Home » Capital Investment Analysis » Capital Investment Analysis and Unequal Proposal Lives

# Capital Investment Analysis and Unequal Proposal Lives:

 New Page 1

1. How alternative proposals are compared when proposals have unequal lives?

## Proposals with Unequal Useful Lives:

There are various methods to evaluate capital investment proposals. Some use present values of the cash flows and some ignore present value concept. If you want to read these methods, click on a link below:

In these articles, we have assumed that all the alternative proposals have equal useful lives. But in practice, however, alternative proposals may have unequal lives. For example, one proposal may have a useful life of 5 years and the other 7 years. Choosing a proposal from various alternatives require more consideration when they have unequal lives. This article explains how to compare alternative proposals when proposals have different useful lives.

The following example uses the net present value method to compare the two alternative proposals with different useful lives:

## Example:

Assume that alternative proposals X and Y are being compared. Each proposal requires an initial investment of \$100,000 and has the following expected cash flow and useful life:

 Year Proposal X Proposal Y 1 \$30,000 \$30,000 2 \$30,000 \$30,000 3 \$25,000 \$30,000 4 \$20,000 \$30,000 5 \$15,000 \$30,000 6 \$15,000 --- 7 \$10,000 --- 8 \$10,000 ---

if the desired rate of return is 10%, each proposals net present value could be determined as follows:

Net Present Value Analysis:

Proposal X   Proposal Y
 Year Present Value of \$1 at 10% Net Cash Flow Present Value of Net Cash Flow 1 .909 \$30,000 \$27,270 2 .826 \$30,000 \$24,780 3 .751 \$25,000 \$18,775 4 .683 \$20,000 \$13,660 5 .621 \$15,000 \$9,315 6 .564 \$15,000 \$8,460 7 .513 \$10,000 \$5,130 8 .467 \$10,000 \$4,670 \$155,000 \$112,060 Amount to be invested 100,000 Net present value \$12,060

 Year Present Value of Annuity of \$1 at 10% Net Cash Flow Present Value of Net Cash Flow 1-5 3.791 \$30,000 \$113,730 Amount to be invested 100,000 Net present value \$13,730

Because of the unequal useful lives of the two proposals, the net present values determined above are not comparable. To make them comparable for the analysis, the proposals can be adjusted to end at the same time. This can be done by assuming that proposal X is to be terminated at the end of five years and the asset sold. This assumption require that the residual value of Proposal X be estimated at the end of five years and that this value be included as a cash flow at that date. Both proposals will then cover five years, and net present value analysis can be used to compare the two proposals over the same five-year period.

To illustrate, assume the Proposal X has an estimated residual value of \$40,000 at the end of year 5. For Proposal X, the excess of the present value over the amount to be invested is \$18,640 for a 5-year life, as shown below:

 Year Present Value of \$1 at 10% Net Cash Flow Present Value of Net Cash Flow 1 .909 \$30,000 \$27,270 2 .826 \$30,000 \$24,780 3 .751 \$25,000 \$18,775 4 .683 \$20,000 \$13,660 5 .621 \$15,000 \$9,315 5 .621 R.V \$40,000 24,840 \$160,000 \$118,640 Amount to be invested 100,000 Net present value \$18,640

If a five year live is used for both proposals, the net present value for Proposal X exceeds the net present value for Proposal Y by \$4,910 (\$18,640 - \$13,730). Therefore, Proposal X may be viewed as the more attractive of the two proposals.

New Page 2

## More study material from this topic:

 Methods for the evaluation of capital investment analysis Average rate of return or accounting rate of return method Cash payback method Net present value method Internal rate of return method Simple interest Future value of a single sum Future value of an annuity Present value of a single sum Present value of an annuity Qualitative consideration in capital investment analysis Capital investment analysis and unequal proposal lives Capital rationing decision process Difference between simple interest and compound interest Difference between nominal and effective interest rate Future value of \$1 table Present value of \$1 table Present value of ordinary annuity table Future value of ordinary annuity table

A D V E R T I S E M E N T