Question

You must analyze a potential new product--a caulking compound that Cory Mateials' R&D people developed for use in the
residential construction industry. Cory's marketing manager thinks the company can sell 115,000 tubes per year for 3
years at a price of $3.25 each, after which the product will be obsolete. The required equipment would cost $150,000, plus
another $25,000 for shipping and installation. Current assets (receivables and inventories) would increase by $35,000,
while current liabilities (accounts payable and accruals) would rise by $15,000. Variable costs would be 60% of sales
revenues, fixed costs (exclusive of depreciation) would be $70,000 per year, and fixed assets would be depreciated under
MACRS with a 3-year life. (Yr1 = 33%, Yr2 = 45%, Yr3 = 15%, Yr4 = 7%) When production ceases after 3 years,
the equipment should have a market value of $15,000. Cory's tax rate is 40%, and it uses a 10% WACC for average-risk
projects.
a. Find the required Year 0 investment and the project's annual net cash flows. Then calculate the project's
NPV, IRR, MIRR, and payback. Assume at this point that the project is of average risk.
b. Suppose you now learn that R&D costs for the new product were $30,000 and that those costs were incurred and
expensed for tax purposes last year. How would this affect your estimate of NPV and other profitability measures?
c. If the new project would reduce cash flows from Cory's other projects and if the new project would be housed
in an empty building that Cory owns and could sell, how would those factors affect the project's NPV?
d. Are this project's cash flows likely to be positively or negatively correlated with returns on Cory's other
projects and with the economy, and should this matter in your analysis? Explain.
e. Unrelated to the new product, Cory is analyzing two mutually exclusive machines that will upgrade its manufacturing
plant. These machines are considered average-risk projects, so management will evaluate them at the firm's 10%
WACC. Machine X has a life of 4 years, while Machine Y has a life of 2 years. The cost of each machine is $60,000;
however, Machine X provides after-tax cash flows of $25,000 per year for 4 years and Machine Y provides after-tax cash
flows of $42,000 per year for 2 years. The manufacturing plant is very successful, so the machines manufacturing
plant is very successful, so the machines will be repurchased at the end of each machine's useful life. In other words,
the machines are "repeatable" projects.
(1) Using the replacement chain approach, what is the NPV of the better machine?
(2) Using the EAA approach, what is the EAA of the better machine?
f. The CEO expressed concern that some of the base-case inputs might be too optimistic or too pessimistic. He
wants to know how the NPV would be affected if these 6 variables were all 20% better or 20% worse than
the base-case level: unit sales, sales price, variable costs, fixed costs, WACC, and equipment cost. Hold
other things constant when you consider each variable, and construct a sensitivity graph to illustrate your
results.
g. Do a scenario analysis based on the assumption that there is a 25% probability that each of the 6 variables itemized
in Part f will turn out to have their best-case values as calculated in Part f, a 50% probability that all will have their
base-case values, and a 25% probability that all will have their worst-case values. The other variables remain at base-case
levels. Calculate the expected NPV, the standard deviation of NPV, and the coefficient of variation.
h. Does Cory's management use the risk-adjusted discount rate to adjust for project risk? Explain.

Answer 1

Since, the question has multiple parts, I have answered the first four parts.

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Part 1)

The year 0 investment and the project's annual net cash flows are calculated as follows:

	0	1	2	3
Cost of Equipment (150,000 + 25,000)	-175,000
Increase in Net Working Capital (35,000 - 15,000)	-20,000
Sales Revenues (115,000*3.25)		373,750	373,750	373,750
Less Variable Cost (115,000*3.25*60%)		224,250	224,250	224,250
Fixed Operating Costs		70,000	70,000	70,000
Depreciation		57,750 (175,000*33%)	78,750 (175,000*45%)	26,250 (175,000*15%)
EBIT		21,750	750	53,250
Less Tax		8,700	300	21,300
EBIT		13,050	450	31,950
Add Depreciation		57,750	78,750	26,250
After-Tax Salvage Value [15,000 + (175,000*7% - 15,000)*40%]				13,900
Recovery of Net Working Capital				20,000
Free Cash Flow	-$195,000	$70,800	$79,200	$92,100

