**Chapter 12 Notes**

**Overview**

- Compute an unadjusted rate of return
- Understand how to use a present-value table
- Compute an internal rate of return
- Understand the payback period theory

**The Time Value of Money**

These computations are used to evaluate the use of money. This will provide a guide to assist the manager in evaluating the different alternatives regarding the resources an organization has on how money should be spent.

**Unadjusted Rate of Return**

This is an unsophisticated method used to determine the return on investment. There are two ways to calculate the unadjusted rate of return.

**1.** **Average Annual Net Income / Original Investment Amount = Rate of Return**

**OR**

**2.** **Average Annual Net Income / Average Investment Amount = Rate of Return**

Given these assumptions:

Average Annual Net Income = $ 200,000

Original Investment amount = $ 600,000

Unrecovered asset cost at the end of the useful life = $ 50,000

An example using the original investment amount, number 1 above:

If the average annual net income is $ 200,000 and the original investment amount is $ 600,000, then

**$200,000 / $600,000 = 33% Unadjusted rate of return**

An example using the average investment amount, number 2 above:

If the average annual net income is $ 200,000, the unrecovered asset cost at the end of the useful life is $ 50,000 and the original investment amount is $600,000, then:

Step 1 – Compute the average investment amount for the unrecovered asset cost.

At the Beginning of estimated useful life = $600,000

At end of useful life = $ 50,000

Sum $650,000

Divided by 2 = $325,000 = average investment amount

$200,000 / $325,000 = 61.53% Unadjusted rate of return

**Present Value Analysis**

The concept of present value analysis is based on the time value of money. The value of a dollar today is more than the value in a future period. The further in the future you look, the less that dollar will be worth.

Using examples in Appendix 12 – A in the textbook.

**Internal Rate of Return – IRR**

This is another return on investment method. It uses a discounted cash flow technique. The IRR is the rate of interest that discounts future net inflows from the proposed investment down to the amount invested. This method is similar to the previous methods but adds the concept of time to the calculation. The IRR calculates from period to period, whereas the other two methods rely on average investments.

To calculate IRR:

Assumptions:

- Find the initial cost of the investment
- Find the estimated annual net cash inflow the investment will generate
- Find the useful life of the asset

Steps:

- Divide the initial cost of the investment by the estimated annual net cash inflow it will generate. The answer is a ratio.
- Use the Look Up Table. Find the number of periods.
- Look across the line for the number of periods and find the column that approximates the ratio computed in Step 1.

Initial cost of the investment = $16,950

Estimated Annual net cash inflow the investment will generate = $3,000

Useful life of the asset – 10 years

$16,950 / $3,000 = 5.650

Using the Look Up Table for Present Value of Annuities on Page 404, match the # of years along left column with where 5.650 intersects, see the interest percentage.

**Payback Period**

The Payback Period is the length of time required for cash coming in from an investment to equal the amount of cash originally spent when the investment was purchased.

The Payback Period concept is used in evaluating whether to invest in plant and/or equipment. We must establish if it’s worth spending the money and to do that, you need to determine a best case and worst case scenario as the calculation is based on assumptions of some type of return.

Please see the Excel spreadsheet with a detailed explanation of the calculation of the payback period.