a.
Compute the
a.
Explanation of Solution
Net present value method:
Net present value method is used to compare the initial
Calculate the net present value of the equipment:
Particulars | Amount ($) |
Present value of annual net cash flows (1) | $4,520,000 |
Present value of residual value (2) | $64,400 |
Total present value | $4,584,400 |
Amount to be invested | ($3,000,000) |
Net present value | $1,584,400 |
Table (1)
Hence, the net present value of the equipment is $1,584,400.
Working Note 1:
Calculate the present value of annual net cash flows:
Working Note 2:
Calculate the present value of annual net cash flows:
b.
Compute the net present value of the equipment, assuming 12% desired
b.
Explanation of Solution
Calculate the net present value of the equipment:
Estimated Annual Net Cash Flow | |||
Particulars | Amount ($) | Amount ($) | Amount ($) |
Estimated annual net cash flows | $400,000 | $600,000 | $800,000 |
Multiply: Present value factor from Exhibit 5 | |||
Present value of annual net cash flows | $2,260,000 | $3,390,000 | $4,520,000 |
Present value of residual value (2) | $64,400 | $64,400 | $64,400 |
Total present value | $2,324,400 | $3,454,400 | $4,584,400 |
Amount to be invested | ($3,000,000) | ($3,000,000) | ($3,000,000) |
Net present value | ($675,600) | $454,400 | $1,584,400 |
Table (2)
Hence, the net present value of the equipment for annual net cash flow of $400,000 is ($675,600), for annual net cash flow of $600,000 is $454,400 and for annual net cash flow of $800,000 is $1,584,400.
c.
Compute the net present value of the equipment, assuming 15% desired rate of return for the given annual net cash flows.
c.
Explanation of Solution
Calculate the net present value of the equipment:
Estimated Annual Net Cash Flow | |||
Particulars | Amount ($) | Amount ($) | Amount ($) |
Estimated annual net cash flows | $400,000 | $600,000 | $800,000 |
Multiply: Present value factor from Exhibit 5 | |||
Present value of annual net cash flows | $2,007,600 | $3,011,400 | $4,015,200 |
Present value of residual value (3) | $49,400 | $49,400 | $49,400 |
Total present value | $2,057,000 | $3,060,800 | $4,064,600 |
Amount to be invested | ($3,000,000) | ($3,000,000) | ($3,000,000) |
Net present value | ($943,000) | $60,800 | $1,064,600 |
Table (3)
Hence, the net present value of the equipment for annual net cash flow of $500,000 is ($811,700), for annual net cash flow of $700,000 is $417,300 and for annual net cash flow of $900,000 is $1,646,300.
Working Note 3:
Calculate the present value of annual net cash flows:
d.
Identify the minimum annual net cash flow required to generate a positive net present value.
d.
Explanation of Solution
Calculate the minimum annual net cash flows:
Hence, the minimum annual net cash flow required to generate a positive net present value is $519,575.
e.
Interpret the results in parts (a), (b) and (c).
e.
Explanation of Solution
Every business desires to get maximum profit with minimum investment. The net cash flow of $800,000 is generated from the investment which has a present value of $1,584,400. This clearly indicates the management could invest in the equipment. However, when there is a decrease in the annual net cash flows there is also a drastic decrease in the present value of the equipment. The annual net cash flow must be above $519,575 to generate a profit by the company.
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