Fincalc - Financial Calculator Help PDF

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Financial Calculator Help...

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USING YOUR FINANCIAL CALCULATOR’S TVM MENUS Getting started: The first step in using a financial calculator is to make sure that all of the settings in the calculator are correct. Many people purchase a financial calculator and try to solve timevalue-of-money problems, only to find out that the calculator is not cooperating (i.e., you cannot convince the blasted thing to give you the correct answer). There are two common adjustments that should resolve such problems. They are as follows: 1) First, make sure that your payments are set to occur at the end of the period, rather than the beginning. Keep in mind that unless otherwise specified, we will assume that all payments occur at the end of the year. If your payments are set to occur at the beginning of the period, your answers will always be a little bit off. Words of advice: It is easy to manipulate the value of an ordinary annuity in order to get the value of a comparable annuity due. Keep in mind that since all payments are effectively advanced one period, the value of an annuity due is simply the value of an ordinary annuity (for the same # of periods, etc.) multiplied by (1+r). Since the conversion to beginning of the period payments is this simple, set the payments to occur at the end of the period and don’t ever mess with it again. 2) Second, make sure that the number of payments is set at 1 per period. Often a financial calculator will have a default setting of 12 payments per period, so you will have to reset this to 1. Upon setting the number of payments to 1 per period, you will need to make the appropriate adjustments to reflect the amount of compounding and the number of periods on your own. However, the conversion is quite simple. If you have the Sharp EL-733A, you need not worry about this problem since the calculator is fixed at 1 payment per period. However, if you have a Hewlett Packard or a Texas Instruments calculator, you may need to make the following adjustment to set the payments to 1 per period. HP 10B: When checking the compounding frequency on the 10B, press the [ ] key, then press and briefly hold the input key. This clears the TVM registers and shows the compounding frequency. Often times, this frequency will come from the factory set at “12 P_YR”. To change this number to 1, enter 1 and then press [ ] {P/YR}. To make sure that the change was successful, shut of the calculator, turn it back on and confirm that the payments remain at 1 per year. BAII-PLUS: You need to set both the payments per year and the compounding frequency to 1. These frequencies are often set at 12 per year from the start. To change these settings to 1, do the following: press [2nd] {P/Y} 1 [enter], then press [ ] 1 [enter]. Pressing [2nd] {quit} will return you to the standard calculator mode.

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Additional advice: Once you get the settings at 1 per period, don’t mess with them. You just need to remember that when you input the number of periods and the interest rate into TVM menus, your entries must be on the appropriate basis (in terms of the number of periods and the compounding basis). The adjustments are simply those you would be making in order to use the TVM formulas. Also, when you start a new problem, make sure you clear the TVM registers! Failure to do so will lead to wrong answers.

Solving Time-Value-of Money Problems with the basic TVM menus: The most important aspect of solving TVM problems is conceptualizing the problem and identifying relevant cash flows. The best way to develop these skills is to practice. After you have mastered how to “set up” TVM problems, the advantages of a financial calculator will become apparent. However, if you fail to correctly identify cash flows, your calculator is of little value (Garbage in => Garbage out). Entering cash flows: Frequently, owner’s manuals for financial calculators advise users to enter present values as negative numbers so that when solving for payments or future values, those numbers will come out as positive. While this method works fine with only two basic cash flow types, it can lead to problems in situations involving all three cash flow types (PV, PMT, and FV). To avoid making mistakes, it is best to sign all cash flows from your perspective. That is, if you are paying money out -- you will sign that cash flow as a negative. If you are receiving the cash flow, you will sign that cash flow as a positive. The following examples will illustrate this point. Example 1: A basic PV to FV lump sum case Suppose you borrow $5000 at 14% interest compounded semiannually and you are to repay the loan with a lump sum payment in 5 years. What is the amount of the payment? --Your entries would have to reflect semiannual compounding in this case, so you would need to divide the interest rate by 2 => 14%/2 = 7%, and then multiply the number of periods by 2 => 5*2 = 10 periods. Now input the appropriate values in the TVM menu as follows (clear the existing registers first): PV = 5000 , I% = 7 , N = 10. On the Sharp and the TI models, you will have to press [comp] or [cpt] and then [FV]. With the HP, you should get the answer by just pressing [FV]. When you solve for the FV, the number should come out as: -$9,835.76. (In this case, the negative number reflects the fact that you would be paying out that amount after 5 years.)

