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Bond Purchased Between Coupons for the HP-38E/C

This program is Copyright © 1978 by Hewlett-Packard and is used here by permission. This program was originally published in "HP-38E/38C Personal Finance Applications" book. This program was transcribed by Kris Collins.

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.

Overview

A bond is a contract to pay interest, usually semi-annually, at a given rate (coupon), and to pay the principal of the bond at some specified future date.  The value or price of a bond is the present value of the coupon payments plus the present value of the principal or redemption value, at a given interest rate (yield).

In periods of high inflation, bonds may be of great interest to investors, because of their high yields.  Bonds are frequently purchased between coupon dates, making determination of their price and interest quite complicated.

In such cases, the Securities Industry Association has established certain formulae1 to determine their price and yield.  For semi-annual bonds held for more than 6 months, the following HP-38E/38C program evaluates bond price and accrued interest on an Actual/Actual day basis.  For bonds calculated on a 30/360 day basis, two additional program steps are needed.  Insert g R↓ after f change days at steps 36 and 40.

1Standard Securities Calculations Methods; Securities Industry Association; 1973.
 
 

KEY ENTRY
DISPLAY
KEY ENTRY
DISPLAY
g P/R g CLP 00- . 12- 73
f CLEAR FIN 01- 24 32 9 13- 9
RCL 1 02- 22 1 9 14- 9
f INTGR 03- 24 61 9 15- 9
6 04- 6 9 16- 9
. 05- 73 9 17- 9
0 06- 0 9 18- 9
1 07- 1 + 19- 51
g x⇔y 08- 25 5 g GTO 24 20- 25 7 24
g GTO 21 09- 25 7 21 RCL 1 21- 22 1
RCL 1 10- 22 1 6 22- 6
5 11- 5 - 23- 41

 
 

KEY ENTRY
DISPLAY
KEY ENTRY
DISPLAY
STO 6 24- 21 6 RCL 7 41- 22 7
RCL 2 25- 22 2 ÷ 42- 71
n 26- 11 n 43- 11
RCL 3 27- 22 3 0 44- 0
PMT 28- 14 PMT 45- 14
RCL 4 29- 22 4 FV 46- 15
i 30- 12 CHS 47- 32
RCL 5 31- 22 5 RCL n 48- 22 11
FV 32- 15 RCL 3 49- 22 3
PV 33- 13 CHS 50- 32
RCL 6 34- 22 6 × 51- 61
RCL 1 35- 22 1 R/S 52- 74
f Change Days 36- 24 41 - 53- 41
STO 7 37- 21 7 g GTO 00 54- 25 7 00
RCL 6 38- 22 6 g P/R
0 39- 22 0
f Change Days 40- 24 41

 
 

REGISTERS
R0 Settlement R1 Next Coupon R2 # periods R3 Coupon
R4 Yield R5 Redemption R6 Last Coupon R7 Used

 

  1. Key in the program.
  2. Set the Payment switch to END.
  3. Key in the settlement (purchase) date.  (MM.DDYYYY); press STO 0.
  4. Key in the date (MM.DDYYY) of the next coupon; press STO 1.
  5. Key in the total number of coupons which are received; press STO 2.
  6. Key in the amount of the semi-annual coupon; press STO 3.*
  7. Key in the semi-annual yield as a percent; press STO 4.
  8. Key in the redemption value; press STO 5.*
  9. Press R/S to obtain the amount of accrued interest (a share of the next coupon to which the seller is entitled).
  10. Press R/S to determine the price of the bond.

Note: If a coupon is received on the last day of the month (i.e., October 31), an error condition may result.  This happens because the count-back routine determines the last coupon date to be exactly 6 months earlier (i.e., April 31), and this may be an illegal date.

Example:

Given the following U.S. Treasury Bond, find its price:

Settlement date January 3, 1977; maturity date December 14, 1990 (28 coupon periods); next coupon date June 14, 1977; coupon rate 4.75%; yield 5%.

Keystrokes:

Begin → End

1.031977 STO 0 1.03 Settlement date
6.141977 STO 1 6.14 Next coupon date
28 STO 2 28.00 Total number of coupons
4.75 ENTER↑ 2 ÷ STO 3 2.38 Semi-annual coupon
5 ENTER↑ 2 ÷ STO 4 2.50 Semi-annual yield
100 STO 5 100.00 Redemption value is not specified and is assumed to be 100
R/S -0.26 Accrued interest
R/S -97.51 Purchase price

To find bond yield, an iteration (trial and error) approach may be used with the bond price program.  The user inputs successive "guesses" at the periodic yield into register 4 and solves for price.  If the calculated price is the actual price paid, the yield is in register 4.  If not, adjust the yield and repeat the procedure until the desired accuracy is obtained.

*Positive for cash received; negative for cash paid out.

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