Ch.7 quiz
Calculate present value PV = FV/(1 + r)n 0 1 2 3 4 5Years $1,762.34 at 12% interest PV = ?
1,001.33
Calculate future value: FV = Principal (1 + r )n, 0 1 2 3 4 5Years $1,000 at 12% interest FV = ?
1,760
LOAN AMORTIZATION SCHEDULE
Preparing a loan amortization schedule that includes years, payment, principal, interest, and balance is easy to do using your calculator. Using a three-year loan as an example, here are the steps involved: Calculate the interest amount: $100,000 10% $10,000 Calculate the principal paid: Payment interest $40,211.48 $10,000 $30,211.48 Calculate the balance: Balance from last payment principal $100,000 $30,211.48 $69,788.52 YEAR 2 (REPEAT STEPS) Calculate the interest amount $69,788.52 10% $6,978.55 Calculate the principal paid: Payment interest $40,211.48 $6,978.85 $33,232.63 Calculate the balance: Balance from last payment principal $69788.52 $33,232.63 $36,555,89 YEAR 3 (REPEAT STEPS) Calculate the interest amount $36,555.89 10% $3,655.59 Calculate the principal paid: Payment interest $40,211.48 $3,655.59 $36,555.89 Calculate the balance: Balance from last payment principal $36,555.89 $36,555.89 $0, as it should be, as this is the end of the loan The second level of your business calculator makes it even easier to prepare an amortization schedule. Above the PV button you will see the word Amort. Illustration 7-16 shows how an amortization schedule can be generated.
Calculating Time Value of Money
The analysis of time value of money has changed dramatically over time. Years ago, complicated mathematical formulas were used to analyze financial transactions. More recently, shorter for- mulas using interest tables were developed. Over the last twenty years, the business calculator has become the most popular method of analyzing investment opportunities. Computer spread- sheets such as Lotus and Excel have also become popular, as they offer special functions to make financial modeling easier. Instead of using long algorithms, an Excel spreadsheet's function wizard assists the user, who simply selects the variables required to perform the investment analysis. This section of the chapter presents time value of money calculations using a business calculator and a computer spreadsheet. While the Texas Instrument BAII Plus business calcu- lator and Microsoft's Excel are featured, other business calculators and computer spreadsheets are available in the marketplace. While the operation of all business calculators and computer spreadsheets is not exactly the same, each is similar enough for you to understand and calculate using your particular business calculator and computer spreadsheet.
Market Value
The concept of market value is an extension of the time value of money concept. An asset's market value is deemed to be the sum of the future cash flow it is likely to generate over its life. Market value takes the following into consideration: The amount of the cash flow The timing of the cash flow The risk of the cash flow not being generated How the cash-flowing asset is to be financed In TVM terms, market value is the present value of the asset.
PRESENT VALUE OF A SINGLE SUM
The earlier scenario can also be considered from the present value perspective. The timeline is much the same, except that now the future value is known and you need to calculate how much the money to be received at the end of five years is worth today: |————|————|————|————|————| 0 1 2 3 4 5YearsPV=? $1,762.34 at 12% interest In this example, the value of the money at the end of five years is $1,762.34 and the market rate of interest is 12%. Your task is to calculate how much the $1,762.34 is worth today—that is, how much you would need to invest today at a 12% rate of interest to have $1,762.34 in five years. To see how to calculate the present value using the formula and table method, please take a look at Illustration 7-3. Again, it is more practical and accurate to perform these calculations using a business calculator or a spreadsheet such as Excel. The steps to accomplish this are listed in Illustration 7-4.
RISK OF NOT RECEIVING THE PROJECTED CASH FLOW
The final factor that impacts an asset's present or market value is risk. Consider the expression ''The greater the risk, the greater the reward.'' Translated into time value of money terms, the CONCEPT OF TIME VALUE OF MONEY 181 riskier the investment, the lower the asset's present or market value. From an equity investor's perspective, the greater the perceived risk of the projected levels of cash flow being achieved, the higher return on investment (ROI) he will demand. If an investor is presented with two acquisition opportunities projected to generate the same amount of cash flow over a five-year period, but investment A has twice the perceived risk of investment B, which of the two would you pay your money to acquire? Of course, opportunity B, the one with the lower risk. Therefore, which one has the higher present value? If you responded that B has the higher present value due to its lower risk, you are correct. As the risk of a potential investment increases, its present value decreases. Conversely, as the risk of a potential investment decreases, its present value increases.
