(11C) Purchase or Lease

09252018, 10:24 AM
(This post was last modified: 09262018 01:39 AM by Gamo.)
Post: #1




(11C) Purchase or Lease
This program is the "Discount Cash Flow Analysis" to find NPV or
Net Present Value. This program was from the HP11C Solutions Handbook I found this interesting that the example shown two set of data, one for Purchase and another for Lease. This program help you to choose which one is the best choice. Procedure: [A] Initial Investment [B] Periodic Interest [C] Key in the number of equal cash flow if greater than 1 [D] Net Present Value [E] Review # of Cash Flow Program: Code:
Registers R0: NPV R1: i / 100 R2: # of equal CF R3: CF R4: (1+n)^n R5: Σn R6R9: Unused Example: Company needs a new photocopier and is considering leasing the equipment as an alternative to buying. The end of the year net cost of each option is: Purchase Year Net Cash Cost 1 533 2 948 3 1,375 4 1,815 5 2,270 Total Net Cash Cost 6,941  Lease Year 1 1,310 2 1,310 3 1,310 4 1,310 5 1,310 Total Net Cash Cost 6,550  Looking at the total cost, leasing appears to be less, But purchasing costs less the first two years. He known that he can make a 15% return on every dollar he puts in the business; the sooner he can reinvent money, the sooner he earn 15%. Therefore, he decides to consider the timing of the costs, discounting the cash flows at 15% to find the present value of the alternatives. Which options should he choose?  Purchase: 0 [A] 15 [B] 533 [D] 948 [D] display 1,180.30 1375 [D] 1815 [D] display 3,122.12 2270 [D] answer 4,250.71 Lease: 0 [A] 5 [C] 1310 [D] answer 4,391.32  Leasing has a present value of 4391.32, while purchasing has a present value of 4250.71. Since these are both expense items, the lowest present value is the most desirable. So, in this case, purchasing is the least costly alternative.  Gamo 

09252018, 01:28 PM
Post: #2




RE: (11C) Purchase or Lease
(09252018 10:24 AM)Gamo Wrote: Company needs a new photocopier and is considering leasing the equipment Is the numbers reversed ? Normally it cost more (mainly depreciation) at the beginning I would use the copier for 1 year, sell it, and buy another If numbers are allowed to input backwards, NPV can be much simpler, with Horner's rule: Discount rate = 1.15 (stored in memory 0): 2270 RCL0 / 1815 + RCL0 / 1375 + RCL0 / 948 + RCL0 / 533 + RCL0 / We get the same NPV of 4250.71, without using X^Y 

09252018, 04:27 PM
(This post was last modified: 09252018 04:29 PM by Dieter.)
Post: #3




RE: (11C) Purchase or Lease
(09252018 10:24 AM)Gamo Wrote: This program is the "Discount Cash Flow Analysis" to find NPV or Yes, it's a regular NPV program. Not a special program to assess buyorlease decisions. Maybe you should explain how the program is used: what exactly do the A, B, C and D keys do and what is the input and output? (09252018 01:28 PM)Albert Chan Wrote: If numbers are allowed to input backwards, NPV can be much simpler, with Horner's rule: I assume that "RCL–0" does not really mean RCL–0 (recall arithmetic, not supported by the 11C) but simply "RCL 0". ;) Yes, the Horner method works nicely here, but why do you want to do it this complicated? 1,15 [1/x] [ENTER] [ENTER] [ENTER] 2270 [x] 1815 [+] [x] 1375 [+] [x] 948 [+] [x] 533 [+] [x] => 4250,71 Good old RPN practice. ;) (09252018 01:28 PM)Albert Chan Wrote: We get the same NPV of 4250.71, without using X^Y Even without RCL 0 and less keystrokes. ;) Dieter 

09252018, 06:36 PM
Post: #4




RE: (11C) Purchase or Lease
(09252018 04:27 PM)Dieter Wrote: Yes, the Horner method works nicely here, but why do you want to do it this complicated? With this, there is no need for a cash flow program I use RCL 0 because of "/" Multiply flipped rate (rounded) might accumulate too much errors. There is no reason to inisist for NPV, it is more accurate to do FV. For purchase / lease decisions, FV comparison is just as good. With FV, reversed cash flow input is not needed. 1.15 [ENTER] [ENTER] [ENTER] 533 [x] 948 [+] [x] 1375 [+] [x] 1815 [+] [x] 2270 [+] => FV (year 5) = 8549.70 If NPV is needed, just "pull back" numbers to Year 0: [X<>Y] 5 [Y^X] [/] => NPV (year 0) = 4250.71 

09262018, 02:11 AM
(This post was last modified: 09262018 02:26 AM by Gamo.)
Post: #5




RE: (11C) Purchase or Lease
Program information is updated.
Added LBL E for review of how many Cash Flow This program is very compact for NPV solver and easy to use. Press A for initial investment Press B for interest in percent Press C for number of same amount of continue CF Press D for NPV Press E for review of how many CF Gamo 

