note

The preceding Chapters discussed the tools necessary to analyze the financial feasibility of an investment for the standpoint of how much it would “ return ” to the investor. This Chapter now formalizes the process, anticipated in the example at the end of the Chapter 4.

5-1 ASSUMPTIONS FOR ECONOMIC ANALYSES

Simplifying assumptions reasonably and closely representing the reality of the characteristics of the situation being analyzed, are generally accepted when conducting economic analyses, we discussed them earlier, let us review them again

End-of-year convention – as said earlier, cash flows - uniform or non-uniform - are assumed to happen at the end of the year, with obvious impact on accrued interest. The cash flow indicated with P is however assumed to happen at the beginning of the investment period, normally the invested capital; The cash flow indicated with F is assumed to happen at the end of the period

Viewpoint of the analysis – to conduct the analysis we must have clear in mind the view point we use. In every economic transaction there are several points of views: the lender, the borrower, any individual having a stake in the transaction and his/her agenda, etc. The view point we chose has determining impact on the analysis approach and therefore the result. For example: for Private Enterprises the deciding criterion is generally profit , while for Public Sector Entities it is benefit to the public

Sunk Costs – the economic analysis among alternatives (i.e. selecting which one is best) is based on their economic difference and since sunk costs are present and identical for all alternatives they do not impact the difference, therefore sunk costs are not accounted for in economic analysis. Note that even when only one alternative is under consideration, in reality the alternative “doing nothing”, which also carries the same sunk costs, is also being considered.

Borrowed Money viewpoint – in the analysis two aspects of monetary transactions are considered:

· Financing – the activity of obtaining the availability of the money necessary for the investment. This activity involves two actors: the Lender, who receives payment for making money available, and the Borrower who pays interest for the availability of money

· Investing – the activity of committing resources (money, time, land, etc.) to a venture with the objective of obtaining benefits, which can be profit, community service, etc.

Effect of Inflation or Deflation (macroeconomic issues) – unless otherwise noted, we will not consider the effects of inflation or deflation, which are due to fluctuation of money’s purchasing power. We will briefly cover this aspect later in the course.

Taxes – taxes impact the “payoff” of economic activities by reducing the fraction of profit available to the investor; in our analyses we will neglect the effect of taxation, which will be briefly covered later in the course.

5-2 ECONOMIC CRITERIA

The Present Worth Analysis resolves the time-distributed outcomes of economic alternatives into equivalent present consequences

When several investment alternatives are available, generally the point of view taken in the analysis is the one of a Private Enterprise, i.e. maximize the present worth of the investment , based on the three possible situations:

1. Nether input nor output are fixed – case normally encountered in practical situations: the amount of resources (money, time, land, etc.) to invest and the amount of benefits to derive are not fixed. In this case the way to proceed is to minimize the invested resources and maximize the derived benefits, therefore maximizing profit

2. Input is fixed – the amount of resources (money, time, land, etc.) available for the investment is fixed. In this case the way to proceed is to maximize the derived benefits, therefore maximizing profit

3. Output is fixed – the level of benefits that can be obtained from the investment is fixed. In this case the way to proceed is to minimizing invested resources, therefore maximizing profit

5-3 NET PRESENT WORTH

The NET PRESENT WORTH (NPW) of an investment, i.e. the value of the investment NOW (hence the importance of the simplifying assumptions) for the investor, is

NPW = PW of benefits – PW of costs

Indicating that the Net Present Worth of an investment is equal to the Present Worth of the deriving Benefits minus the Present Worth of the invested Resources

NOTE: in economic analyses the terms WORTH and VALUE have the same meaning, so the terms PV (present value) and PW (present worth) are synonymous.