Based on the calculations in the above table, we can identify different values as below:

Year 0 Investment = -$195,000

Year 1 Annual Net Cash Flow = $70,800

Year 2 Annual Net Cash Flow = $79,200

Year 3 Annual Net Cash Flow = $92,100

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NPV:

The NPV of the project can be calculated with the use of following formula:

NPV = Year 0 Investment + Year 1 Annual Net Cash Flow/(1+WACC)^1 + Year 2 Annual Net Cash Flow/(1+WACC)^2 + Year 3 Annual Net Cash Flow/(1+WACC)^3

Substituting values in the above formula, we get,

NPV = -195,000 + 70,800/(1+10%)^1 + 79,200/(1+10%)^2 + 92,100/(1+10%)^3 = $4014.27 or $4,014

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IRR:

IRR is the minimum rate of return acceptable from a project. IRR can be calculated with the use of IRR function/formula of EXCEL/Financial Calculator. The basic formula for calculating IRR is given below:

NPV = 0 = Year 0 Investment + Year 1 Annual Net Cash Flow/(1+IRR)^1 + Year 2 Annual Net Cash Flow/(1+IRR)^2 + Year 3 Annual Net Cash Flow/(1+IRR)^3

IRR is calculated with the use of EXCEL as follow:

where

IRR = IRR(B2:B5) = 11.11%

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MIRR:

MIRR is the modified internal rate of return. It can be derived with the use of following formula:

MIRR =  ((Year 1 Annual Net Cash Flow*(1+WACC)^2 + Year 2 Annual Net Cash Flow*(1+WACC)^1 + Year 3 Annual Net Cash Flow*(1+WACC)^0)/(Initial Investment))^(1/Years) - 1

Substituting values in the above formula, we get,

MIRR = ((70,800*(1+10%)^2 + 79,200*(1+10%)^1 + 92,100*(1+10%)^0)/(195,000))^(1/3) - 1 = 10.75%

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Payback Period:

Payback period is the timeframe within which the original investment is recovered by the company. The initial investment is recovered as follows:

Year	Cash Flow	Cumulative Cash Flows
0	-195,000	-195,000
1	70,800	-124,200
2	79,200	-45,000
3	92,100	47,100

As can be seen from the above table that the value of cumulative cash flows turn positive between Year 2 and Year 3. Therefore, the payback period will lie between Year 2 and Year 3. The formula for calculating payback period can be derived as below:

Payback Period = Years Upto which Partial Recovery is Made + Balance Amount/Cash Flow of the Year in which Full Recovery is Made = 2 + 45,000/92,100 = 2.49 Years

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Part 2)

The cost of $30,000 towards R&D expenses has already been incurred in the previous year. Such costs are treated as sunk costs as they cannot be recovered irrespective of whether the project is undertaken by the company or not. Therefore, the value of R&D expenses will have no impact on the estimate of NPV and other profitability measures.

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Part 3)

In both the cases, the NPV of the project would get reduced as described in the following manner:

1) Reduction of cash flows from other projects (as a result of new project) would be treated as the cost of undertaking the new project which in turn would cause a decrease in the value of cash inflows resulting from the new project. This will finally result in a reduction in NPV of the new project.

2) The NPV of the project would get reduced with the after-tax sales value of the empty building. It is because the building could have otherwise been sold (resulting in cash inflow for the company) if it had not been used for the new project resulting in an opportunity cost for the company.

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Part 4)

In the given case, the project's cash flows are most likely to be positively correlated with returns correlated with returns on Cory's other projects and with the economy. It is because the company is engaged in the development/production of building materials. Caulking compound is also a building material which is supposed to be used in the residential construction industry. Therefore, the new project will be somewhat related to the current product profile/range of the company and will contribute to an expansion of its product base. Further, with a boom in the economy, the demand for property would increase which would mean an increase in the use of caulking compound again creating a positive impact on the company's overall cash flows position.

Yes, the fact whether the new project's cash flows are likely to be positively or negatively correlated with the firm's other projects and the economy should be taken into account. It is because this correlation helps in assessing the overall risk associated with the new project and in arriving at the relevant cost of capital at which the new project should be evaluated.