MGAB03H3 Lecture Notes - Lecture 5: Net Present Value, Sensitivity Analysis, Investment
Document Summary
Get access
Related Documents
Related Questions
The discounted dividend model can be used to value divisions and firms that do not pay dividends. For the discounted dividend model, a firm's weighted average cost of capital is used as the discount rate. For the corporate valuation model, a firm's cost of equity is used as the discount rate. |
For the constant growth model to hold, a firm's cost of equity needs to be greater than its constant dividend growth rate (i.e., rs > g). From the constant growth model, if the constant dividend growth rate is equal to zero, a firm's share price is equal to the constant dividend divided by the cost of equity (i.e., g=0). If a company's constant dividend growth rate is negative, the formula for the constant growth model cannot be applied. |
The internal rate of return method (IRR) assumes that cash flows are reinvested at the internal rate of return. The modified internal rate of return method (MIRR) assumes that cash flows are reinvested at the weighted average cost of cpaital. For mutually exclusive projects, if there is a conflict between NPV and IRR, the project with the highest IRR is chosen. The IRR is independent of a firm's weighted average cost of capital. |
The WACC only represents the "hurdle rate" for a typical project with average risk. Therefore, the project's WACC should be adjusted to reflect the project's risk. Firms with riskier projects generally have a lower WACC. Holding all else constant, an increase in the target debt ratio tends to lower the WACC. |
Short-term bond prices are less sensitive than long-term bond prices to interest rate changes. Companies are not likely to call bonds unless interest rates have declined significantly. Thus, the call provision is valuable to firms but detrimental to long term investors. On balance, bonds that have a sinking fund are regarded as being safer than those without such a provision. |
If beta < 1.0, the security is less risky than average. According to the Security Market Line (SML), in general, a companyâs expected return will double when its beta doubles. According to the Security Market Line (SML), if a portfolio of real world stocks has a beta of zero, the required rate of return for the portfolio is equal to the risk-free rate. |
7.37%. 11.05%. 8.32%. |
It ignores cash flows occurring after the payback period. It ignores the time value of money, that is, dollars received in different years are all given the same weight. |
1.82. 2.00. 1.94 |
undervalued. overvalued. |
13.92%. 16.34%. 12.17%. |
$221.86. $195.23. $257.35. |
10.82%. 11.76%. 9.64%. |
10 years. 4.58 years. 6.12 years. |
12.04%. 14.93%. 9.15%. |
1.24 years. 1.62 years. 1.15 years.
|
IntegrativeâDetermining relevant cash flows Atlantic Dry dock is considering replacing an existing hoist with one of two newer, more efficient pieces of equipment. The existing hoist is 3 years old, cost $31,500, and is being depreciated under MACRS using a 5-year recovery period. Although the existing hoist has only 3 years (years 4, 5, and 6) of depreciation remaining under MACRS, it has a remaining usable life of 5 years. Hoist A, one of the two possible replacement hoists, costs $39,500 to purchase and $8,500 to install. It has a 5-year usable life and will be depreciated under MACRS using a 5-year recovery period. The other hoist, B, costs $54,900 to purchase and $5,800 to install. It also has a 5-year usable life and will be depreciated under MACRS using a 5-year recovery period. Increased investments in net working capital will accompany the decision to acquire hoist A or hoist B. Purchase of hoist A would result in a $4,200 increase in net working capital; hoist B would result in a $5,500 increase in net working capital. The projected profits before depreciation and taxes with each alternative hoist and the existing hoist are given in the following table.
| Earning before depreciation,interest,and taxes | |||
| year | with hoist A | with hoist B | WITH EXISTING HOIST |
| 1 | 20,700 | 21,700 | 14,900 |
| 2 | 20,700 | 24,000 | 14,900 |
| 3 | 20,700 | 25,400 | 14,900 |
| 4 | 20,700 | 25,400 | 14,900 |
| 5 | 20,700 | 25,400 | 14,900 |
The existing hoist can currently be sold for $18,600 and will not incur any removal or cleanup costs. At the end of 5 years, the existing hoist can be sold to net $1,400 before taxes. Hoists A and B can be sold to net $11,500 and $21,000 before taxes, respectively, at the end of the 5-year period. The firm is subject to a 40% tax rate on both ordinary income and capital gains. (Table 3.2 on page 100 contains the applicable MACRS depreciation percentages.)
a. Calculate the initial investment associated with each alternative.
b. Calculate the incremental operating cash inflows associated with each alternative. (Note: Be sure to consider the depreciation in year 6.)
c. Calculate the terminal cash flow at the end of year 5 associated with each alternative.
d. Depict on a time line the relevant cash flows associated with each alternative.
| Rounded Depreciation Percentages by Recovery Year Using MACRS for | ||||
| Percentage by recovery year* | ||||
| Recovery year | 3 years | 5 years | 7 years | 10 years |
| 1 | 33% | 20% | 14% | 10% |
| 2 | 45% | 32% | 25% | 18% |
| 3 | 15% | 19% | 18% | 14% |
| 4 | 7% | 12% | 12% | 12% |
| 5 | 12% | 9% | 9% | |
| 6 | 5% | 9% | 8% | |
| 7 | 9% | 7% | ||
| 8 | 4% | 6% | ||
| 9 | 6% | |||
| 10 | 6% | |||
| 11 | 4% | |||
| Totals | 100% | 100% | 100% | 100% |
a) Calculate the NPV, IRR, Payback Period and Discounted Payback Period (the cost of capital of 10%)
b)By using you own assumption or probability of occurring for new machine only (others remain unchanged), prepare a scenario analysis and recalculate the incremental operating cash inflow for year 1 to 5 associated with the proposed replacement.
