**The pay back method**

The pay back method evaluates capital budgeting opportunities by determining the number of periods (months or years) required for the sum of the benefits to be equal to the investment. For example a project that require Shs 50,000 investment and yields a benefit of Shs 10,000 per year has a payback of 5 years i.e. it takes 5 years for the firm to recover its investment (Shs 50,000) in this project. Managers normally determine the maximum time period that the business is willing to wait to recover its investment and accept all investment opportunities with pay back periods less than or equal to that maximum. Any investment that requires more time than the maximum is not acceptable. When faced with two or more investment alternatives that solve the same problem, the one with a shorter pay back period is preferred.

Although the pay back method is widely used in making capital budget decisions, it has disadvantages that limit its ability to reveal the best investment for the firm. Assume two competing investment alternative A and B each require an investment of Shs. 1000. Investment A has a life of 5 years. Investment B has a life of 6 years. Assume further that management has set its maximum pay back period to 4 years. The after tax incremental cash flows for each year are given in the table below;

After tax benefits | |||

Year | A | B | |

1 | 500 | 100 | |

2 | 400 | 200 | |

3 | 300* | 300 | |

4 | 200 | 400* | Maximum payback allowed |

5 | 100 | 500 | |

6 | _ | 600 | |

Total benefits | 1500 | 2100 | |

Payback in years | 2.3 | 4 |

Investment A has a payback of 2.3 years while investment B returns the full value of its investment by the end of year 4. Since the firm’s maximum payback period is 4 years, both investments are acceptable. However if only one can be chosen the firm should choose investment A because it recovers its investment more quickly than investment B.

The major disadvantage of the payback method is that the benefits after the payback period are ignored. The total benefits from investment B are Shs 600 greater than those from investment A. Thus, the payback method violates the second criterion of a good investment that when faced with alternative solutions, always select the one that gives the firm the highest long-term benefit. The payback method also violates the third criterion of a good investment-early benefits are preferred to later benefits-because a benefit received in the first year is given the same weight as one received in the last period. A method needs to be devised to compensate the investor for having to wait to receive those distant benefits. The payback method, though quick and easy, does not always give managers a way to consistently select the alternative that gives the highest net benefit to the firm, and it makes no adjustment for the timing of benefits and costs.

**Rate of Returns (RR)**

Estimated as the ratio of profits net taxes and depreciation on capital employed

RR = __Profits (net of taxes & depreciation)__

Capital used

Decision Rule: Project is considered worthwhile for choice and acceptance if the rate of

Returns (RR) is greater or equal to the cost of capital employed.

RR could be calculated using different approaches.

Net profits as Initial profit i.e profit in the 1st year of operating the project

**OR**

Average profit i.e over the life span of the project or profit in the first 5 -10 years of the project.

Capital: Initial capital or average capital employed

**Disadvantages of using Rate of Returns criterion**

- Fails to account for the time value of the capital outlays and earnings i.e a shilling earned is also assumed to be the same value in future which is not so.
- It underestimates yield if it fails to take into consideration the earnings and capital employed throughout the life span of the project.
- Cannot be used to compare internal investments (within the farm) and external investments (outside the farm) which yield over time. It is therefore difficult to use the rate of returns measures to determine the worthiness of investment and compare it with other investment opportunities

** **

**DISCOUNTED MEASURES**

**Net present value**

In finance, the net present value (NPV) or net present worth (NPW) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows of the same entity. In the case when all future cash flows are incoming and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). NPV is a central tool in discounted cash flow analysis, and is a standard method for using the time value of money to appraise long-term projects.

Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is the sum of all terms,

where

*t* – the time of the cash flow

*i* – the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.); the opportunity cost of capital

*R _{t}* – the net cash flow (the amount of cash, inflow minus outflow) at time

*t.*

**NPV in decision making**

If… |
It means… |
Then… |

NPV > 0 | the investment would add value to the firm | the project may be accepted |

NPV < 0 | the investment would subtract value from the firm | the project should be rejected |

NPV = 0 | the investment would neither gain nor lose value for the firm | We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria, e.g. strategic positioning or other factors not explicitly included in the calculation. |

**Example**

A corporation must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years. This project will have an immediate cash outflow of $100,000 (which might include machinery and employee training costs). Other cash outflows for years 1–6 are expected to be $5,000 per year. Cash inflows are expected to be $30,000 each for years 1–6. All cash flows are after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. The present value (PV) can be calculated for each year:

Year |
Cash flow |
Present value |

T=0 | -$100,000 | |

T=1 | $22,727 | |

T=2 | $20,661 | |

T=3 | $18,783 | |

T=4 | $17,075 | |

T=5 | $15,523 | |

T=6 | $14,112 |

The sum of all these present values is the net present value, which equals $8,881.52. Since the NPV is greater than zero, it would be better to invest in the project than to do nothing, and the corporation should invest in this project if there is no mutually exclusive alternative with a higher NPV.

# Internal rate of return

The internal rate of return (IRR) is a rate of return used in capital budgeting to measure and compare the profitability of investments. In the context of savings and loans the IRR is also called the effective interest rate. The term *internal* refers to the fact that its calculation does not incorporate environmental factors (e.g., the interest rate or inflation). The internal rate of return on an investment or project is the “annualized effective compounded return rate” or “rate of return” that makes the net present value of all cash flows (both positive and negative) from a particular investment equal to zero.

In more specific terms, the IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment. Internal rates of return are commonly used to evaluate the desirability of investments or projects. The higher a project’s internal rate of return, the more desirable it is to undertake the project. Assuming all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first.

A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital. Investment may be limited by availability of funds to the firm and/or by the firm’s capacity or ability to manage numerous projects. Because the internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield of an investment. This is in contrast with the net present value, which is an indicator of the value or magnitude of an investment.

## Calculation

Given the (period, cash flow) pairs (*n*, *C _{n}*) where

*n*is a positive integer, the total number of periods

*N*, and the net present value NPV, the internal rate of return is given by

*r*in:

If an investment may be given by the sequence of cash flows

Year (n) |
Cash Flow (C)_{n} |

0 | -4000 |

1 | 1200 |

2 | 1410 |

3 | 1875 |

4 | 1050 |

Then the IRR *r* is given by

.

In this case, the answer is 14.3%.

### Decision Criterion

If the IRR is greater than the cost of capital, accept the project. If the IRR is less than the cost of capital, reject the project.

## Problems with using internal rate of return

As an investment decision tool, the calculated IRR should not be used to rate mutually exclusive projects, but only to decide whether a single project is worth investing in.IRR assumes reinvestment of interim cash flows in projects with equal rates of return (the reinvestment can be the same project or a different project). Therefore, IRR overstates the annual equivalent rate of return for a project whose interim cash flows are reinvested at a rate lower than the calculated IRR. This presents a problem, especially for high IRR projects, since there is frequently not another project available in the interim that can earn the same rate of return as the first project.

Since IRR does not consider cost of capital, it should not be used to compare projects of different duration. Modified Internal Rate of Return (MIRR) does consider cost of capital and provides a better indication of a project’s efficiency in contributing to the firm’s discounted cash flow.

**Benefit: Cost Ratio Analysis**

In comparing alternative investment for decision making on choice of the investments, there is a need to compare the costs and benefits in relation to the time of the streams, by discounting method. One of such measures of project worth is the Benefit/Cost ratio or the

Cost/Benefit ratio. This is the ratio of the discounted stream of project benefits to the discounted stream of project costs. A Benefit /cost ratio greater than one implies a potentially viable project and such project could be chosen. Often used in economic analysis to measure the social benefits of investments.

Benefit: Cost = __Present Values of Benefits __

Present Values of Costs

**Decision Rule:**

(i) B: C < 1 implies PVB < PVC. The cost may not be recovered. It is better not to invest but to save the money at the existing interest rate. Note that the absolute value of Benefit: Cost ratio depends on the interest rate charges. The greater the rate of interest the less the

Benefit: Cost

(ii) B: C > 1 implies PVB > PVC. Accept the project

(i) B: C = 1 implies PVB = PVC. Break-even point