Chapter 5. Investment and Analysis methods Summary (2016)Resumen Inglés
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FINANCES II: Investment and analysis
1. The Internal Rate of Return (IRR)
IRR is the discount rate (r) that makes the NPV be = 0.
Rules: Companies are interested only in those investments that have r > opp.cost of k.
Companies choose the investment with the higher r.
Distinguishing r and k - - Both r and opp. cost of k appear as a discount rate in NPV formula.
The r is a relative profitability measure that depends only on the amount and timing of the project cash flows. “Relative” means that regardless of the amount of the principal, this will be my investment cost.
The opp. cost of k is established in the capital market, and represents the expected rate of return (ROR) offered by other assets with the same risk.
Different types of IRR Constant cash flows (C1 = C2 = C3 =…= Cn) Constant cash flows + Nº of years unlimited Methodology to calculate IRR *It is quite difficult to calculate IRR for long term projects, since we have to solve an equation of n-degrees. Anyway, currently we use special financial software to solve it.
Example 1 Example 2 *Note that the higher the r is, the lower the NPV.
The hypothesis of reinvestment of net cash flows in “r” If reinvestment rate “ r’ “ is equal to r (r’ = r) we can verify: *It is very unrealistic though.
IRR’s inconsistency *We will work only with Simple Investment.
Example 1’: Multiple IRRs, cash flows in billions of m.u.
*There can be as many internal rates of return (IRR) as changes in the sign of the cash flows! Example 2’: there is no valid solution for IRR There is no internal rate of return (r or IRR), which means that this project will have a positive NPV at all discount rates.
The Effective Annual Interest Rate or the Annual Equivalent Rate (AER) The “r” can be used in terms of months, quarters, years…, but normally an AER is often used a reference to “r” but always in a yearly basis.
So we need to distinguish between quoted (nominal) interest rate and the effective annual interest rate (or AER) An Annual Equivalent Rate (AER) is an indicative reference of a cost of effective yield of a financial product. It includes a nominal interest rate, expenses, bank charges and a term of transaction.
Calculates an overall/global profitability on an annual basis Applies to the savings products as well as to the loans Its homogeneous character facilitates easier comparative analysis between various financial products.
Example Suppose a bank offers you an automobile loan at an annual percentage rate of 12% with interest to be paid monthly. What is the effective annual rate(EAR)? The EAR is needed to use comparable “r” for the investment projects with the different timing of cash flows.
Example 1: AER A bank gives a 2-year loan of 10.000€ to one of its clients. The annual interest to be charged is 7%. On maturity date of a loan, the client has to return the loan (a principal value) and pay the interests corresponding to a period.
1. What is the IRR that a bank obtains in this operation? 2. What is the AER, assuming that an interest has to be paid each semester? (2 year loan with a 7% interest annually) (2 year loan, with a 7% interest annually, so a 3,5% interest semianually or semestrally) (TAE=AER) Example 2: AER A bank gives a 2-year loan of 20.000€ to one of its best clients. The annual interest to be charged is 7%. So, each year a client has to pay the interests (annually interests). On maturity date of a loan, a client must return a principal value of a loan and pay the interests corresponding to a period.
1. What is the IRR that a bank obtains in this operation? 2. What is the AER, assuming that an interests has to be paid each quarter? (2 year loan with a 7% annual interest) (2 year loan with a 7% annual interest, so a 1,75% quarter interest. TAE=AER) Similarities and differences between NPV and IRR For simple investment projects, IRR is a profitability limit which determines the viability of the project, which depends on the opp. cost of capital (k).
The Fisher rate The Fisher rate (f) is the interest rate that equates the NPV of 2 investment projects.
IRR and NPV give the same ranking to the projects, only if fisher rate doesn’t exist in the first quadrant. In case of existence of intersection, the ranking between IRR and NPV doesn’t match.
*What does it mean that “it gives the same ranking”? Example: Fisher rate Example 1: Fisher Rate The company you work for decided to install a new equipment for which there are 2 alternative simple investment projects with the following financial flows: In order to make a final decision you have to present the following information: a) To calculate IRR for each project b) To check whether the Fisher rate exists or not in the first quadrant c) To make a graphical analysis and financial interpretation Example 2: IRR vs NPV choice if exist different reinvestment ratios): A company ACEROX S.A. is considering to buy a new playback machine that produces video faster than it did the previous one.
After running a market’s study it was found that there were two possibilities such as Acex and Laxus machines for which a financial department made an estimation of the expected cash flows for 2 years.
In case of choosing Laxus, the company would have 100.000 m.u available to make a temporary financial investment.
Knowing that the financing cost (k) was 7%, financial director asked the project’s director to make a complete analysis of these 3 investments.
The selection and ranking of the projects taking into consideration homogeneous initial payments compare an option of purchase of Acex with the set of the other 2 possibilities of investment.
FINAL SOLUTION FINAL SOLUTION II ...