THE BUSINESS CALCULATOR
The main difference between a business calculator and a regular calculator is the additional functions it performs. In addition to basic math, a business calculator includes a set of function keys that allow the user to calculate future value and present value. As a hospitality manager, you need to familiarize yourself with the five basic function keys of a business calculator and learn how to perform each function. The five basic function keys are: N number of years I/Y interest or discount rate PV present value PMT annuity payment FV future value There is also a second set of functions whose keys are directly above these five basic function keys. For example, above the N key is xP/Y, which stands for number of compounding periods per year. Above the I/Y key is P/Y, which stands for the number of payments per year. To invoke any of these functions, you must use the 2nd key, which is found between the CPT key and the N key. We discuss these keys further in a moment. As some business calculators are equipped with default settings from the manufacturer, always check the settings before using the calculator. For example, the BAII Plus calculator comes with a factory setting for two decimal places. When working with percentages, two dec- imal places are usually fine. Some calculations, however, require four decimal places. Before you perform the calculations presented is this chapter, please check your calculator to make sure it is set for annual compounding and four decimal positions. Here are the steps to follow: 1. The 2nd key lets you perform the function printed above each of the other keys. 2. For example, the function description above the . key says FORMAT. 3.To format the calculator for decimals, press the 2nd key and the . key. 4. Once these two keys are pressed, your calculator will display DEC 2.00. 5. Now enter 4 and press ENTER. This tells the calculator you want four decimal places calculated rather than two. As soon as you press the ENTER key, the display will change to DEC 4.0000, showing four decimal places. To exit and return to normal calculations, press the 2nd key and the CPT key to quit the function. The quit function is above the CPT key. Now, all you see on the display is 0.0000. Another factory setting you must change is the number of compounding periods per year. While we do some monthly compounding, most calculations we ask you to do are on an annual basis. Because the factory default for most calculators is set at twelve compounding periods per year, you need to set your calculator for annual calculations. Remember, the P/Y function directly above the I/Y key? P/Y stands for the number of compounding periods per year. In order to see the number of compounding periods per year, you will need to: Press 2nd and I / Y. By pressing these two keys, you are letting the calculator know you want to access the P/Y function to look at the number of compounding periods per year. If your calculator is a new one from the factory, it will display P/Y 12. Set your calculator for annual compounding; thus, you need to press the 1 key and the ENTER key, which is on the top row of your calculator. The display will show P/Y 1.00. Press 2nd and CPT (QUIT) to exit. Now that your calculator is set correctly, the last step before we perform some calculations is to clear it of any previous calculations. The calculator is a storage device; therefore, if you have not cleared a previous calculation, the information is still stored in the calculator. It is always good practice to clear the calculator before starting a new calculation. There are two clear keys on your calculator. Above the FV key is the CLR TVM, which stands for ''clear time value of money calculations.'' The other clear key is on the lower left-hand corner above the CE / C key, which says CLR WORK. This key clears any work you have recently performed other than time value of money calculations. To clear all previous time value of money calculations, press 2nd and FV. To clear all other calculations, press 2nd and CE/C.
Time Value of Money
The time value of money concept (TVM) is the cornerstone of investment analysis. The decision-making skills regarding investments that you will learn in chapters 8 and 9 are based on the concept of the time value of money. It is one of the most difficult concepts for a hospitality manager to grasp. The TVM concept is based on the premise that the value of money is not only its face value but also the interest or profit that can be earned by investing it wisely. For example, if today you placed $1.00 in a certificate of deposit (CD) that pays an annual interest of 10%, at the end of the year your $1.00 investment would be worth $1.10. If you left your money in the CD for another year, at the end of year two your investment would be worth $1.21. If someone wanted to sell you an I.O.U. for $1.21 that was payable two years from now, how much would you pay for it today? The answer is no more than $1.00 if you believe you can earn at least a 10% annual return on your money. Whoever owns money wants to invest it and make a return on it, either in the form of interest income or a profit. If you have to wait two years to receive payment of the I.O.U., you would have lost two years' worth of investment income. The value of the I.O.U., therefore, is the face value of the I.O.U ($1.00) less the twenty-one cents you could have earned on the $1.00 over the two years. 180 CHAPTER 7 THETIMEVALUEOFMONEY In time value of money terminology, the $1.00 is the asset's present value (PV) and the $1.21 is the asset's future value (FV).
FUTURE VALUE OF A SINGLE SUM
To make this example a little more interesting, let us assume the present value is $1,000, the compounding period is five years, the interest rate is 12%, and the future value is what the investment will be worth at the end of the five years, with the principal and interest added together. When calculating time value of money problems, it is helpful to list all the particulars of the problem on a timeline:. You may remember that you can calculate time value of money problems using the formula and table method, a business calculator, or a spreadsheet. Illustration 7-1 shows how this future value calculation is performed using a formula and the interest factor table respectively.
