Problem 18 - Accounting

Question

Mr. Pop Popcorn Company is considering two possible investments: a delivery truck or a bagging machine. The delivery truck would cost \(\$ 36,506\) and could be used to deliver an additional 40,000 bags of popcorn per year. Each bag of popcorn can be sold for a contribution margin of \(\$ 0.35\). The delivery truck operating expenses, excluding depreciation, are \(\$ 0.32\) per mile for 16,000 miles per year. The bagging machine would replace an old bagging machine, and its net investment cost would be \(\$ 27,555\). The new machine would require 2 fewer hours of direct labor per day. Direct labor is \(\$ 14\) per hour. There are 260 operating days in the year. Both the truck and the bagging machine are estimated to have 6-year lives. The minimum rate of return is \(11 \%\). However, Mr. Pop has funds to invest in only one of the projects. a. Compute the internal rate of return for each investment. Use the table of present values of an annuity of \(\$ 1\) in the chapter. b. I?rovide a memo to management with a recommendation.

Step-by-Step Solution

Answer

Invest in the bagging machine; it has a higher IRR and a shorter payback period.

Step 1: Calculate Additional Contribution for Delivery Truck

First, calculate the additional annual revenue generated by the delivery truck. The truck allows for the delivery of an additional 40,000 bags of popcorn. Multiply the number of bags by the contribution margin per bag: \[ 40,000 \times 0.35 = \$14,000 \]

Step 2: Calculate Additional Costs for Delivery Truck

The delivery truck incurs an additional operating cost of \(\\(0.32\) per mile for 16,000 miles each year. Calculate this cost:\[ 0.32 \times 16,000 = \\)5,120 \]

Step 3: Determine Net Cash Flow for Delivery Truck

Subtract the annual operating costs from the additional revenue to find the net cash flow for the delivery truck:\[ 14,000 - 5,120 = \$8,880 \]

Step 4: Calculate Payback Period for Delivery Truck

The initial cost of the delivery truck is \$36,506. Determine the payback period using the net cash flow:\[ \frac{36,506}{8,880} \approx 4.11 \text{ years} \]

Step 5: Determine Cash Savings for Bagging Machine

Calculate the annual savings in labor costs as the new machine saves 2 hours per day. With direct labor at \(\\(14\) per hour for 260 days a year:\[ 2 \times 14 \times 260 = \\)7,280 \]

Step 6: Calculate Payback Period for Bagging Machine

The net investment cost of the bagging machine is \$27,555. Determine the payback period using the annual savings:\[ \frac{27,555}{7,280} \approx 3.78 \text{ years} \]

Step 7: Estimate Internal Rate of Return (IRR) for Truck

To estimate IRR, refer to an annuity table to find the factor closest to the value of \( \frac{36,506}{8,880} = 4.11 \). Use the useful life of 6 years to find the rate (IRR approx. 10.6%).

Step 8: Estimate Internal Rate of Return (IRR) for Bagging Machine

Using a similar approach, refer to an annuity table for the factor \( \frac{27,555}{7,280} = 3.78 \). For a 6-year life, find the rate (IRR approx. 13.8%).

Step 9: Memo to Management

Given the IRR calculations, recommend investing in the new bagging machine. It provides a higher internal rate of return (13.8% vs. 10.6%) and has a shorter payback period. This investment aligns better with the company's objective of achieving a minimum return of 11%.

Key Concepts

Capital Budgeting

Capital budgeting is the process businesses use to evaluate potential major projects or investments. It helps companies determine which investments are worth pursuing by analyzing the future cash flow and profitability associated with the ventures. In our case with Mr. Pop Popcorn Company, two investment opportunities are being considered — a delivery truck and a bagging machine.

The process begins with identifying potential investments and estimating each project's potential costs and benefits. For capital budgeting, the company considers the following key aspects:

• Initial Investment Costs: Includes all costs needed to acquire the asset and get it ready for use. For instance, the delivery truck costs $36,506, while the bagging machine has a net investment cost of $27,555.
• Cash Flow Projections: Estimation of income and expenses associated with each investment. Calculate net cash flow for each year of the asset's life.
• Project Lifetime: The expected duration over which the project will yield benefits, here it is 6 years for both the truck and bagging machine.
• Discount Rate: The minimum required rate of return, Mr. Pop's company has set this at 11%.

Capital budgeting ensures that companies efficiently allocate their capital resources to the most profitable projects, optimizing returns and supporting strategic goals.

Investment Analysis

Investment analysis involves evaluating the profitability and financial impact of an investment. For Mr. Pop Popcorn Company, this means scrutinizing each project (the delivery truck and the bagging machine) to decide where to best allocate financial resources.

Here are some key factors considered in investment analysis:

• Net Cash Flow: Evaluate how much additional cash each project will bring. For instance, the delivery truck results in a net cash flow of $8,880 annually after accounting for additional revenue and operating costs.
• Internal Rate of Return (IRR): A critical metric in investment analysis, IRR is the discount rate at which the net present value (NPV) of an investment is zero. A project's IRR is compared to the required rate of return to decide its feasibility. For the delivery truck, the IRR is 10.6%, while for the bagging machine, it's 13.8%, making the latter more favorable.
• Comparative Analysis: Compare the projects against criteria such as IRR and payback period. Although the delivery truck has significant revenue potential, the bagging machine shows a better IRR and quicker return on investment.

Accurate investment analysis helps ensure that Mr. Pop invests wisely, optimizing returns while minimizing risks.

Payback Period Calculation

Calculating the payback period is a straightforward way to assess how quickly an investment can repay its initial cost. This method calculates the time required to recoup the original investment in a project.

Here's how it is applied in Mr. Pop’s scenario:

• Delivery Truck: The initial investment is \(36,506, and the net annual cash inflow is \)8,880. Thus, the payback period is calculated as \[\frac{36,506}{8,880} \approx 4.11 \text{ years}\]
• Bagging Machine: With an initial cost of \(27,555 and savings of \)7,280 annually from reduced labor costs, the payback period is \[\frac{27,555}{7,280} \approx 3.78 \text{ years}\]

While the payback period is easy to understand and use, it's important to remember that it doesn't account for the time value of money or cash flows after the payback period. Despite its limitations, it's a handy rule of thumb for preliminary assessments of potential investments.