Question #229024

4.3 REQUIRED

Study the information given below and answer the following questions:

4.3.1 Calculate the net present value. (7)

4.3.2 Should ABC Limited consider acquiring the machine? Explain. (1)

4.3.3 Calculate the value of the initial investment at the end of five years, if it is

invested at a rate of 12%.

(2)

INFORMATION

The project manager of ABC Limited is contemplating the import of a machine in order to expand

the production capacity at one of its projects. The estimated cost of the machine is R500 000 and

the revenues from the sales it is expected to generate are R350 000 per year for four years. The

cash costs associated with the project are estimated at R150 000 per year. The machine is

expected to have a scrap value of R50 000. The cost of capital is 12%.

Expert's answer

**Solution:**

4.3.1). Net present value:

Net Present Value = "\\sum \\frac{Cashflow}{(1 + r)^{t} } - Initial \\; Investment"

Where: r = Discount rate = 12% or 0.12

Â Â Â Â Â Â Â Â Â Â Â Â t = Number of time periods

Net cashflows = Revenues â€“ Cash costs

Year 1 to 3 Net cashflows = 350,000 â€“ 150,000 = 200,000

Year 4 Net cashflows = (Revenues â€“ Cash costs) + Residual value = (350,000 â€“ 150,000) + 50,000 = 250,000

NPV = "\\frac{200,000}{(1 + 0.12)^{1} } +\\frac{200,000}{(1 + 0.12)^{2} } + \\frac{200,000}{(1 + 0.12)^{3} } + \\frac{250,000}{(1 + 0.12)^{4} } - 500,000"

= (178,571.43 + 159,438.78 + 142,356.05 + 158,897.52) â€“ 500,000

NPV = 639,245.78 â€“ 500,000 = 139,245.78

NPV = 139,245.78

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4.3.2). ABC Ltd should consider acquiring the machine since NPV is positive, which means that the value of the revenues is greater than the costs. Therefore, ABC Ltd will be making profits when they acquire the machine.

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4.3.3). The value of the initial investment at the end of five years:

F = P(1 + r)^{n}

Where: F = Future value of the investment =?

Â Â Â Â Â Â Â Â Â Â Â Â P = Initial investment = 500,000

Â Â Â Â Â Â Â Â Â Â Â Â r = Discount rate = 12% or 0.12

Â Â Â Â Â Â Â Â Â Â Â Â t = Number of time period

Â

F = 500,000 (1 + 0.12)^{5} = 500,000 "\\times" 1.762342 = 881,170.80

The value of initial investment at the end of five years = 881,170.80

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