The Museum of HP Calculators

# Discounted Cash Flow Analysis Net Present Value for the HP-67

This program is Copyright © 1976 by Hewlett-Packard and is used here by permission. This program was originally published in the HP-67 Business Decisions Pac.

This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

 Discounted Cash Flow Analysis Net Present Value Shift P? Label Inv i (%) # CF->NPV ->n Key A B C D E

## Overview

Assuming a minimum desired yield (cost of capital, discount rate), this program finds the present value of the future cash flows generated by the investment and subtracts the initial investment from this amount. If the final net present value is a positive value, the investment exceeds the profit objectives assumed. If the final net present value is a negative value, then the investment is not profitable to the extent of the desired yield. If the net present value is zero, the investment meets the profit objectives.

The function associated with the C key (#) is designed to accommodate those situations where a series of the cash flows are equal. You enter the number of times these equal periodic cash flows occur with C, and then the amount only once with D. The program automatically assumes 1 for #. If the cash flow occurs only once, there is no need to enter anything for #.

Zero must be entered for all periods with no cash flow. When a cash flow other than the initial investment is an outlay (additional investment, loss, etc.) the value must be entered as a negative number with CHS

Cash flows are assumed to occur at the end of cash flow periods.

This program can also be used to find the present value of a series of irregular cash flows that cannot be accommodated by the Direct Reduction Loans program by simply entering zero as the initial investment.

An option is provided to print the initial investment and the NPV after each cash flow. Pressing f E sets and clears the print flag. Successive use of f E will alternately display 1.00 and 0.00, indicating that the print mode is on or off respectively

## Instructions

 Step Instructions Input Data/Units Keys Output Data/Units 1 Load side 1. 2 Optional: Select print/pause mode. f E 1.00 or 0.00 3 Key in: Initial investment amount INV A INV Periodic interest (discount) rate i (%) B i (%) 4 Key in the number of equal cash flows if greater than 1. # C # 5 Key in cash flow amount(s) and calculate net present value. CF D NPV 6 Optional: Display total number of cash flows entered so far. E n 7 For next cash flow(s) go to step 4. 8 For a new case go to step 2.

## Example 1

An investor has an opportunity to purchase a piece of property for \$70,000. If the going rate of return on this type of investment is 13.75%, and the after-tax cash flows are forecast as follows, should the investor purchase the property?

```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           71,000 (property sold in 10th year)
```
```Keystrokes                     Outputs
70000 A 13.75 B
14000 D                       -57692.31 (NPV after 1 cash flow)
11000 D                       -49190.92 (NPV after 2 cash flows)
3 C 10000 D                   -31172.57 (NPV after 5 cash flows)
9100 D                        -26971.76 (NPV after 6 cash flows)
2 C 9000 D                    -20108.39 (NPV after 8 cash flows)
E                                  8.00 (checking that we've entered
8 periods cash flows so far)
4500 D                        -18696.99 (NPV after 9 cash flows)
71000 D                          879.93 (NPV after 10 cash flows)
```

Since the final NPV is positive, the investment meets the profit objectives.

## Example 2

The Cooper Company needs a new photocopier and is considering leasing the equipment as an alternative to buying. The end-of-the-year net cash 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               Net Cash Cost
1                   \$1,310
2                    1,310
3                    1,310
4                    1,310
5                    1,310
-------------
Total Net Cash Cost        \$6,550
```

Looking at total cost, leasing appears to be less. But, purchasing costs less the first two years. Mr. Cooper knows that he can make a 15% return on every dollar he puts in the business; the sooner he can reinvest money, the sooner he earns 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 option should he choose?

```Keystrokes                     Outputs
PURCHASE
0 A 15 B 533 D 948 D
1375 D 1815 D 2270 D            4250.71

LEASE
0 A 5 C 1310 D                  4391.32
```

Leasing has a present value cost of \$4391.32, while purchasing has a present value cost of \$4250.71. Since these are both expense items, the lowest present value is the most desirable. So, in this case, purchase is the least costly alternative.

## The Program

```LINE  KEYS
001  *LBL A     -NPV->RA
002   CHS       0->R9
003   STO A     1->RC
004   0
005   STO 9
006   1
007   STO C
008   RCL A
009   CHS
010   GSB 9
011   RTN
012  *LBL B     i/100->R8
013   EEX
014   2
015   ÷
016   STO B
017   LST X
018   x
019   RTN
020  *LBL C     #->RC
021   STO C
022   RTN
023  *LBL D
024   STO D
025   1
026   RCL B
027   +         Calculate present value of series
028   RCL C
029   STO + 9
030   YX
031   STO E
032   RCL A
033   x
034   RCL E
035   1
036   -
037   RCL B
038   ÷
039   RCL D
040   x
041   +
042   STO A
043   1
044   RCL B
045   +
046   RCL 9
047   YX
048   ÷
049   1
050   STO C
051   roll dn   Reset n to 1
052   GSB 9
053   RTN
054  *LBL E
055   RCL 9     Recall n
056   RTN
057  *LBL e     Print option
058   F0?
059   GTO 1
060   SF 0
061   1
062   RTN
063  *LBL 1
064   0
065   CF 0
066   RTN
067  *LBL 9
068   F0?
069   GTO 2
070   R/S
071   RTN
072  *LBL 2
073   PRTX
074   R/S
```

## Register Use

```R9  sum n
A   NPV
B   i/100
C   #
D   CF
E   (1+i)n
```