Question 2 (10 Marks) A business is considering a proposal to install a new devi

Question

Question 2 (10 Marks) A business is considering a proposal to install a new device in their small factory. The device costs $23,000 and will save the business $400 per month in expenses. Assume that the device will last for 8 years, that the savings remain constant and are at the end of each month. The first saving commences in one month from now. The effective annual interest rate is 12.6825%, and the effective monthly interest rate is 1%. a) Calculate the Net Present Value (NPV) of the proposal. (4 marks) b) Calculate the payback period for the device (in years to two decimal places) (3 marks)

Explanation / Answer

Answer a.

Cost of Device = $23,000
Monthly Cost Saving = $400
Monthly Interest Rate = 1%
Period of Proposal = 8 years or 96 months

NPV = -$23,000 + $400 * PVIFA(1%, 96)
NPV = -$23,000 + $400 * (1 - (1/1.01)^96) / 0.01
NPV = -$23,000 + $400 * 61.52770
NPV = $1,611.08

So, NPV of this proposal is $1,611.08

Answer b.

Payback Period = Cost of Device / Monthly Cost Saving
Payback Period = $23,000 / $400
Payback Period = 57.50 months

Number of years = 57.50 / 12
Number of years = 4.79 years

So, payback period of this device is 4.79 years.

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