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Chapter 7: Problem 23

Abandonment Decisions Allied Products, Inc., is considering a new product launch. The firm expects to have an annual operating cash flow of \(\$ 22\) million for the next 10 years. Allied Products uses a discount rate of 19 percent for new product launches. The initial investment is \(\$ 84\) million. Assume that the project has no salvage value at the end of its economic life. 1\. What is the NPV of the new product? 2\. After the first year, the project can be dismantled and sold for \(\$ \mathbf{3 0}\) million. If the estimates of remaining cash flows are revised based on the first year's experience, at what level of expected cash flows does it make sense to abandon the project?

Short Answer

Expert verified
The NPV of the new product is approximately \$5.21 million. It makes sense to abandon the project after the first year if the estimated remaining cash flows are below approximately \$23.28 million.

Step by step solution

01

Calculate the NPV of the new product

To calculate the NPV, we need to find the present value of the cash flows, minus the initial investment. Let's consider the cash flows for the 10 years and the discount rate of 19%. The formula for calculating NPV is: \[NPV = \sum_{t=1}^T \frac{CF_t}{(1 + r)^t} - I\] Where: - \(T\) is the number of years - \(CF_t\) is the cash flow at year \(t\) - \(r\) is the discount rate - \(I\) is the initial investment In this case, \(T = 10\), \(CF_t = \$ 22 \; million\), \(r = 0.19\), and \(I = \$ 84 \; million\). Calculate the NPV: \[NPV = \sum_{t=1}^{10} \frac{\$ 22 \; million}{(1 + 0.19)^t} - \$ 84 \; million\] \[NPV 鈮� \$ 5.21 \; million\] So, the NPV of the new product is approximately \$ 5.21 million.
02

Determine the level of expected cash flows to abandon the project

To determine the level of expected cash flows at which it makes sense to abandon the project, we must compare the NPV if the project continues with the NPV if the project is abandoned after the first year. First, let's calculate the NPV if the project is abandoned after the first year. We will remove the cash flow of the remaining 9 years and add the sale value in the second year. \[NPV_{abandoned} = \frac{CF_1}{1 + r} + \frac{\$ 30 \; million}{(1 + r)^2} - I\] Substituting given values: \[NPV_{abandoned} = \frac{\$ 22\; million}{1 + 0.19} + \frac{\$ 30 \; million}{(1 + 0.19)^2} - \$ 84 \; million\] \[NPV_{abandoned} 鈮� -\$ 0.15 \; million\] Now let's find the level of expected cash flows, \(CF^*\), at which it makes sense to abandon the project. We can set the NPV of the abandoned project equal to the NPV of the original project: \[NPV_{abandoned} = NPV\] Or, \[\frac{CF_1^*}{1 + r} + \frac{\$ 30 \; million}{(1 + r)^2} - I = \$ 5.21 \; million\] Solving for \(CF_1^*\): \[CF_1^* = (1 + r)(\$ 5.21\; million + I) - \frac{\$ 30 \; million}{(1 + r)}\] \[CF_1^* = (1 + 0.19)(\$ 5.21\; million + \$ 84\; million) - \frac{\$ 30 \; million}{(1 + 0.19)}\] \[CF_1^* 鈮� \$ 23.28 \; million\] So, it makes sense to abandon the project if the estimated remaining cash flows after the first year are below approximately \$ 23.28 million.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Net Present Value
Net Present Value (NPV) is a financial metric used to assess the profitability of an investment or project. It represents the difference between the present value of cash inflows and the present value of cash outflows over a period of time. The NPV formula is:
\[NPV = \sum_{t=1}^T \frac{CF_t}{(1 + r)^t} - I\]
In this formula, \(T\) represents the total number of time periods, \(CF_t\) is the cash flow at time \(t\), \(r\) stands for the discount rate, and \(I\) refers to the initial investment. When calculating NPV, a positive value indicates that the expected earnings exceed the costs, considering the time value of money, and that the project is potentially a good investment. If the NPV is negative, the project would likely result in a net loss. It's also crucial to note that NPV includes all cash flows, including the initial investment and any final liquidation or salvage values, if applicable.
Discount Rate
The discount rate in NPV calculations plays a critical role as it adjusts future cash flows to their present value, reflecting both the time value of money and the risk of the investment. The time value of money concept suggests that money available today is worth more than the same amount in the future due to its potential earning capacity.

The higher the discount rate, the lower the present value of future cash flows. The discount rate may reflect the cost of capital, the rate of alternative investments, or the risk level associated with the project. It's a tool that investors and companies use to determine the risk-adjusted return on an investment. A project with a high discount rate suggests higher risk, as investors require more substantial returns to compensate for that increased risk.
Cash Flow Analysis
Cash Flow Analysis is a vital component in evaluating the financial health of a business or the viability of a project. By tracking the cash inflows and outflows, analysts can determine the liquidity, flexibility, and overall financial performance of an entity.

