3.14. Payback Period and Discounted-Payback Period (Advantages and disadvantages)

Some companies that the initial outlay on any project should recoverable within a specified period. The Payback Period (PP) of a project is found by counting the number of years it takes before the cumulative forecasted cash flow equals the initial investment. For example, manager has the cash flows as follows:

Cash Flows ($)	0	1	2	3	4
	-100 000 (b)	34 432	39 530 (a)	39 359 (d)	32 219

Table 3.3

Manager sum up the cash flows up one to four and they have progressive total of cash flows.

Progressive total Cash Flows	1	2	3	4
	34 432	73 962 (c)	113 321	145 540

Table 3.4

year (3.2)

Why PP could give us misleading answers:

1. The rules of PP ignore all cash flows after the cutoff date.

2. The rules of PP give equal weight to all cash flows before the cutoff date.

In order to use the PP, a firm has to decide on an appropriate cutoff date. If it uses the same cutoff regardless of project life, it will tend to accept many poor short-lived projects and reject many good long-lived ones.

Discounted-Payback Period (DPP) – some company’s discount the cash flow before they compute the payback period. The DPP ask how many periods does the project have to last in order to make sense in terms of NPV? This modification to the PP surmounts the objection that equal weight is given to all flows before the cutoff date. However, the DPP still takes no account of any cash flow after the cutoff date. The simplicity of PP and DPP makes them easy devices for describing invest projects.

3.15. Internal (or discounted-cash-flow) rate of return (irr) and mirr (Advantages and disadvantages)

Whereas payback and return on book are ad hoc measures, internal rate of return gives a much more respectable ancestry and is recommended in many finance text. The net present value rule could also be expressed in terms of rate of return, which would lead to the following rule : Accept investment opportunities offering rates of return in excess of their opportunity cost of capital. The statement is absolutely correct, but interpretation isn’t always easy for long-leaved investment projects. This is a formula the true rate of return of an investment that generates a single payoff after one period:

Rate of return = (3.3)

Alternatively, it possible to write down the NPV of the investment and find that discount rate which makes NPV=0.

NPV = (3.4), therefore Discount rate = (3.5)

The discount rate that that makes NPV=0 is also the rate of return. Unfortunately, I can not to find satisfactory definition the rate of return for a long-lived asset. The best available concept is the so-called discounted-cash-flow (DCF) or internal rate of return (IRR).

The internal rate of return is defined as rate of discount which makes NPV =0.

NPV = (3.6)

Some managers confuse the internal rate of return and the opportunity cost of capital both appear as discount rates in the NPV formula. The internal rate of return is a profitability measure that depends on the amount and timing of the project cash flows. The opportunity cost of capital is a standard of profitability which usually manager use to calculate how much the project is worth. The opportunity cost of capital is established in capital markets. It is expected rate of return offered by other assets with the same risk as project being evaluated. The IRR rule is technique based on discounted cash flow. It will therefore give the correct answer if properly used. The problem is that it is easily misapplied. There are four things to look out for: