 
periodic payment to be received by the lessor. 
6.  For a new case, return to step 2. The values changed from the previous case 
are the only values which need to be entered.  
						

							 Section 14: Leasing 153 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 153 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 2:
 Using the preceding program, solve for the monthly payment using 
the information given in example 1. Then change the yearly interest to 15% and 
solve for the new payment amount. 
Keystrokes Display  
12?0 
12.00 Duration of lease. 
3?1 
3.00 Number of advance payments. 
10\12z 
  
?2 
0.83 Periodic interest rate. 
750?3t 
64.45 Monthly payment to be received. 
15\12z 
  
?2t 
65.43 Monthly payment to achieve a 15% 
yield. 
Example 3:
 Using the information from example 1, what monthly payment is 
necessary to yield the lessor 15% annually if one payment is due at the time of 
closing?
 
Assuming that the previous example was just solved, the keystrokes are as follows: 
Keystrokes Display  
1?1t 
66.86 Monthly payment to be received. 
Since this problem is an annuity due situation (one payment at the beginning of the 
period) the calculation could also be done as follows: 
Keystrokes   Display   
g× 
  
fCLEARG 
  
12n15gC 
1.25 Periodic interest rate (into i
). 
750Þ$P 
66.86 Monthly payment to be received.  
						

							154 Section 14: Leasing 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 154 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Solving for Yield 
To calculate the periodic yield, information is entered as follows: 
1. Press g and fCLEARG. 
2.  Key in the total number of payments in the lease then press \. 
3.  Key in the total number of payments made in advance then press   
?0-n. 
4.  Key in the periodic payment to be received then press P. 
5.  Key in the total amount of the loan then press Þ:0:P§+$. 
6. Press ¼ to obtain the periodic yield. 
Example 1:
 A lease has been written to run for 60 months. The leased 
equipment has a value of $25,000 with a $600 monthly payment. The lessee has 
agreed to make 3 payments at the time of closing ($1800). What is the annual 
yield to the lessor?
 
Keystrokes Display  
g 
  
fCLEARG    
60\3 
  
?0-n 
57.00 Number of periodic payments. 
600P 
  
25000Þ:0 
3.00 Number of advance payments. 
:P§+$ 
-23,200.00 PV. 
¼ 
1.44 Monthly yield (calculated). 
12§ 
17.33 Annual yield (as a percentage).  
						

							 Section 14: Leasing 155 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 155 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
If solving for yield will be done repetitively, key in the following hp 12c program: 
KEYSTROKES DISPLAY  KEYSTROKES DISPLAY 
fs  :3 09-  45   3 
fCLEARÎ 00- Þ 10-    16 
g 01-  43   8:1 11-  45   1 
fCLEARG 02-  42  34:P 12-  45  14 
:0 03-  45   0§ 13-    20 
:1 04-  45   1+ 14-    40 
- 05-    30$ 15-    13 
n 06-    11¼ 16-    12 
:2 07-  45   2:gC 17-45, 43   12 
P 08-    14fs  
 
REGISTERS 
n: n–#Adv. Pmts.  i: i  PV: Used  PMT: Pmt. 
FV: 0 
R0: n  R1: Adv. Pmts.  R2: Pmt. 
R3: Loan  R4–R.7: Unused   
 
1.  Key in the program. 
2.  Key in the total number of payments in the lease then press ?0. 
3.  Key in the total number of payments made in advance then press ?1. 
4.  Key in the periodic payment to be received then press ?2. 
5.  Key in the total amount of the loan, then press ?3; then press t to 
obtain the periodic yield. 
6.  For a new case, return to step 2. The values changed from the previous case 
are the only values which need to be re-entered. 
Example 2:
 Using the program, solve for yield using the same information given 
in example 1. Then change the payment to $625 and solve for the yield. 
Keystrokes Display  
60?0 
60.00 Number of payments. 
3?1 
3.00 Number of advance payments. 
600?2 
600.00 Periodic payment.  
						

							156 Section 14: Leasing 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 156 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
25000?3t 
17.33 Annual yield (as a percentage). 
625?2t 
19.48 Annual yield (as a percentage) 
when PMT is increased $25. 
Advance Payments With Residual 
Situations may arise where a transaction has advance payments and a residual 
value (salvage value) at the end of the normal term. 
Solving for Payment 
The following program solves for the periodic payment amount necessary to 
achieve a desired yield. 
KEYSTROKES DISPLAY  KEYSTROKES DISPLAY 
fs  M 14-    15 
fCLEARÎ 00- :n 15-  45  11 
g 01-  43   8:4 16-  45   4 
fCLEARG 02-  42  34- 17-    30 
:0 03-  45   0n 18-    11 
n 04-    111 19-     1 
:1 05-  45   1Þ 20-    16 
¼ 06-    12P 21-    14 
:3 07-  45   3$ 22-    13 
M 08-    15:4 23-  45   4 
$ 09-    13+ 24-    40 
:2 10-  45   2:5 25-  45   5 
+ 11-    40~ 26-    34 
?5 12-  44   5z 27-    10 
0 13-     0fs  
  