In the context of NPV calculations, each cash flow needs to be forecasted and then discounted to its present value. This includes the initial outlay of funds, followed by inflows from operations or investment returns. Critical factors affecting cash flow analysis include the timing of cash flows, the magnitude, and certainty. Cash flow analysis can also be used to identify how changes in business operations, such as cost reductions or revenue improvements, will affect the profitability of a project or investment.
Abandonment Decision
An abandonment decision is a strategic choice to discontinue a project or investment before its planned conclusion, often due to changes in market conditions, operational challenges, or revised cash flow expectations. The key economic question is whether continuing with the project outweighs the benefits of ceasing operations and potentially recouping some of the investment through salvage value.

Financial analysis tools like NPV help inform this decision. If the value of the cash flows that one would forego by abandoning the project is less than the liquidation value plus the project's NPV if it were continued, it may make financial sense to abandon the project. This decision-making process involves recalculating the NPV based on revised cash flow estimates and comparing it with the salvage value available if the project is terminated prematurely.

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Most popular questions from this chapter

Abandonment Decisions M.V.P. Games, Inc., has hired you to perform a feasibility study of a new video game that requires a \(\$ 5\) million initial investment. M.V.P. expects a total annual operating cash flow of \(\$ 880,000\) for the next 10 years. The relevant discount rate is 10 percent. Cash flows occur at year-end. 1\. What is the NPV of the new video game? 2\. After one year, the estimate of remaining annual cash flows will be revised either upward to \(\$ 1.75\) million or downward to \(\$ 290,000\). Each revision has an equal probability of occurring. At that time, the video game project can be sold for \(\$ 1,300,000\). What is the revised NPV given that the firm can abandon the project after one year?

Project Analysis McGilla Golf has decided to sell a new line of golf clubs. The clubs will sell for \(\$ 750\) per set and have a variable cost of \(\$ 390\) per set. The company has spent \(\$ 150,000\) for a marketing study that determined the company will sell 55,000 sets per year for seven years. The marketing study also determined that the company will lose sales of 12,000 sets of its high-priced clubs. The high-priced clubs sell at \(\$ 1,100\) and have variable costs of \(\$ 620\). The company will also increase sales of its cheap clubs by 15,000 sets. The cheap clubs sell for \(\$ 400\) and have variable costs of \(\$ 210\) per set. The fixed costs each year will be \(\$ 8,100,000\). The company has also spent \(\$ 1,000,000\) on research and development for the new clubs. The plant and equipment required will cost \(\$ 18,900,000\) and will be depreciated on a straight-line basis. The new clubs will also require an increase in net working capital of \(\$ 1,400,000\) that will be returned at the end of the project. The tax rate is 40 percent, and the cost of capital is 14 percent. Calculate the payback period, the NPV, and the IRR.

Option to Wait Your company is deciding whether to invest in a new machine. The new machine will increase cash flow by \(\$ 340,000\) per year. You believe the technology used in the machine has a 10 -year life; in other words, no matter when you purchase the machine, it will be obsolete 10 years from today. The machine is currently priced at \(\$ 1,800,000\). The cost of the machine will decline by \(\$ 130,000\) per year until it reaches \(\$ 1,150,000\), where it will remain. If your required return is 12 percent, should you purchase the machine? If so, when should you purchase it?

Sensitivity Analysis Consider a four-year project with the following information: Initial fixed asset investment \(=\mathbf{\$ 3 8 0 , 0 0 0}\); straight-line depreciation to zero over the four-year life; zero salvage value; price \(=\$ 54\); variable costs \(=\$ 42 ;\) fixed costs \(=\$ 185,000\); quantity sold \(=90,000\) units; tax rate \(=34\) percent. How sensitive is OCF to changes in quantity sold?

Sensitivity Analysis and Break-Even Point We are evaluating a project that costs \(\$ 724,000\), has an eight-year life, and has no salvage value. Assume that depreciation is straightline to zero over the life of the project. Sales are projected at 75,000 units per year. Price per unit is \(\$ 39\), variable cost per unit is \(\$ 23\), and fixed costs are \(\$ 850,000\) per year. The tax rate is 35 percent, and we require a 15 percent return on this project. 1\. Calculate the accounting break-even point. 2\. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure? Explain what your answer tells you about a 500-unit decrease in projected sales. 3\. What is the sensitivity of OCF to changes in the variable cost figure? Explain what your answer tells you about a \(\$ 1\) decrease in estimated variable costs.
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