# What's It Worth? Bond Calculations Using the HP 95LX

### By Ralph Butler

Consider the following problem: A firm has a bond with an annual coupon rate of 8%, face value of \$1000, annual yield to maturity of 10%, and makes semi-annual payments. What is the current selling price of the bond?

It's an easy problem to solve with a number of HP calculators, including the HP 12C, 17BII, and the 19BII. You can also solve this problem using the 95LX's HP CALC "Time Value of Money" (TVM) function or the Lotus 123 _CFLOW.WK1 spreadsheet included with the HP 95LX.

Determining the Selling Price of a Bond using HP CALC

The selling price of a bond in this example is simply the present value (PV) of all expected future yields of the bond. Since bonds usually make periodic interest payments through the life of the bond and make a lump sum payment equal to the face value of the bond at maturity, this problem can be stated as:

Selling Price = PV of interest payments + PV of maturity value.

On the HP 95LX, press (HPCALC) (MENU) TVM to get to the TVM screen. Next, enter the problem data as indicated in the next column below the graphic.

Number of periods. . . . . N = 20

(10 years of semiannual payments)

Annual interest. . . . . I%YR = 10

(Current YTM % not face value %)

Present value. . . . . PV = 0

(HP CALC will solve for this value)

Payment. . . . . PMT = 40

(Face value of bond x face value %)

Future value. . . . . FV = 0

(Not used in this calculation)

Payments per year. . . . . P/YR = 2

(Semiannual payments)

Begin/End mode. . . . . B/E = END

(Payments made at end of period)

Press (F8) to calculate PV, and you get -498.49 (rounded) or \$498.49. This is the PV of the interest payments half of the solution.

For the PV of the maturity value enter the following values:

Number of periods. . . . . N = 20

(10 years of semiannual payments)

Annual interest. . . . . I%YR = 10

(Current YTM % not face value %)

Present value. . . . . PV = 0

(HPCALC will solve for this value)

Payment. . . . . PMT = 0

Future value. . . . . FV = 1000

(Face value of bond)

Payments per year. . . . . P/YR = 2

(Semiannual payments)

Begin/End mode. . . . . B/E = END

(Payments made at end of period)

Press (F8) to calculate PV, -376.89 (rounded) or \$376.89. This is the PV of maturity value half of the solution.

Therefore, the current selling price of the bond is the sum of the two present value calculations = \$498.49 + \$376.89 = \$875.38 (rounded).

Determining the Selling Price Using Lotus _CFLOW.WK1 Spreadsheet

This bond problem can be solved in a single step using the _CFLOW.WK1 spreadsheet included with the HP 95LX. Press (123) (MENU) File Retrieve, highlight C:\_CFLOW.WK1 and press (ENTER). Next, press (ALT)-E Yes (ENTER) to erase the data in the worksheet.

Enter the problem data as follows. At t=0 (cell B44), enter 0 and press (<DownArrow>). Then at t=1 (cell B45), press (ALT)-G 40 (ENTER) 20 (ENTER) to copy the \$40 interest payment for 20 periods. Next, add 1000 to the t=20 (cell B64) payment to represent the maturity value (t=20 now equals 1040).

To calculate the present value press (ALT)-N, and after a couple of seconds, NPV = 489.18617681 appears. We didn't get the right answer because the default interest value is 10% and we need to use the semiannual period interest rate which is 5%. Press 5 (ENTER) and the correct answer appears (NPV = 875.37789657) (rounded to 875.38).

I find it a lot easier to use the _CFLOW.WK1 spreadsheet to solve this type of bond problem.

You Try It!

Now, consider the same bond except that the current selling price is \$1055. What is the annual yield to maturity? This is left as an exercise for the reader or perhaps the subject of a future article.