To find: The period when the machine must be purchased.
Introduction:
The variations between the present value of the
Answer to Problem 13QP
The company should purchase a machine at 2 years from the present at which the net present value should be high.
Explanation of Solution
Given information:
The company of Person X is planning to make its investment in a new machine. The new machine increases the cash flow by $273,000 per year. Person X has a belief that the technology that is utilized in the machine has a ten year life, it means no matter when the machine is purchased, it will be obsolete in ten years from now.
The current price of the machine is $1,400,000. There will be a decline in the machine to $95,000 for a year until it reaches $925,000. The required
Formula to calculate the net present value:
Note: The net present value is calculated by the above formula and this formula is used if the machine is bought today. PVIFA is the present value interest factor of an
Computation of the net present value:
Note: The value of the PVIFA at 14% for 10 years is 5.2161.
Hence, the current net present value is $23,999.57.
Note: It is not essential to buy the machine today, but it is essential to buy the machine when there is a higher net present value. It is necessary to compute the net present value every year. In order to make a right decision, the net present value for every year has to be taken at general date.
Formula to calculate the net present value:
Note: The net present value is calculated using the above formula and this formula is used only if the machine is bought today. PVIFA is the present value interest factor of an annuity.
Computation of the net present value for the Year 1:
Note: The value of PVIFA at 14% for 9 years is 4.9464.
Hence, the net present value at year 1 is $39,795.78.
Computation of the net present value for the Year 2:
Note: The value of the PVIFA at 14% for 8 years is 4.6389.
Hence, the net present value at year 2 is $43,413.12.
Computation of the net present value for the Year 3:
Note: The value of the PVIFA at 14% for 7 years is 4.2883.
Hence, the net present value at year 3 is $37,600.
Computation of the net present value for the Year 4:
Note: The value of the PVIFA at 14% for 6 years is 3.8887.
Hence, the net present value at year 4 is $24,639.48.
Computation of the net present value for the Year 5:
Note: The value of the PVIFA at 14% for 5 years is 3.4331.
Hence, the net present value at year 5 is $6,355.15.
Computation of the net present value for the Year 6:
Note: The value of the PVIFA at 14% for 4 years is 2.9137.
Hence, the net present value at year 6 is -$59,024.22.
The company must buy the machine at 2 years from now as the net present value remains the highest.
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Chapter 24 Solutions
Fundamentals of Corporate Finance
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