						

							 Section 14: Leasing 157 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 157 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
REGISTERS 
n: Used.  i: Interest  PV: Used  PMT: –1. 
FV: Residual 
R0: # Pmts (n)  R1: Interest.  R2: Loan. 
R3: Residual  R4: # Adv. Pmt.  R5: Used  R6–R.6: Unused 
 
1.  Key in the program. 
2.  Key in the total number of payments then press ?0. 
3.  Key in or calculate the periodic interest rate then press ?1. 
4.  Key in the loan amount then press ?2. 
5.  Key in the residual value then press ?3. 
6.  Key in the total number of payments made in advance then press ?4. 
Then press t to obtain the payment amount received by the lessor. 
7.  For a new case, return to step 2. The values changed from the previous case 
are the only values which need to be re-entered. 
Example 1:
 A copier worth $22,000 is to be leased for 48 months. The lessee 
has agreed to make 4 payments in advance, with a purchase option at the end of 
48 months enabling him to buy the copier for 30% of the purchase price. What 
monthly payment is necessary to yield the lessor 15% annually: 
 
Keystrokes Display  
48?0 
  
15\ 
  
12z?1 
1.25 Monthly interest rate. 
22000?2 
  
30b?3 
  
4?4t 
487.29 Monthly payment received by lessor.  
						

							158 Section 14: Leasing 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 158 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 2:
 Using the information from example 1, what would the monthly 
payments be if the lessor desired a yield of 18% annually?
 
Keystrokes Display  
 
487.29 From previous example. 
18\12z 
1.50 Monthly interest rate. 
?1t 
520.81 Monthly payment received by lessor. 
Solving For Yield 
Solving for yield is essentially the same as solving for Internal Rate of Return (IRR). 
The keystrokes are as follows: 
1. Press fCLEARH. 
2.  Key in the amount of the first cash flow then press gJ. This initial amount 
is the difference between the initial loan amount and any payments received 
at closing time. Observe the sign convention: positive for cash received and 
negative for cash paid out. 
3.  Key in the amount of the first cash flow then press gK. Then key in the 
number of times that cash flow occurs then press ga. 
4.  Key in 0gK then the number of advance payments minus one. Then 
press ga. 
5.  Key in the residual then press gK. Then press fL to solve for 
periodic yield. 
Example:
 Equipment worth $5000 is leased for 36 months at $145 per month. 
The lessee has agreed to pay the first and last month’s payments in advance. At 
the end of the lease, the equipment may be purchased for $1500. What is the 
annual yield to the lessor if the equipment is purchased?
 
 
Keystrokes   Display   
fCLEARH 
  
5000Þ\ 
  
145\2 
   
						

							 Section 14: Leasing 159 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 159 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes   Display   
§=gJ 
–4,710.00 Net amount of cash advanced. 
145gK34ga 
34.00 Thirty-four cash flows of $145.00. 
0gK 
0.00 Thirty-fifth cash flow. 
1500gK 
1,500.00 Thirty-sixth cash flow. 
fL12§ 
18.10 Annual yield to lessor.  
						

							 
160 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 160 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
  Section 15 
Savings 
Nominal Rate Converted to Effective Rate 
Given a nominal interest rate and the number of compounding periods per year, 
this keystroke procedure computes the effective annual interest rate. 
1. Press g and fCLEARG. 
2.  Key in the annual nominal rate as a percentage, then press \. 
3.  Key in the number of compounding periods per year, then press nz¼. 
4.  Key in 100 then press Þ\$.  
5. Press M+ to obtain the effective annual interest rate. 
Example 1:
 What is the effective annual interest rate if the annual nominal rate 
of 5
1/4% is compounded quarterly?
 
Keystrokes Display  
g 
  
fCLEARG    
5.25\ 
5.25 Nominal rate. 
4nz¼ 
1.31 Percent quarterly interest rate. 
100Þ\ 
  
$M+ 
5.35 Percent effective interest rate. 
For repeated calculations, the following hp 12c program can be used: 
KEYSTROKES DISPLAY  KEYSTROKES DISPLAY 
fs  0 07-     0 
fCLEARÎ 00- 0 08-     0 
g 01-  43   8Þ 09-    16 
fCLEARG 02-  42  34\ 10-    36 
n 03-    11$ 11-    13 
z 04-    10M 12-    15 
¼ 05-    12+ 13-    40 
1 06-     1fs