Question

IBX Pty Ltd is considering the purchase of a new machine that is expected to save the company $89,000 at the end of each year in reduced wages.

The machine costs $270,000, plus another $14,000 to be installed. It is expected to last for five years after which it can be sold as scrap for $42,000. Operating expenses (such as fuel and maintenance) are $8,000 pa.

a)Determine the annual net cash flows of this investment (ignore the effect of taxes). Enter the information in the following table. Indicate whether cash flows are + or -:

Time 0 1 2 3 4 5

Net Cash Flow _____________ __________ ___________ ________ __________ _________________

b)Calculate the NPV if the required rate of return is 15% pa. Give your answer in dollars and cents to the nearest cent. NPV15% = $_________

c)Calculate the NPV if the required rate of return is 17% pa. Give your answer in dollars and cents to the nearest cent. NPV17% = $__________

Answer 1

Part a)

The annual net cash flows of the investment are calculated as below:

Cash Flow Year 0 = - (Cost of Machine + Installation Cost) = -(270,000 + 14,000) = -$284,000

Cash Flow Year 1 to Year 4 = Annual Savings - Annual Operating Expenses = 89,000 - 8,000 = $81,000

Cash Flow Year 5 = 81,000 + Scrap Value = 81,000 + 42,000 = $123,000

____

Tabular Representation:

Time	0	1	2	3	4	5
Net Cash Flow	-$284,000	$81,000	$81,000	$81,000	$81,000	$123,000

____

Part b)

The NPV is calculated as follows:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Required Rate of Return)^1 + Cash Flow Year 2/(1+Required Rate of Return)^2 + Cash Flow Year 3/(1+Required Rate of Return)^3 + Cash Flow Year 4/(1+Required Rate of Return)^4 + Cash Flow Year 5/(1+Required Rate of Return)^5

Substituting values in the above formula, we get,

NPV (15%) = -284,000 + 81,000/(1+15%)^1 + 81,000/(1+15%)^2 + 81,000/(1+15%)^3 + 81,000/(1+15%)^4 + 123,000/(1+15%)^5 = $8,405.99 or $8,406

____

Part c)

The NPV is determined as below:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Required Rate of Return)^1 + Cash Flow Year 2/(1+Required Rate of Return)^2 + Cash Flow Year 3/(1+Required Rate of Return)^3 + Cash Flow Year 4/(1+Required Rate of Return)^4 + Cash Flow Year 5/(1+Required Rate of Return)^5

Substituting values in the above formula, we get,

NPV (17%) = -284,000 + 81,000/(1+17%)^1 + 81,000/(1+17%)^2 + 81,000/(1+17%)^3 + 81,000/(1+17%)^4 + 123,000/(1+17%)^5 = -$5,696.29