Question

The modern Age Copier Company is considering purchasing a copier for use by customers. Data for the copier under consideration is reflected in the table below. The copier is expected to last 8 years. The tax rate is 30%. The Company will not accept a project with a return of less than 12% Copier Equipment Cost $64,000 Annual Revenues $80,000 Annual Paper Costs $33,100 Annual Maintenance Costs $20,000 Annual Depreciation $ 8,000 All of the items in the table above are taxable or tax deductible except for the initial cost of the copier Equipment. Although the initial cost is not tax deductible, the initial cost will be subject to depreciation. Assume straight line depreciation with no residual value. 1. Should Modern Age Copier undertake this project? Explain and support with analysis. 2. Compute the Payback period (Round to one decimal place) Show analysis.

Answer 1

Question 1:

Since nothing had been mentioned in the question about the method to be used to analyse the project's profitability, the NPV method has been used since it is the best method for this purpose. The NPV method measures the overall profitability of the project by finding out the difference between the sum of discounted cash flows of the project from the initial cost incurred for the project. If this difference gives a positive figure, the project is profitable. If it is a negative figure, the project should not be chosen because it will give a loss. The NPV method is best because it quantifies the profit/loss possible from the project. The other methods like irr, payback period and discounted payback period do not quantify the profit or loss.

To find the sum of discounted cash flows, we have to find the annual cash flow after tax as shown below:

Particulars	$
Annual revenue	80000
(-) annual paper costs	(33100)
(-) annual maintenance costs	(20000)
(-) annual depreciation	(8000)
Annual profit	18900
(-) tax@30%	5670
Profit after tax	13230
(-) depreciation	8000
Cash flow after tax	21230

Note: depreciation had been added back because it is a non cash expense. Non cash expenses have to be added back to arrive at the cash flow after tax because it was already reduced from revenue to find the tax liability.

Next, we have to find the cumulative discount factor. We do not have to multiply the yearly discount factor to the yearly cash flows after tax separately because the yearly cash flows are same throughout the years. Sum of discounted cash flows can be found by multiplying the cumulative discount factor for 8 years with the yearly cash flow after tax. Discount factors can be found by referring a discount factor table.

Cumulative discount factor for 8 years at 12% interest rate.

Year	discount factor
1	0.8929
2	0.7972
3	0.7118
4	0.6355
5	0.5674
6	0.5066
7	0.4523
8	0.4039
Cumulative discount factor for 8 years@12%	4.9676

Sum of discounted cash flows= 21230*4.9676= $105462.148

Initial cost= $64000

NPV= Sum of discounted cash flows- initial cost

=105462.148-64000= $41462.148= $41462.1( rounded off)

NPV analysis shows high profits, therefore the project should be undertaken

Question 2:

Payback period is the number of years it takes for the company to realise the amount invested in the project. However, this method ignores the time value of money and hence is not the most accurate method for analysis of a project.

Payback period= initial investment/ yearly cash flow after tax

= 3.0146 years= 3 year ( rounded off to one decimal)

Please note that the above formula cannot be used when the yearly cash flows are not same.