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Capital Investment Analysis and Unequal Proposal Lives:

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Learning Objectives of this article:

  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:

  1. Average rate of return method
  2. Cash payback method
  3. Net present value method
  4. Internal rate of return

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.

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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

 

Financial Accounting Topics


  Introduction to Accounting
 ----------------------------------------------------------------------------
  Transactions and Accounting Equation
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  Analysis of Business Transactions
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  Journal, Ledger and Trial Balance
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  Accounting for Bills of Exchange
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  Special Journals
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  Cash Book
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Bank Reconciliation Statement
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  Final Accounts
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  Work Sheet
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  Capital and Revenue Items
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  Valuation of Inventories
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  Accounts of Non-profit Making Organizations
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  Statement of Cash Flows
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  Accounting Ratios Analysis
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  Depreciation, Provisions and Reserves
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  Accounting Dictionary
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  Financial Calculators
 
 
 
Managerial Accounting Topics

  Financial Statements
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  Cost Volume Profit Relationship
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  Variable Costing System
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  Materials and Inventory Cost Control
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  Activity Based Costing System
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  Standard Costing and Variance Analysis
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  Balanced Scorecard
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  Capital Investment Analysis/Capital Budgeting
 

 

 

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