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Instructions

Your probationary period at the Cosmo K Manufacturing Group continues.

For this week’s project, Gerry has asked you to consider two mutually exclusive investments and incorporate risk considerations into the process of evaluation.

The Cosmo K Manufacturing Group is considering the addition of a new smelting machine or a new paving machine. The two investments are mutually exclusive; if one is selected, the other is rejected. The annual cash flows after taxes and the effects of depreciation, which begin one year from project start, and their respective probabilities are given below:

Smelting Machine

Paving Machine

Probability

Net Cash Flows per Year

Probability

Net Cash Flows per Year

0.2

$14,100.00

0.2

  $2,000.00

0.5

$16,000.00

0.5

$16,000.00

0.2

$17,000.00

0.2

$22,000.00

0.1

$20,000.00

0.1

$33,000.00

Each project has an expected life of 4 years and will cost $45,000. The riskier project will be evaluated at the company’s WACC plus 3%, and the less risky project will be evaluated at the company’s WACC. Cosmo K has the following capital structure:

Debt:

30%

Preferred stock:

16%

Common stock:

54%

This capital structure is current and consistent with the company’s objectives and so will be used to raise any new funds. All new debt will be raised using long-term bonds, with no short-term debt being used for the new project. New bonds will have a coupon rate of 13%. The company’s common stock is currently selling for $65 per share, paid a dividend of $4.25 last year, and has an expected growth rate of 6% indefinitely. There will be no floatation costs on new common stock. Preferred stock can be sold for $90 per share and pays a dividend of $10, with a floatation cost of $2 per share. Currently, the market risk premium is 5% and the risk-free rate is 8%. Cosmo K’s beta coefficient is currently 1.23 and is expected to be consistent for the foreseeable future. The tax rate is expected to be 40% for the next decade.

Tasks:

Answer the following questions:

• What is the component cost of capital for the company? Calculate using the CAPM.
• What is the company’s WACC?
• What are the expected cash flows for the investments?
• What is the standard deviation for each investment?
• What is the coefficient of variation for each investment?
• Given the data above, which investment has the higher risk?
• What is the expected net present value (NPV) for each investment?
• What is the internal rate of return (IRR) of the investments?
• According to the decision rules for the NPV and those for the IRR, is there an acceptable project? Explain your answer.
• Is there a conflict between the two decision methods? If so, what would you use to recommend a project?

Submission Details:

• Show the data used and the calculations for each question in a Microsoft Excel sheet and the analysis in a Microsoft Word document.
• Name your Microsoft Excel sheet MBA6010_W4_LastName_
  FirstName.xls and your Microsoft Word document MBA6010_W4_LastName_FirstName.doc.
• Submit your assignment to the Submissions Area by the due date assigned.
  

  Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!

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  ✅ Step-by-Step Guide to Completing the Assignment

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  Step 1: Calculate the Component Cost of Capital

  A. Cost of Debt (after tax):

  • Formula:
    rd(1−T)=0.13(1−0.40)=0.078r_d (1 – T) = 0.13 (1 – 0.40) = 0.078rd​(1−T)=0.13(1−0.40)=0.078 or 7.8%

  B. Cost of Preferred Stock

  • Formula:
    rps=DP−F=1090−2=1088=11.36%r_{ps} = \dfrac{D}{P – F} = \dfrac{10}{90 – 2} = \dfrac{10}{88} = 11.36\%rps​=P−FD​=90−210​=8810​=11.36%

  C. Cost of Equity (CAPM):

  • Formula:
    re=Rf+β(Rm−Rf)r_e = R_f + \beta (R_m – R_f)re​=Rf​+β(Rm​−Rf​)
    re=8%+1.23(5%)=14.15%r_e = 8\% + 1.23 (5\%) = 14.15\%re​=8%+1.23(5%)=14.15%

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  Step 2: Calculate WACC (Weighted Average Cost of Capital)

  Use the weights from the capital structure:

  $$WACC=(0.30)(7.8\%)+(0.16)(11.36\%)+(0.54)(14.15\%)$$ $$WACC=2.34\%+1.82\%+7.64\%=11.80\%$$

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  Step 3: Calculate Expected Annual Cash Flows

  A. Smelting Machine

  $$E(CF)=(0.2)(14,100)+(0.5)(16,000)+(0.2)(17,000)+(0.1)(20,000)=2,820+8,000+3,400+2,000=\text{16,220}$$

  B. Paving Machine

  $$E(CF)=(0.2)(2,000)+(0.5)(16,000)+(0.2)(22,000)+(0.1)(33,000)=400+8,000+4,400+3,300=\text{16,100}$$

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  Step 4: Calculate Standard Deviation

  Use the formula:

  σ=∑P(xi−μ)2σ = \sqrt{\sum P(x_i – \mu)^2}σ=∑P(xi​−μ)2​

  Do this in Excel by computing:

  • xi−μx_i – \muxi​−μ

  • Squared deviation

  • Multiply by probability

  • Sum all

  Apply separately for both machines using their expected cash flows.

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  Step 5: Calculate Coefficient of Variation (CV)

  CV=σE(CF)CV = \dfrac{σ}{E(CF)}CV=E(CF)σ​

  • Lower CV = Lower relative risk

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  Step 6: Identify Higher Risk Project

  • Compare CVs

  • Higher CV = Riskier project

  Use WACC + 3% (14.80%) for riskier project in NPV/IRR

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  Step 7: Calculate Expected NPV

  NPV=∑E(CF)(1+r)t−Initial InvestmentNPV = \sum \dfrac{E(CF)}{(1 + r)^t} – \text{Initial Investment}NPV=∑(1+r)tE(CF)​−Initial Investment

  • Use WACC for less risky, WACC + 3% for riskier

  • Use Excel’s NPV() function or manual discounting over 4 years

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  Step 8: Calculate IRR

  • Use Excel’s =IRR() function

  • Input expected cash flow stream over 4 years (constant each year), include initial investment as negative

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  Step 9: Interpret NPV and IRR

  • If NPV > 0 → Accept

  • If IRR > Cost of Capital → Accept

  • If both are true, it’s a good project

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  Step 10: Resolve Conflicts Between NPV and IRR

  If NPV and IRR suggest different choices:

  • Use NPV as the final decision tool

  • NPV directly measures value added to the firm

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  📄 Final Submission Checklist

  • ✅ Excel file includes:

    • All formulas and calculations (clearly labeled)

    • Cash flows, standard deviation, CV, NPV, IRR

  • ✅ Word file includes:

    • Answers and analysis for each question

    • Explanation of decision-making

  • ✅ File naming:

    • Excel: MBA6010_W4_LastName_FirstName.xls

    • Word: MBA6010_W4_LastName_FirstName.doc

  • ✅ Submit in the Submissions Area by the due da

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