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Example 2: A basic consumer loan Suppose you are to get a car loan totaling $15,000. The loan has a stated rate of 10% and you are to make 5 years of monthly payments (Note: the monthly payments here imply monthly compounding). How much are the payments? => The inputs needed to solve this problem are as follows: PV = 15,000 (you are receiving the proceeds from the loan) I% = 10/12 = 0.833 (for more accurate answers, enter information such as this in as the fraction (10/12) rather than a decimal when the decimal is not a precise number). N = (5*12) = 60 When you now solve for the payment, you should get an answer of -$318.71. (The negative number indicates that you would be paying this amount each month.) Further wisdom: Each time you use your financial calculator, make sure the settings are correct (this is especially important for exams). Double check to make sure your answers are correct by working simple problems that you know the answers to already. Finally, use common sense! Look at all answers to see if they appear reasonable.

Solving for bond prices and Yield to Maturity (YTM) using TVM menus: Solving for a bond’s price: Most bonds pay coupons (an annuity cash flow), which vary across bonds according to the coupon rate and then a lump sum (usually $1,000) when the bond matures. The value of the bond (its market price) is simply the present value of these cash flows when discounted by the appropriate rate (the bond’s YTM). In mathematical terms: => Bond price = $Coupon * PVIFA(YTM%,t) 1 1 (1 YTM) t => Bond price = $Coupon * [ ] YTM number of periods until the bond matures.

+

$1,000 * PVIF(YTM%,t)

+

$1,000 , where t = the 1 ( YTM ) t

If we know the bond’s YTM, we can simply solve the above-listed equations or use financial tables to determine the bond’s market price. However, if we know a bond’s price and are asked to solve for the YTM, this is a trial-and-error process that can become rather tedious without a financial calculator. The following examples show how simple it actually is to solve bond problems with a financial calculator. All examples are based on annual coupon payments. If a bond pays semi-annual coupons, you will have to make the appropriate adjustments to both the coupons and the YTM.

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Example 3: Solving for a bond’s price

A bond with a face value of $1,000 has an annual coupon rate of 9% (which implies an annual coupon of $90) and has 10 years till maturity. If the YTM on the bond is 11%, what is the market price of the bond? => The bond produces cash flows of $90 per year for the next ten years and also pays a lump sum of $1,000 at the end of the 10 years. At an 11% YTM, you can solve for the bond’s current price as follows: 1 Bond price

=

$90 * [

1 (111 . ) 10 ] .11

+

$1,000 (111 . )10

=

$882.22

Alternatively, you can solve for the bond price using the TVM menus on a financial calculator! Simply enter the following: FV = $1,000 PMT = $90 I% = 11 N = 10 => Now, when you solve for the PV, you get an answer of -$882.22. (The negative indicates that you must pay this amount in order to receive the later cash inflows.)

Solving for a bond’s YTM: As shown mathematically above, you can solve for a bond’s price rather easily by applying the appropriate TVM formulas. However, what if you have the bond’s price, years till maturity, and its coupon rate and you are asked to solve for the YTM? As discussed in class, since there are two types of cash flows (both an annuity and a lump sum) and the YTM appears in both the numerator and denominator of the PVIFA formula, solving for the YTM is a trial-and-error process. While you can use financial tables and common sense to eventually produce the answer, your calculator can solve this problem rather easily. Refer to the following example. Example 4: Solving for a bond’s YTM

A bond has a face value of $1,000, a coupon rate of 5%, and 15 years till maturity. The 5% coupon payments are made on an annual basis. If the market price of the bond is $850, what is its YTM?

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The mathematical set up of this problem would be as follows: 1 => Bond price = $850 =

$50*[

1 15 (1 YTM) ] YTM

+

$1,000 (1 YTM )15

=> Solve on your calculator with the following entries (after clearing the TVM menu). FV = $1,000 PMT = $50 N = 15 PV = -$850 (you will need to pay for the bond to receive its cash flows) Now, when you solve for I%, your calculator should come up with @6.61%.

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