Instructions: The assignment is based on the mini case below. The instructions relating to the assignment are at the end of the case.
Lucy Hawkins and Andy Chen are facing an important decision. After having discussed different financial scenarios into the wee hours of the morning, the two computer engineers felt it was time to finalize their cash flow projections and move to the next stage â decide which of two possible projects they should undertake.
Both had a bachelor degree in engineering and had put in several years as maintenance engineers in a large chip manufacturing company. About six months ago, they were able to exercise their first stock options. That was when they decided to quit their safe, steady job and pursue their dreams of starting a venture of their own. In their spare time, almost as a hobby, they had been collaborating on some research into a new chip that could speed up certain specialized tasks by as much as 25%. At this point, the design of the chip was complete. While further experimentation might improve the performance of their design, any delay in entering the market now may prove to be costly, as one of the established players might introduce a similar product of their own. The duo knew that now was the time to act if at all.
They estimated that they would need to spend about $5,000,000 on plant, equipment and supplies. As for future cash flows, they felt that the right strategy at least for the first year would be to sell their product at dirt-cheap prices in order to induce customer acceptance. Then, once the product had established a name for itself, the price could be raised. By the end of the fifth year, their product in its current form was likely to be obsolete. However, the innovative approach that they had devised and patented could be sold to a larger chip manufacturer for a decent sum. Accordingly, the two budding entrepreneurs estimated the operating cash flows for this project (call it Project A) as follows:
| Year | Project A Expected Cash flows ($) |
| 0 | (5,000,000) |
| 1 | 200,000 |
| 2 | 875,000 |
| 3 | 2,130,000 |
| 4 | 3,110,000 |
| 5 | 3,110,000 |
An alternative to pursuing this project would be to sell the patent for their innovative chip design to one of the established chip makers. They estimated that they would receive around $800,000 for this. It would probably not be reasonable to expect much more as neither their product nor their innovative approach had a track record.
They could then invest in some plant and equipment that would test silicon wafers for zircon content before the wafers were used to make chips. Too much zircon would affect the long-term performance of the chips. The task of checking the level of zircon was currently being performed by chip makers themselves. However, many of them, especially the smaller ones, did not have the capacity to permit 100% checking. Most tested only a sample of the wafers they received.
Lucy and Andy were confident that they could persuade at least some of the chip makers to outsource this function to them. By exclusively specializing in this task, their little company would be able to slash costs by more than half, and thus allow the chip manufacturers to go in for 100% quality check for roughly the same cost as what they were incurring for a partial quality check today. The life of this project too is expected to be only about five years.
The initial investment for this project is estimated at $ 5,000,000. After taking into account the sale of their patent, the net investment would be $4,200,000. As for the future, Lucy and Andy were pretty sure that there would be sizable profits in the first year. But thereafter, the zircon content problem would slowly start to disappear with advancing technology in the wafer industry. Keeping this in mind, they estimate the future cash inflows for this project (call it Project B) as follows:
| Year | Project B Expected Cash flows ($) |
| 0 | (4,200,000) |
| 1 | 2,500,000 |
| 2 | 2,000,000 |
| 3 | 900,000 |
| 4 | 550,000 |
| 5 | 250,000 |
Lucy and Andy now need to make their decision. For purposes of analysis, they plan to use a required rate of return of 15% for both projects. Ideally, they would prefer that the project they choose have a payback period of less than 3.5 years and a discounted payback period of less than 4 years.
Below are the results of the analysis they have carried out so far:
| Metrics | Project A | Project B |
| Payback period (in years) | 3.58 | 1.85 |
| Discounted payback period (in years) | 4.64 | 2.87 |
| Net Present Value (NPV) | $560,421 | $516,723 |
| Internal Rate of Return (IRR) | 18.37% | 22.47% |
| Profitability Index | 1.11 | 1.12 |
| Modified Internal Rate of Return (MIRR) | 17.47% | 17.70% |
One of the concerns that Lucy and Andy have is regarding the reliability of their cash flow estimates. All the analysis in the table above is based on âexpectedâ cash flows. However, they are both aware that actual future cash flows may be higher or lower.
Assignment:
Suppose that Lucy and Andy have hired you as a consultant to help them make the decision. Please draft an official memo to them with your analysis and recommendations.
Your submission should cover the following questions:
1.Briefly, summarize the key facts of the case and identify the problem being faced by our two budding entrepreneurs. In other words, what is the decision that they need to make? (10 points)
An excellent paper will demonstrate the ability to construct a clear and insightful problem statement while identifying all underlying issues.
2.What are some approaches that can be used to solve this problem? What are some various criteria or metrics that can be used to help make this decision? (10 points)
An excellent paper will propose solutions that are sensitive to all the identified issues.
3.a) Rank the projects based on each of the following metrics: Payback period, Discounted payback period, NPV, IRR, Profitability Index, and MIRR. (10 points)
b) Andy believes that the best approach to make the decision is the NPV approach. However, Lucy is not so sure that ignoring the other metrics is a good idea. Which of the approaches or metrics would you propose? In other words, would you prefer one or more of these approaches over the others? Explain why. (20 points)
An excellent paper includes an evaluation of solutions containing thorough and insightful explanations, feasibility of solutions, and impacts of solutions.
4.a) Which of these projects would you recommend? Explain why. (10 points)
b) Briefly state the limitations of the approach you used in making this decision, and outline what further analysis you would recommend. (20 points)
An excellent paper provides concise yet thorough action-oriented recommendations using appropriate subject-matter justifications related to the problem while addressing limitations of the solution and outlining recommended future analysis.