Calculate the present value of an annuity (PVA) PVA n = PMT [1- {1/(1 + r)n }] r PVA = ?
2,162.80
Calculate the present value of an annuity due (PVAD) PVAD = PMT [1- {1/(1 + r)n }] (1 + r) r PVAD =
2,422.34
Calculate future value of annuity FVA 5 = PMT [(1 + r)n -1/r] PMT = 600 FVA = ?
3,810
calculate the future value of an annuity due FVADn = PMT [(1 + r)n -1/r] (1+r) FVAD =
4,267.20
PERPETUITY
A perpetuity is a special type of annuity that pays or receives cash with no time limit. One method of valuation, known as the capitalization method, uses the basics of a perpetuity. The cap rate method of valuation is an investment analysis tool that will be discussed in the next chapter. The formula for a perpetuity is simple: PV perpetuity PMT, where PMT = annuity payment , r = interest rate You don't necessarily need to use a business calculator or Excel to calculate the value of a perpetuity. Simply divide the annuity payment by the interest or cap rate. To prove the formula, select a hypothetical annuity payment and calculate its present value using a large N of 1,000. You will find that your answer is exactly the same as you calculated by dividing the payment by the cap rate.
SINGLE SUM
A single sum investment is the most basic form of a time value of money calculation. For example, if you invested $100 today and it yields a 10% annual interest, at the end of one year you would have $100 plus $10 of interest earned, or a total value of $110. The present value is $100, the future value is $110, the compounding period is one year, and the interest rate is 10.0%.
ANNUITY
An annuity can be either a regular annuity or an annuity due. A regular annuity is a fixed amount of money received or paid at the end of each compounding period for a set time. Consider the following timeline, where $600 is to be received at the end of each year for five years at a 12% interest rate: Regular Annuity |————|————|————|————|————| 0 1 2 3 4 5Years$600 $600 $600 $600 $600 at 12% interest An annuity due is the same as a regular annuity, except the money is received or paid at the beginning of each period. Annuity calculations are similar to lump sum calculations, except now you are dealing with multiple sums of the same amount.
IMPORTANCE TO THE HOSPITALITY MANAGER
As a hospitality manager, understanding the time value of money concept, the concept of market value, and learning the investment analysis skills based on these concepts is important to your success. Investment analysis skills also come in handy when you need to request capital for a new project such as an additional meeting room for the hotel where you work, a guest room expansion, a new restaurant concept, or purchasing new computer equipment. When requesting capital, you must demonstrate that the money you are asking for will generate a favorable return on investment for your company. This is critical whether you are requesting capital from your general manager, owner, lender, or public shareholders.
FUTURE VALUE OF AN ANNUITY DUE
As mentioned earlier, the difference between an annuity and an annuity due is the timing of the cash flow. While the cash flow for a regular annuity is received or paid at the end of each period, the cash flow for an annuity due occurs at the beginning of each period. Please note that in order to perform annuity due calculations, business calculators have a button that says Begin or BGN. Once your calculator is in the BGN mode, simply enter the same information as you would for a regular annuity, and the calculator will provide you with answers for an annuity due. Once these calculations are made, you will see that while the future value of a regular annuity was $3,811.71, the future value of an annuity due would be $4,269.11.
HOW THE ASSET IS TO BE FINANCED
As you learned in chapter 6, capital has a cost. The cost of debt is debt service divided by the amount of the loan. The cost of equity is the investor's hurdle rate. The mix of capital used to finance the asset determines the weighted average cost of capital (WACC). The more equity required to finance the deal, the higher the WACC. The higher the WACC, the lower the asset's present or market value. The lower the present or market value, the less an investor will likely pay to acquire the asset.
FUTURE VALUE OF AN UNEVEN CASH FLOW
Because the cash flow [CF] functions only work with net present value [NPV] and internal rate of return [IRR], to compute the future value [FV] of an uneven cash flow stream, you must first compute its present value [PV] and then compute its future value. In this case, the present value [PV] was calculated to be $760.49. To calculate its future value, enter the present value as calculated, the interest rate, and 5 as the period. The future value is $1,224.78.
FUTURE VALUE OF AN ANNUITY
Consider the following timeline, where $600 is to be received at the end of each year for five years at a 12% interest rate: Using this timeline and the other information provided, let us calculate the future value of this annuity. The calculations using the formula and table method are shown in Illustration 7-5. The calculations using a business calculator or an Excel spreadsheet are detailed in Illus- tration 7-6. This calculation indicates that an investment of $600 per year with a 12% interest rate yields a total value of $3,811.71 in five years.
