Should We Purchase That New Copier?
Campus Print Shop is thinking of purchasing a new, modern
copier that automatically collates pages. The machine would
cost $22,000 cash. A service contract on the machine, considered
a must because of its complexity, would be an additional
$200 per month. The machine is expected to last eight
years and have a resale value of $4,000. By purchasing the new
machine, Campus would save $450 per month in labor costs
and $100 per month in materials costs due to increased efficiency.
Other operating costs are expected to remain the same.
The old copier would be sold for its scrap value of $1,000.
Campus requires a return of 14% on its capital investments.
1. As a consultant to Campus, compute:
a. The payback period.
b. The unadjusted rate of return.
c. The net present value.
d. The internal rate of return.
2. On the basis of these computations and any qualitative
considerations, would you recommend that Campus purchase
the new copier?
To determine whether purchasing the new copier is a good financial decision for Campus Print Shop, we need to calculate several financial metrics. These metrics include the payback period, the unadjusted rate of return, the net present value, and the internal rate of return. Let's go through each calculation step by step:
1a. The Payback Period:
The payback period is the time it takes for the initial investment to be recovered. To calculate the payback period, divide the initial investment by the monthly cash inflow.
Initial Investment: $22,000
Monthly Cash Inflow: ($450 labor cost savings + $100 material cost savings) = $550
Payback Period = Initial Investment / Monthly Cash Inflow
Payback Period = $22,000 / $550
Payback Period ≈ 40 months
Therefore, the payback period for the new copier is approximately 40 months.
1b. The Unadjusted Rate of Return:
The unadjusted rate of return measures the annual profit earned as a percentage of the initial investment. To calculate the unadjusted rate of return, divide the average annual profit by the initial investment.
Average Annual Profit = (Annual Cash Inflow - Annual Cash Outflow) / 2
Annual Cash Inflow = $550/month * 12 months = $6,600
Annual Cash Outflow = $200/month * 12 months = $2,400
Average Annual Profit = ($6,600 - $2,400) / 2 = $2,100
Unadjusted Rate of Return = Average Annual Profit / Initial Investment * 100
Unadjusted Rate of Return = $2,100 / $22,000 * 100
Unadjusted Rate of Return ≈ 9.55%
Therefore, the unadjusted rate of return for the new copier is approximately 9.55%.
1c. The Net Present Value:
The net present value considers the time value of money and calculates the present value of all future cash inflows and outflows. To calculate the net present value, we need to discount the cash flows using the required return on capital (14%) and sum them up.
Net Present Value = PV(Cash Inflows) - PV(Cash Outflows)
Cash Inflows:
The monthly labor and material cost savings are $550, which results in an annual cash inflow of $6,600.
PV(Cash Inflows) = $6,600 / (1 + 0.14)^1 + $6,600 / (1 + 0.14)^2 + ... + $6,600 / (1 + 0.14)^8
Cash Outflows:
The initial investment is $22,000, and the monthly service contract cost is $200.
PV(Cash Outflows) = $22,000 + ($200 * 12) / (1 + 0.14) + ($200 * 12) / (1 + 0.14)^2 + ... + ($200 * 12) / (1 + 0.14)^8 + $1,000 / (1 + 0.14)^8
Subtract the present value of cash outflows from the present value of cash inflows to get the net present value.
1d. The Internal Rate of Return:
The internal rate of return is the discount rate that makes the net present value of the investment equal to zero. This rate indicates the annual return on investment.
To calculate the internal rate of return, solve for the discount rate that makes the net present value zero using trial and error or financial software.
2. Qualitative Considerations:
Consider qualitative factors such as the copier's technology, the printing needs of Campus Print Shop, potential efficiency gains, service reliability, and any other relevant aspects to complement the quantitative analysis.
After calculating all the financial metrics and considering qualitative factors, you can make a recommendation on whether Campus should purchase the new copier based on the overall evaluation.
It is important to note that the financial calculations provided above are based on the given information and assumptions. To get accurate results and make an informed decision, it is advisable to conduct a comprehensive financial analysis considering all relevant factors and seeking advice from professionals if needed.
To analyze whether Campus Print Shop should purchase the new copier, we will calculate the payback period, unadjusted rate of return, net present value, and internal rate of return. These metrics will help us evaluate the financial feasibility of the investment.
1. Payback Period:
The payback period is the time required for the initial investment to be recovered. To calculate the payback period, we need to determine the cumulative cash inflow each year until it equals or exceeds the initial investment.
Year 1: Savings in labor costs = $450/month * 12 months = $5,400
Year 2: Savings in labor costs = $450/month * 12 months = $5,400
Year 3: Savings in labor costs = $450/month * 12 months = $5,400
Year 4: Savings in labor costs = $450/month * 12 months = $5,400
Year 5: Savings in labor costs = $450/month * 12 months = $5,400
Year 6: Savings in labor costs = $450/month * 12 months = $5,400
Year 7: Savings in labor costs = $450/month * 12 months = $5,400
Year 8: Savings in labor costs = $450/month * 12 months = $5,400
Total cumulative cash inflow over 8 years = $5,400 x 8 = $43,200
Payback period = Initial investment / Annual cash inflow
Payback period = $22,000 / $5,400 = 4.074 years
2. Unadjusted Rate of Return:
The unadjusted rate of return is calculated by dividing the average annual profit by the initial investment.
Average annual profit = (Savings in labor costs + Savings in materials costs + Resale value of old copier) / Number of years
Average annual profit = ($450/month + $100/month + $4,000 + $1,000) / 8 = $825
Unadjusted Rate of Return = Average annual profit / Initial investment
Unadjusted Rate of Return = $825 / $22,000 ≈ 0.0375 or 3.75%
3. Net Present Value (NPV):
To calculate the net present value, we need to discount the cash inflows to their present value and subtract the initial investment.
Annual cash inflow = Savings in labor costs + Savings in materials costs + Resale value of old copier
Annual cash inflow = $450/month + $100/month + $4,000 / 8 = $693.75
NPV = Present value of cash inflows - Initial investment
NPV = ($693.75 / (1 + 0.14)^1) + ($693.75 / (1 + 0.14)^2) + ... + ($693.75 / (1 + 0.14)^8) - $22,000
Using a financial calculator or spreadsheet software, the NPV is calculated as follows:
NPV ≈ -$4,478.02
4. Internal Rate of Return (IRR):
The internal rate of return is the discount rate that makes the NPV of cash inflows equal to zero. We can calculate this using a financial calculator or spreadsheet software, which yields the following result:
IRR ≈ 11.46%
2. Based on these computations and qualitative considerations, it is recommended to analyze the results.
a. Payback Period: The payback period of approximately 4.074 years indicates that the initial investment will be recovered within that time frame.
b. Unadjusted Rate of Return: The unadjusted rate of return of 3.75% suggests a relatively low profit compared to the initial investment.
c. Net Present Value: The negative NPV of -$4,478.02 indicates that the investment is not expected to generate a positive return at a 14% discount rate.
d. Internal Rate of Return: The calculated IRR of approximately 11.46% is below the required rate of return, indicating that the investment may not meet Campus Print Shop's 14% return expectation.
Considering both the quantitative results and qualitative factors, such as the potential efficiency and convenience of the new copier, it is recommended to further assess the financial feasibility, explore alternative options, or negotiate a better deal before making a final decision.