5-4 TIME PERIOD CONSIDERED IN THE ANALYSIS

The time period considered in economic analyses is the period of time over which we want to consider the “effect” of the cash flow generated by the investment over its Net Present Worth; as we have seen, such effect is a function of timing and cost of money availability (time value of availability of money). The time period over which the economic analysis of an investment is considered is of paramount importance, and it is normally referred to as analysis period, planning horizon, or project life : from the economic analysis point of view these names identify the same period of time being analyzed. There are three possible situations

a) The useful life of each alternative is equal to the period being analyzed ; example is an investment in equipment that will last for the entire analysis period

b) The useful life of each alternative differs from the period being analyzed ; example is an investment in equipment that needs to be replaced during the analysis period. In this case the universally accepted simplifying assumption is that the replacement is made with a new equipment identical (type, cost, useful life) to the replaced one .

c) The analysis period is ∞

Example 5.1 – Useful Life equals analysis period

Consider investing in a high-speed high capacity new computer to manage all the administrative requirements of your Company for the next 10 years. The cost of money for your Company is 7.33%. Two types of new computers are available for consideration, and “neither input nor output are fixed” . The data available for the analysis are

Computer Option # 1 Computer Option # 2

· Cost $1,000,000 $1,500,000

· O&M $12,000/yr $10,000/yr

· Useful Life 10 yrs 10 yrs

· Decrease in Admin Cost $50,000/month $70,000/month

· Salvage value $80,000 $100,000

The Net Present Worth (NPW) for Option 1 is

NPW = -1,000,000 – 12,000 (P/A, 7.33, 10) + 50,000 (P/A, 7.33/12, 120) +

+80,000 (P/F, 7.33, 10) =

= -1,000,000 – 12,000 x 6.918 + 50,000 x 84.915 + 80,000 x 0.493 =

= -1,000,000 – 83,016 + 4,245,750 + 39,440 = $3,202,174

The Net Present Worth (NPW) for Option 2 is

NPW = -1,500,000 – 10,000 (P/A, 7.33, 10) + 70,000 (P/A, 7.33/12, 120) + +100,000 (P/F, 7.33, 10) =

= -1,500,000 – 10,000 x 6.918 + 70,000 x 84.915 + 100,000 x 0.493 =

= $4,562,530

(The Compound Interest Factors were obtained using the Excel Tool)

The analysis clearly indicates that Option # 2 is the preferred one since it

maximizes the investment’s Net Present Worth NPW.

(Note that the “profitability” issue has not been considered)

Example 5.2 – Useful Life differs from analysis period

Consider the example above with the following additional assumptions:

Computer Option # 1 Computer Option # 2

· Cost $1,000,000 $1,500,000

· O&M $12,000/yr $10,000/yr

· Useful Life 10 yrs 5 yrs

· Decrease in Admin Cost $50,000/month $70,000/month

· Salvage value (end of life) $80,000 $100,000

The Net Present Worth (NPW) for Option 1 is still $3,202,174

For Option # 2 the Cash Flow Diagram becomes

And the NPW is calculated as follows

NPW = -1,500,000 – 1,500,000 (P/F, 7.33, 5) + 100,000 (P/F, 7.33, 5) –

-10,000 (P/A, 7.33, 10) + 70,000 (P/A, 7.33/12, 120) +

+100,000 (P/F, 7.33, 10) =

= -1,500,000 – 1,500,000 x 0.702 + 100,000 x 0.702 – 10,000 x 6.918 +

+ 70,000 x 84.878 + 100,000 x 0.493 = $3,433,280

Even in this scenario Option # 2 is still the most desirable. Option # 2 computer is more expensive and has a shorter useful life, but the benefits it offers (i.e. decrease in administration cost) are larger than its cost.

This example shows that in performing NPW economic analyses of alternatives, each alternative must be considered over the same entire time horizon of the investment; it would have been incorrect to evaluate Option # 1 over a 10-year period, and Option # 2 over a 5-year period

Example 5.3 – The time horizon of the investment is infinite (∞ )

This is often the case of Government Investments (highways, dams, hospitals, schools, etc.). This analysis focus on the periodic service costs necessary to maintain and operate the investment, the cost of maintaining highways, dams, etc. This type of investments produce benefits to the community which are not quantifiable in economic (monetary) terms , therefore the relative analysis cannot determine a NPW, instead it focus on defining the sum of money that must be “set aside” at the beginning of the investment in order to yield the funds required to provide the necessary services for an indefinite period of time . This kind of analysis is called Capitalized Cost Analysis, based on the assumption that the required periodic service payments are made using only the interest accumulated in the preceding period, without withdrawing any portion of the principal amount set aside at the beginning of the investment in an interest earning account . This approach guarantees the availability of funds to pay for the necessary services, for an indefinite length of time.

