PRESENT WORTH ANALYSIS

 

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• Present Worth Method of comparison

  In this method of comparison the cash flow of each alternative will be reduced to time zero by assume that interest rate I then depending on the type of decision the best alternative will be selected by comparing the present what amount of the alternatives.

  The sign of various amounts at different points in time in a cash flow diagram is to be decided based on the type of the decision problem.

  In a cost dominated cash flow diagram the cost (outflows) will be assigned with positive sign and the profit revenue Salvage value all the inflows etc. will be assigned with negative sign.

  In a revenue/profit dominated cash flow diagram the profit revenue Salvage value or inflows to an organisation will be assigned with positive signs. The cost or outflows will be assigned with negative sign.

  In case the decision is to select the alternative with the minimum cost than alternative with the least present worth amount will be selected. On the other hand if the decision is to select alternative with the maximum profit then all alternative with the maximum present worth will be selected.

  • REVENUE-DOMINATED CASH FLOW DIAGRAM

    A generalized revenue-dominated cash flow diagram to demonstrate the present worth method of comparison is presented in below figure.

    
    
    
    
    
    
    

    
    

    In figure P represent an initial investment and Rj the net revenue at the end of the jth year. The interest rate is i, compounded anually. S is the salvage value at the end of the nth year.

    To find the present worth of the above cash flow diagram for a given interest rate, the formula is

    $$ PW(i) = -P + r1/[1/(1+i)^1] + R2/[1/(1+i)^2] + ... + Rj/[1/(1+i)^j] + ... + Rn/[1/(1+i)^n] + s/[1/(1+i)^n] $$

    In this formula, Expenditure is assinged a negative sign and revenues are assingned a positive sign.

    If we have some more alternatives which are to be compared with this alternative, then the corresponding present worth amounts are to be computed and compared. FInally, the alternative with the maximum present worth amount should be selected as the best alternative.

  • COST- DOMINATED CASH FLOW DIAGRAM

    A generalized cost-dominated cash flow diagram to demonstrate the present worth method of comparison is presented in below figure.

    
    
    

    
    

    In figure P represent an Initial investment, Cj the net cost of operation and maintenance at the end of the Jth year, and S the salvage value at the end of the nth year.

    To compute the present worth amount of the above cash flow diagram for a given interest rate i, we have the formula

    $$ PW(i) = P + C1/[1/(1+i)^1] + C2/[1/(1+i)^2] + ... + Cj/[1/(1+i)^j] + ... + Cn/[1/(1+i)^n] - S/[1/(1+i)^n] $$

    In the above formula, the expenditure is assinged a positive sign and the revenue a negative sign.

    If we have some more allternatives which are to be compared with this alternative, then the corresponding present worth amounts are to be computed and compared. FInally, the alternative with the minimum present worth amount should be selected as the best alternative.

  • EXAMPLES

  • Q1

    Alpha industry is palnning to expand its production operation. It has identified three different technologies for meeting the goal. the initial outlay and annual revenues with respect to each of the technologies are given in below table. Suggest the best technology which is to be implemented based on the present worth method of comparison assuming 20% interest rate, compounded annually.

    	Initial outlay	Annual revenue	Life(years)
    Technology 1	12,00,000	4,00,000	10
    Technology 2	20,00,000	6,00,000	10
    Technology 3	18,00,000	5,00,000	10

    • Solution

      • TECHNOLOGY 1

      initial outlay = 12,00,000

      Annual revenue = 4,00,000

      interest rate = 20%

      life = 10 years

      PW(20%) = -12,00,000 + 4,00,000(P/A,20%,10)

      = -12,00,000 + 4,00,000 x 4.1925

      = -12,00,000 + 16,77,000

      = 4,77,000

      • TECHNOLOGY 2

        initial outlay = 20,00,000

        Annual revenue = 6,00,000

        interest rate = 20%

        life = 10 years

        PW(20%) = -20,00,000 + 6,00,000(P/A,20%,10)

        = -20,00,000 + 6,00,000 x 4.1925

        = -20,00,000 + 25,15,500

        = 5,15,500

      • TECHNOLOGY 3

        initial outlay = 18,00,000

        Annual revenue = 5,00,000

        interest rate = 20%

        life = 10 years

        PW(20%) = -18,00,000 + 5,00,000(P/A,20%,10)

        = -20,00,000 + 5,00,000 x 4.1925

        = -20,00,000 + 20,96,250

        = 2,96,250

  • Q2

  • An engineer has two bids for an elevator to be installed in a new building. The details of the bids for the elevators are as follows:

  • 	Initial cost	Service Life(years)	Annual operation and maintenance cost
    Alpha Elevator inc.	4,50,000	15	27,000
    Beta Elevator inc.	5,40,000	15	28,500

  • Determine which bid should be accepted, based on the present worth method of comparison assuming 15% interest rate, compounded annually.

  • SOLUTION

  • ALPHA ELEVATOR INC.

    initial cost p = 4,50,000

    Annual cost = 27,000

    life = 15 years

    interst rate = 15%

    PW(15%) = 4,50,000 + 27,000(P/A,15%,15)

    = 4,50,000 + 27,000 x 5.8474

    = 6,07,879.80

  • BETA ELEVATOR INC.

    initial cost p = 5,40,000

    Annual cost = 28,500

    life = 15 years

    interst rate = 15%

    PW(15%) = 5,40,000 + 28,500(P/A,15%,15)

    = 4,50,000 + 27,000 x 5.8474

    = 7,06,650.90

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