LOAN AMORTIZATION
Earlier in the book, we discussed loan terms such as principal, length of loan, interest rate, and amortization rate. Recall that in one illustration, a loan of $100,000 that charged a 10% annual interest rate was calculated for both a three-year and five-year period, compounded annually. Now that you know the basic time value of money calculations, the debt service calculation for a loan is easy. It's an annuity calculation where: PV = loan amount, N = number of compounding periods I/Y = interest per compounding period With three variables, you can compute the fourth—PMT, in this case—the debt service payment you need to make each period. Illustration 7-15 provides the steps necessary to calculate PMT using a business calculator and Excel.
UNEVEN STREAM OF CASH FLOW
Now that you have a working knowledge of the basic mathematics of finance, let's apply this knowledge to simple investment analysis. In the real world, not everything comes in neat pack- ages. For example, the cash flow for a particular business is not usually the same each month or each year. Thus, the concept of an uneven stream of cash flow mirrors reality much better than an annuity does
PRESENT VALUE OF AN UNEVEN CASH FLOW
Illustration 7-13 presents an uneven stream of cash flow a hospitality manager has projected for his business over a five-year period. In this example, he expects business to be a little slow during the initial years. He expects business to pick up a bit in the second year, really take off in Year 3, and then stabilize and earn around $300 annually thereafter. Based on the projections, how much is this stream of cash flow worth today? One approach is to calculate the present value of each year's cash flow individually and add them together, as shown in Option 1. This option takes a little longer but will result in the correct answer of $760.49. Alternatively, you can use the cash flow function key on your business calculator, enter each year's cash flow as instructed, and compute the present value a little faster. Illustration 7-13 details the steps you should take if using a Texas Instrument BAII Plus business calculator. Using this calculator for cash flow calculations may be daunting the first time you try; however, you need to learn this method because you will use it to calculate net present value and internal rate of return a little later in the text. Learning the steps, practicing them a few times, and mastering them will save you a lot of time and headaches later.
PRESENT VALUE OF AN ANNUITY DUE
In financial management, present value is used to evaluate investment opportunities. The for- mula and table method is shown in Illustration 7-11. Let us now calculate the present value of this annuity due using a business calculator or Excel. In this case, while the regular annuity yielded a present value of $2,162.87, the present value is now $2,422.41. Because an annuity due is received or paid at the beginning of the period, as opposed to the end, the present value of an annuity due will always be more than the present value of a regular annuity.
Time Period and Compounding
In terms of debt financing, a monthly versus annual compounding period favors the lender over the borrower because interest expense is accrued or paid monthly. Thus, compounding can make a big difference when calculating debt service payments. Let us look at how compounding can change results. Using the example shown earlier in Illustration 7-2, we will use the same variables but change the compounding period from annual to monthly and see what happens.
TIMING OF THE CASH FLOW
Intuitively, if we told you we would give you $100 in five years or $100 in ten years, you would choose the five-year payday. This, as we learned earlier, is the basis for the time value of money concept. In other words, one dollar received today is worth more than one dollar to be received in the future. The sooner you receive the money, the more value it has today and the higher its present value. Consider purchasing a U.S. savings bond. You could purchase a $100 bond today for less than $100 because you won't receive your $100 until sometime in the future. The actual pur- chase price depends on how long you have to wait to receive your $100. The longer you have to wait to receive your money, the less the bond is worth today.
PRESENT VALUE OF AN ANNUITY
Let's refer to Illustrations 7-5 and 7-6 once again. Consider that you have won a small lottery and now have the choice of receiving $600 per year for five years or a lump sum payment today. The lump sum payment today would represent the present value of the five-year $600 annuity using a 12% rate of interest. To calculate the present value of an annuity using the formula and table method, see Illustration 7-7. The present value of an annuity can be calculated using the PV, N, I/Y, and PMT keys on a business calculator. Illustration 7-8 shows the timeline of the payments and the interest rate, and takes you through the calculations using both the business calculator and the Excel spread- sheet.
AMOUNT OF CASH FLOW
We are sure you would agree that the more cash flow an asset is likely to generate in the future, the more you would pay to acquire it today. Therefore, the higher the amount of cash flow to be generated, the higher the asset's present or market value. With this in mind, it's clear that the more cash flow an asset is generating at the end of five years, the more an investor would pay to acquire it at that time. Therefore, the more you could sell the asset for in the future, the more the asset is worth today and the higher its present or market value. In other words, the present value of an asset is a function of its future cash flow, including its terminal selling price.
