Present value methods are used to evaluate the feasibility of capital investments such as the purchase of fixed assets. A good investment is one where the present value of the net cash inflows exceeds the initial cash outflow. Present value concepts can be applied to an amount or an annuity. The present value of an amount is based upon a single sum, whereas the present value of an annuity is based upon a series of payments or receipts. Consider the investment presented here. If you invest $1 at 12% for 3 years you will earn 12% for the first year and have $1.12 that amount will be invested for another year and gain 12% interest, compound interest will give you a better return than simple interest. By the end of year 3, your investment will be worth $1.40 and 4/10 cents. If simple interest had been used, the investment would be worth $1.36. That seems like a small difference for an investment of $1 but when the investment is much larger, the difference in total value is significant. This illustration shows the effects of compound interest. Notice that the principle amount increases each period as interest is added then interest is computed on the principle. Present value tables based upon the concept of compound interest are used to quickly compute the present value of a future amount. The present value of $1.40 and 4/10 cents to be received in 3 years using a 12% interest rate can be quickly determined using a present value table. The present value factor at the intersection of 12% and 3 years is 0.712. The present value of $1.40 and 4/10 cents to be received in 3 years equals $1. This is determined by multiplying the future amount of $1.40 and 4/10 cents by the table value of 0.712. An annuity is a series of equal net cash flows paid or received at fixed time intervals. The present value of an annuity is the amount of cash needed today to yield a series of equal net cash flows at fixed time intervals in the future. If you want to know the present value of an annuity of $100, you can use a present value of $1 table and multiply each payment by the corresponding table value. However, using the table for the present value of an annuity is much simpler. This illustration shows that the present value of an annuity is the sum of all the present value of $1 values. The present value of $100 received annually for 5 years at 12% can be determined by using the present value factor for each year as shown here or by using the present value of an annuity factor. This illustration shows the computation of the present value of an annuity of $1 from the present value of $1 factors. This table shows the present value of an annuity of $1. Notice that for the first year, the values are identical to the present value of $1 table. For the 5th year at 12%, they match the sum of the present value of $1 factors. The net present value method and present value index are often used in combination. The net present value method gives a $1 amount while the present value index provides an index value based upon the relationship between the present value of future cash flows and the amount to be invested. Net present value is the difference in the present value of the cash inflows and outflows associated with a project. The interest rate used in the net present value analysis is the company's minimum desired rate of return. If the present value of the cash inflows equals or exceeds the amount to be invested, the proposal is considered to be desirable under the net present value method. Equipment with an expected life of 5 years and no residual value can be purchased for $200,000. A net cash flow of $70,000 from the equipment is expected at the end of year 1. The net cash flow is expected to decline $10,000 each year except year 5 until the machine is retired. The firm expects a minimum rate of return of 10%. Net cash flow analysis can be used to determine if the equipment should be purchased. The net present value method can be used to evaluate the proposal. Since the cash inflows are unequal, each cash flow is discounted using present value tables. For the first year cash flow, $70,000 is multiplied by 0.909 the present value factor for 1 year at 10%. The net present value of the cash flows equals $2,900. This is calculated by subtracting the initial cash outflow of $200,000 from the net cash inflows of $202,900. Since the net cash inflows are greater than the net cash outflows, the net present value is positive and the equipment should be purchased. The computation to graphically illustrated here. Advantages of the net present value method are that it considers both cash flows and the time value of money. The disadvantages of this method are its complexity and the assumption that received can be reinvested at a particular rate of return. This may not be possible because of changes in interest rates. A present value index can be used to rank investments when funds are limited and the alternative proposals involve different amounts of investment. The present value index expresses the total present value of net cash flows as a percentage of the cash outflows. In the case of the preceding investment, divide it's total present value of the net cash flows of $202,900 by the initial investment of $200,000. The resulting present value index is 1.0145. An index that is greater than 1 is positive and a good investment. If the index is less than 1, this indicates the net present value is negative and, therefore, not a good investment. When considering the proposed investments shown here, proposal B has the highest present value index. Management should, however, consider the possible use of the $20,000 difference between proposal A and proposal B before making a decision. Proposal C has a negative present value as indicated by the present value index of less than 1. It should not be considered. The internal rate of return method uses present value concepts for computing the rate of return from capital investment proposals. Should management acquire equipment costing $33,530 that will provide annual cash flows of $10,000 for 5 years when management requires a 12% rate of return? The net present value of the investment is $2,520 calculated by subtracting the investment of $33,530 from the present value of the cash flows of $36,050. Since the net present value is greater than the initial investment, the rate of return is greater than 12%. The internal rate of return method calculates the actual rate of return on the investment the rate of return at which the net cash flows from the investment equal the initial investment. Because the present value of the cash flows is greater than the amount to be invested, the internal rate of return must be greater than the target amount of 12%. Using a trial and error process, the $10,000 annual cash flows for 5 periods are discounted using a 15% rate of return. Using this rate of return, the net present value of the cash flows equals the initial investment in the asset. Computing the internal rate of return is straightforward when the cash flows are equal. First, determine the present value factor to locate by dividing the amount to be invested by the equal annual net cash flows. Second, locate the present value factor in the present value of an annuity table in the row for the period matching the expected useful life. The column heading of the located factor indicates the rate of return. Presented is a proposal to purchase new equipment with an expected useful life of 7 years. What is the internal rate of return? Divide the initial outflow by the cash inflows to be received. Search for the result in the row containing the number of years of useful life and trace it to the percentage in the column where the result is found. In this case, 4.868 can be found at the intersection of 7 years and 10%. Thus, the IRR is 10%. This result is compared with the company's desired rate of return. The advantages of the internal rate of return method are that it considers cash flows and the time value of money. It also provides the ability to compare projects on a common basis. The disadvantages of this method are that more complex computations are necessary to apply the method and that the method assumes that cash can be reinvested at the internal rate or return which may not be the case.

1. Which of the following is NOT an advantage to using the net present value method of evaluating an investment proposal?

A. It considers the cash flows of the investment.

B. It considers the time value of money.

C. It can rank projects with equal lives, using the present value index.

D. It assumes cash flows can be reinvested at the minimum desired rate of return.

2. The present value index is computed as the

A. total present value of net cash flow divided by amount to be invested.

B. cost divided by amount to be invested.

C. total future value of net cash flows divided by amount to be invested.

D. None of these choices are correct.

3. A method of evaluating an investment proposal that uses present value concepts to compute the rate of return based on the investment's expected net cash flows is called the

A. net present value method.

B. internal rate of return method (IRR).

C. payback period method.

D. None of these choices are correct.