Assuming the periodic cost of services is A , and the investing Entity can secure an interest rate i for the “set aside” principal P, the resulting cash flow diagram is:

Where

P = Sum of Capital that must be set aside into an interest earning account

(NOTE: it is NOT the initial cost of the investment)

i= interest rate that the investing Entity is able to secure

The periodic sum iP is the amount of periodic payments for services, therefore

A = iP P = A / i

Consider a Municipality has built a new road which will need an indefinite servicing costing an estimated $8,000 per year . The Municipality secured an interest rate i= 3% through a local Savings & Loans Institution. How much should the Municipality set aside into an account to be able to pay for the needed services indefinitely? The amount is

P = 8,000 / 0.03 = $266,667

This amount set into the saving account will allow payments for services for an indefinite period of time, assuming : (a) the periodic cost of service remains unchanged, and (b) the interest rate also remains unchanged

5-5 BONDS

Bonds are loans from the BOND PURCHASER to the BOND ISSUER, which “bonds”, i.e. commits the Bond Issuer to periodically pay to the to the Bond Purchaser the agreed upon interests at the due dates, and the face value at maturity

Bonds are normally issued by Public Entities ( Bond Issuers ) with the intent of raising funds for investments of public interest. The interest rate offered by the Bond Issuer to the Bond Purchasers is normally lower than the going rate on the open money market because the risk of default (i.e. missing payments) by a Public Entity is rather low.

Bonds have the following structure:

· PAR or FACE VALUE - is the amount of the loan from Bond Purchaser to Bond issuer. It is normal practice that Bonds are issued in $1,000 increments, i.e. buying 5 Bonds means lending to the Bond Issuer $5,000

· CUPONS – are coupons issued with the bond, each coupon is redeemable at fixed intervals, normally 6 months, and pays the amount of interest accrued by the lent amount (i.e. normally $1,000) over the fixed interval, at the agreed interest. For instance, each coupon of a $1,000 bond issued at 6% interest will pay every 6 months 1,000 x 0,03 = $30.00

· MATURITY – defines the period of time, normally in years, that the lent amount is available to the Bond Issuer. At maturity, the Bond Issuer must pay back to the Bond Purchaser the Par or Face Value of the bond.

Graphically, the Bond Structure, from the standpoint of the Bond Purchaser, is:

From the standpoint of the Bond Issuer the graph is obviously inverted.

Example 5.4 – Calculate the NPW, from the standpoint of the Bond Purchaser, of a Bond with face value of $1,000, issued for the Maturity Period of 10 years at the interest rate of 4.33%

Since the Coupons are paid every 6 months, the amount of payment is

1,000 x (0.0433 /2) = 1,000 x (0.02165) = $21.65

And it is paid 10 x 2 = 20 Coupons, one every 6 months

The NPW for the Bond Purchaser (investor) is (using the Excel Tool)

NPW = -1,000 + 21.65 (P/A, 0.02165, 20) + 1,000 (P/F, 0.0433, 10) =

= -1,000 + 21.65 x 16.094 + 1,000 x 0.654 = $2.435 ≈ 0

The NPW of the bond investment, when calculated at the bond’s interest rate, is zero, in other words the PW of the string of payments received by the Bond Purchaser equals the sum P invested . As indicated above, the interest rate given by the Bond Issuer is normally not very high, however, there are considerations, such as (a) the investment is very safe, i.e. the Issuer will honor the repayment, and (b) the fixed interest rate is not subject to market fluctuations, which can make the purchase of a bond attractive.

Suppose now the Bond Purchaser (the investor in bond), half way through the maturity period, i.e. 5 years down the road, realizes that he/she can better invest the money now stuck in a bond, so he/she decides to sell the bond and make a different investment. How much should he/she sell the remainder of the bond’s 5 years for?

There are 10 remaining Coupon payments of $21.65, and the final Face Value payment of $1,000. The Present Value, at year 5, of these future payments for the Bond Purchaser is

NPW = 21.65 (P/A, 0.02165, 10) + 1,000 (P/F, 0.0433, 5) =

= 21.65 x 8.906 + 1,000 x 0.809 = $1,001.815

That is the minimum price he/she should ask to avoid a loss, i.e. getting less than the NPW of the bond at the time of sale.

