Using Financial Functions in Excel or a TI-83 to Solve TVM Problems

This explains how to use the Excel Finite Functions to solve Time Value of Money Problems related to annuities and bonds

(Press <F5> to run Slide Show)

Note: This PowerPoint presentation is under construction. Currently, this only shows how to do this in Excel and we intend to make improvements in that presentation. Then we will add slides to explain how to use the TI-83 to do the same.

RATE= 1%NPER= 120PMT= $100

PV= ?

FV= 0

Problem: Consider an annuity where you are paid $100 at the end of each year for ten years. Assuming that we discount at a rate of 12%, compounded monthly, determine the present value of this annuity.

If we determined this using the annuity formula, we would have determined this as shown below:

nr)1(

11

r

C annuity)y PV(ordinar

05.6970$697.000,1001.1

11

01.

100120

01.%112

%12r

12010*12 n

How to use the annuity formula to determine the PV of an ordinary annuity.

RATE= 1%NPER= 120PMT= $100

PV= ?

FV= 0

Problem: Consider an annuity where you are paid $100 at the end of each year for ten years. Assuming that we discount at a rate of 12%, compounded monthly, determine the present value of this annuity.

To determine this in Excel, click on the paste function symbol.

How to use Excel Spreadsheet to determine the PV of an ordinary annuity

This will open the Insert Function Window.

Next, click to select the Financial category.

Then click on the PV function

Finally, click on the OK button.

This then brings up the PV function window.

First, type in the rate per compound period.

1%120

100Second, type in the number of payments.Third, type in the amount of each payment.Either leave FV blank or type

in 0 since there is no balloon-type of payment at the end of the annuity.

Either leave type blank or type in 1 since this is an ordinary annuity as opposed to an annuity due.

Excel Shows the answer as a negative number since that is the cash outlay you would incur now in order to be able to buy the annuity.

If you then click on OK, Excel will put the result and the formula in the current cell in the Excel spreadsheet.

This is the function.

This shows the result in the current cell.

We will do the example again, except we will put in cell references instead of numbers. Also, we will put the payment as a negative number instead of positive. This will make the PV a positive number.

Step 1: Enter the interest rate.Step 2: Enter the number of payment periods (Nper).Step 3: Enter the amount of the annuity payment.

We do not have a FV at this point so we leave FV blank or enter a 0.

Answer in positive terms

The screen shown here is where we need to begin. This is where we input our variables to solve for the PV of an Annuity.To arrive at this screen:

This opens the FINANCE functions.

To enter the above screen, we choose: 1:TVM Solver… by highlighting it and pressing enter. We can now input our variables.

Things to note:

1. Be sure to enter your interest rate as a whole number.2. Make sure PV= and FV= are set at 0.3. Make sure P/Y= and C/Y= are set at 1. 4. Select the proper Annuity. For this problem, END should be highlighted.

1. Press the “2nd” button

2. Press the “x-1” button

Question: To solve for the PV of an Annuity, what variables do we need?

2. The corresponding interest rate (I%).

3. The amount of the payment being made (PMT).

Answer:1. The number of payments made (N).

After you have entered your N, I%, and PMT:

2. Press the “x-1” button

1. Press the “2nd” button

This will bring you back to the FINANCE functions menu.

3. On the menu, select: 4: tvm_PV and press enter.

4. Press enter once more to get the PV of an annuity.

SHORTCUT:If all your defaults are set (N=0, I%=0, PV=0, PMT=0, FV=0, P/Y=1, C/Y=1, PMT: END) Then you can skip the TVM Solver… steps and go right into the tvm_PV function.

When you get tvm_PV on your screen you can enter the N, I% and PMT in parentheses and press enter to get the same answer.

Example: tvm_PV(120, 1, 100)

This is how it would look on your TI-83 screen.

RATE= 1%NPER= 120PMT= $100

PV= ?

FV= 0

Problem: Consider an annuity where you are paid $100 at the end of each year for ten years. Assuming that we discount at a rate of 12%, compounded monthly, determine the future value of this annuity.

If we determined this using the annuity formula, we would have determined this as shown below:

1)1(r

C annuity)y FV(ordinar nr

87.003,23$30.2000,101)01.1(01.

100 120 01.%112

%12r

12010*12 n

How to use the annuity formula to determine the FV of an ordinary annuity.

Problem: Consider an annuity where you are paid $100 at the end of each year for ten years. Assuming that we discount at a rate of 12%, compounded monthly, determine the future value of this annuity.

To determine this in Excel, click on the paste function symbol.

How to use Excel Spreadsheet to determine the FV of an ordinary annuity

Select the FV function

Click OK

Select the Financial Category

This will open the FV function window.

This will open the Insert Function Window

Determining Future Value

Step 1: Enter the interest rate.Step 2: Enter the number of payment periods (Nper).Step 3: Enter the amount of the annuity payment.

We do not have a PV at this point so we leave PV blank or enter a 0.

Answer

Same drill as PV...

Determining Payment in PV Problem

Select the Financial Category

Highlight the PMT function

Click OK

Determining Payment in PV Problem

Enter the interest rate

Enter the number of periods

We calculated the PV in our 1st example. If you are not given a PV then you will have to calculate like in the 1st example because PV is required to find the payment.

Answer

Determining Payment in FV Problem

Determining # Payments in FV Problem

Determining # Payments in PV Problem

Determining # Payments in FV Problem

Determining Rate in PV Problem

To get the stated annual rate, you would need to multiply the 1% by the number of compound periods per year:

%1212*%1

Determining Rate in PV Problem

Determining Rate in FV Problem

PV(annuity Due)

Problem: Consider an annuity where you are paid $100 at the beginning of each year for ten years. Assuming that we discount at a rate of 12%, compounded monthly, determine the present value of this annuity.

PV(bond)

nn r

F

rr

CbondPV

)1()1(

11)(

2828 )04.1(

1000

)04.1(

11

04.

30)(

bondPV

Problem: Consider a $1000 bond with a 6% coupon rate, paid semiannually that matures 14 years from now. Assuming that similar bonds now pay 8% interest, compounded semiannually, determine what should be the value of this bond today.

= 499.89 + 333.48 = $833.37

PV(bond)

Yield to Maturity

4%*2 coupon periods per year = 8%

Determine # periods in Bond Problem

Internal Rate of Return (IRR)