09262018, 05:40 AM
Post: #6




RE: (11C) Purchase or Lease
(09262018 02:11 AM)Gamo Wrote: Press A for initial investment You forget an essential point: Where and how to enter the cash flows. ;) As far as I can see you enter the CF, press [D] and the NPV for all cash flows up to that one is returned. So it's: Enter initial investment, press [A] Enter interest rate in percent, press [B] If there is a number of continuous identical cash flows, enter this number and press [C] (else 1 single CF is assumed) Enter cash flow, press [D], see NPV up to that period Continue with all other cash flows. But please correct me if I'm wrong. Dieter Dieter 

09262018, 07:37 AM
(This post was last modified: 09262018 09:35 AM by Gamo.)
Post: #7




RE: (11C) Purchase or Lease
Dieter
Yes that correct. Here is another example from 12C Owner's Handbook on page 62 This example is not about purchase or lease matter. Below example show how to input data. An investor has an opportunity to purchase a piece of property for 79,000; and he would like 13.5% return. He expects to be able to sell it after 10 years for 100,000 and anticipates the yearly cash flows in the table below: Year Cash Flow 1 14,000 2 11,000 3 10,000 4 10,000 5 10,000 6 9,100 7 9,000 8 9,000 9 4,500 10 100,000 Keystrokes: FIX 2 79000 [CHS] [A] display 79000.00 // Initial Investment 13.5 [B] display 13.50 // Interest 14000 [D] display 66665.20 11000 [D] display 58126.32 3 [C] 10000 [D] display 39952.08 // 3 [C] is three continue identical cash flows 9100 [D] display 35695.45 2 [C] 9000 [D] display 28718.37 // 2[C] is two continue identical cash flows 4500 [D] display 27278.75 100000 [D] display 907.77 // Last cash flow show final result of NPV [E] display 10 // check for how many cash flows this case is 10 Cash Flows NPV is 907.77 Since NPV is positive, the investment would increase the financial value of the investor's assets by 907.77 Gamo 

09262018, 12:53 PM
Post: #8




RE: (11C) Purchase or Lease
(09262018 07:37 AM)Gamo Wrote: An investor has an opportunity to purchase a piece of property for 79,000; What is the actual NPV (with all digits) ? Exact NPV (10 places) should be 907.76893 37698 HP12C, Horner's for NPV (cashflow input in reverse) Multiply flipped rate => 907.76891 00 Divide discount rate => 907.76893 00 HP12C, Horner's for FV, then back to NPV => 907.76892 51 HP12C buildin CFj/Nj code => 907.76893 37 ... Amazingly Good How does HP12C code get it so close ? My guess is calculations all done in 13 internal digits, only 1 rounding for the NPV result ... 

09262018, 06:59 PM
Post: #9




RE: (11C) Purchase or Lease
(09262018 12:53 PM)Albert Chan Wrote: HP12C, Horner's for NPV (cashflow input in reverse) Hey, that's a difference of 0,002 Cents!!!!1111eleven!!! (09262018 12:53 PM)Albert Chan Wrote: HP12C, Horner's for FV, then back to NPV => 907.76892 51 Simple. Since 1976 most HPs use three additional guard digits for their internal functions. So the 10digit 12C internally works with 13 digits. Only this way the usual 10digit accuracy for scientific or financial functions can be achieved. Well, mostly, but not always. Try the infamous 3^{201} example on a regular 10digit HP. ;) (09262018 12:53 PM)Albert Chan Wrote: My guess is calculations all done in 13 internal digits, only 1 rounding for the NPV result ... That's the main reason. But there is more. As far as I remember the financial calculators have special internal functions that evaluate (1+i)^{n} and (1+i)^{n}–1 with higher accuracy. I assume this means they have something like ln(1+x) and e^{x}–1 implemented so that these expressions can be accurately calculated even for small interest rates. There is a nice example in the HP15C Advanced Functions Handbook that shows what happens when these expressions are evaluated with standard functions. Dieter 

09272018, 01:23 AM
Post: #10




RE: (11C) Purchase or Lease
Albert Chan
Just put this program on a real HP11C The full digits answer NPV answer on 11C is 907.7689308 Answer on 12C Owner's Handbook is 907.77 I think for businesses two digits is more than enough. Gamo 

09302018, 05:45 PM
(This post was last modified: 09302018 05:49 PM by Dieter.)
Post: #11




RE: (11C) Purchase or Lease
(09252018 10:24 AM)Gamo Wrote: This program is the "Discount Cash Flow Analysis" to find NPV or For the record: here is a slightly modified program. The math has been streamlined a bit, the current NPV value can always be recalled with a simple RCL 0, the user may enter CF_{0} and the interest rate in any order, and finally only R0...R3 are used. Code: 001 LBL A Registers: R0: accumulated NPV R1: i%/100 R2: number of consecutive identical CFs (default: 1) R3: total number of periods Usage: Enter CF_{0} (with correct sign) and press [A] Enter interest rate and press [B] For all cash flows: Optional: Enter CF frequency and press [C] Enter CF (with correct sign) and press [D] => NPV for all cash flows up to this one Press [X⇄Y] to see the number of periods Example: –10000 [A] 3,5 [B] 2000 [D] => –8067,63 3 [C] 3000 [D] => 53,05 1000 [D] => 895,03 [X⇄Y] 5 So after 5 years the NPV is 895,03. Dieter 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)