NOTE: the analysis above assumes that the value of money availability for the Bond Purchaser is the same as the interest rate applied by the Bond Issuer, which is not normally the case. If the value of money availability for the Purchaser is not the same, then the correct NPW calculation must be done using the Purchaser’s value of money availability.

The correct analysis of the desirability of purchasing a bond requires considering three factors, two of which we have considered above: (a) the Bond Issuer, which is the entity asking for availability of money (i.e. a loan) at a fixed interest rate and for a number of years (periods to maturity), and (b) the Bond Purchaser, which is the entity lending money to the Bond Issuer at the conditions of the bond (interest and periods to maturity); the third factor is (c) the Money Market which determines the cost of money, i.e. the value of money availability, for the Bond Purchaser.

Keep in mind that once the bond is purchased, the sum invested in the bond is not available to the Bond Purchaser before maturity is reached (generally several years). The money is “frozen” in the bond at a fixed interest rate, but the prevailing interest rate which the Money Market is willing to apply to the entity asking for money availability (a loan) is not at all fixed, it actually can (and probably will) become bigger or smaller than the fixed bond interest rate.

The NPW of the bond for the Bond Purchaser therefore varies with the money market interest rate which the Bond Purchaser experiences. If we indicate

iB = Interest Rate paid by the Bond Issuer

iM = Prevailing Money Market Interest Rate

Considering that the value of the bond’s Coupons is calculated to make the PW of the string of payments (coupons and face value at maturity) equal to the P (face value at time 0) invested at the fixed interest rate of the bond, in other words NPW=0 for the investment, we can visualize the dynamic of bond ownership in the diagram below. When the market rate iM is bigger than the Bond Rate iB the Bond Purchase realizes an NPW smaller than what he/she/it could have realized lending the money on the open market. The reverse happens when the Market Rate iM is smaller than the Bond Rate iB. Obviously, when iM = iB the NPW is zero, i.e. the Present Value of the payments (Coupons and Face Value) the Bond Purchaser receives equals to the sum P spent for purchasing the bond(s).

5-6 INTRODUCING THE USE OF EXCEL FINANCIAL FUNCTION NPV

Excel Financial Function NPV (which, as we have said before is the same as NPW) allows to directly calculate the Net Present Value of a string of cash flows, not necessarily uniform, once the interest rate is defined . The function requests the following inputs:

Rate the applicable interest rate

Value the list of cells containing the cash flows

Example 5.5 - An industrial grade Farm wants to permanently expand its production and increase profits by an estimated 15,000 $/yr for the next 20 yrs. The expansion would need additional irrigation over the expected 20 years life of the expansion, therefore additional water consumption. The Farm has two options for increasing availability of water: bring the needed water from a nearby reservoir, or dig a well on its property; each alternative has its own characteristics:

A) Bring water from a nearby reservoir: the farm would have to install a pipeline from the reservoir to the field, however the reservoir is at an higher elevation so the water would flow to the field by natural gravity without the need of a pump. The installation would be simple and would not require extensive maintenance. The farm will have to pay the Reservoir’s Consortium for the required water.

B) Drill a well: the well will need a pump to deliver water to the field, the system will require regular maintenance, and the pump will have to be replaced every ten years. The well would be on Farm’s property and the extracted water would be at no cost.

The Farm will have to borrow the necessary capital from a Lending Institution at an interest of 10%, and the farmer assumes the following parameters for the two alternatives:

Installation Cost O&M/yr Replacement Water

Alternative A 25,000 1,000 N/A 4,000

Alternative B 35,000 3,000 5,000/10 yrs N/A

Question 1: Which of the two alternatives presents the best NPW?

Question 2: It is evident that the values of the two NPW are a function of the interest rate which the Farm will be able to secure. Construct the NPW curves as function of i.

The cash flow diagrams for the two alternatives are:

The solution will be discussed referring to the excel file Chapter 5 – Example 5.5

As shown in the spreadsheet, Alternate B is the best choice, and it would remain the best for interest rates up to 17%

Example 5.6 – You have been required to analyze how the NPW of three potential investments vary with the variation of the cost of capital. The given input data are:

The solution will be discussed referring to the excel file Chapter 5 – Example 5.6