The Cosmo K Manufacturing Group is considering the addition of a new smelting ma
ID: 2778966 • Letter: T
Question
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:
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:
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.
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?
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 $33,000.00Explanation / Answer
Answer (a)
Component costs of the capital of the company
Cost of Equity = 14.15%
Cost of Preferred Stock = 11.36%
Cost of Debt = 13%
Answer (b)
Weighted Average Cost of Capital WACC = 11.80%
Answer (c)
Expected Cash Flows of Smelting Machine = $16200
Expected Cash Flows of Paving Machine = $16,100
Answer (d)
Standard Deviation of cash flows of smelting machine = 1572.90
Standard Deviation of cash flows of paving machine = 8676.98
working
Market Risk Premium = 5% or 0.05
Risk-free rate = 8% or 0.08
Beta of stock = 1.23
Expected Rate of Return on equity re= rf + Beta * market risk premium
= 0.08 + 1.23 * 0.05
= 0.08 + 0.0615 = 0.1415 or 14.15%
Market price = $65
Dividend last year = $4.25
Dividend growth rate = 6%
Next year expected dividend D1 = $4.25*1.06 = $4.505 or $4.51
Let r be the return on equity
$65 = $ 4.51/r – 0.06 ==> r – 0.06 = $4.51/$65 ==> r = 0.06938 + 0.06 = 0.12938 or 12.94%
However as the problem suggested using CAPM we will be taking the rate of 14.15% only into account.
Sale price of Preferred Stock = $90 per share
Floatation cost =$2 per share
Annual Dividend = $10 per share
Expected return on preferred stock rp = Dividend paid / share issue price - floatation costs
= $10/($90-$2)
=$10/$88
= 0.113636 or 11.36% (rounded off)
Coupon rate on new bonds rd = 13% or 0.13
Capital Structure of Company
Debt = 30% or 0.3
Preferred stock – 16% or 0.16
Common stock – 54% or 0.54
Tax Rate = 40%
Weighted Average Cost of Capital WACC = weight of debt * cost of debt * (1-tax rate) +weight of preferred stock * cost of preferred stock + weight of common stock * cost of common stock
= 0.30 * 0.13 * (1-0.40) + 0.16 *0.1136 + 0.54 * 0.1415
= 0.30 * 0.13 * 0.60 + 0.16 *0.1136 + 0.54 * 0.1415
= 0.0234 + 0.018176 + 0.07641
= 0.117986 or 11.80% (rounded off)
Expected Cash Flows for Smeling Machine CFs = Sum ( probability * expected cash flow)
CFs = 0.2 * $14100 + 0.5 * 16000 + 0.2 * 17000 + 0.1 * 20000
= $2820 + $8000 + $3400 + $2000
= $16200
Variance of cash flows VCFp = [0.2 * (14100-16200)^2 + 0.5 * (16000-16200)^2 + 0.2 * (17000-16200)^2 + 0.1 * (20000-16200)^2
VCFp = 0.2 * (-2100)^2 + 0.5 * (-200)^2 + 0.2 * 800^2 + 0.1 * 3800^2
=0.2 * 4410000 + 0.5 * 40000 + 0.2 *640000 + 0.1 * 14440000
= 882000 + 20000 + 128000 + 1444000
= 2,474,000
Standard Deviation of Cash Flows = Square root of (variance)
= (2474000)^1/2 = 1572.8954 or 1572.90 (rounded off)
Expected Cash Flows of Paving machine (CFp)
CFp = 0.2 * $2000 + 0.5 * $16000 + 0.2 * $22000 + 0.1 * $33000
= $400 + $8,000 + $4,400 + $3,300
= $16,100
Variance = 0.2 * (2000 – 16100)^2 + 0.5 * (16000-16100)^2 + 0.2 * (22000-16100)^2 + 0.1 * (33000-16100)^2
= 0.2 * (-14100)^2 + 0.5 * (-100)^2 + 0.2 * 5900^2 + 0.1 * 16900^2
= 0.2 * 198810000 + 0.5 *10000 + 0.2 * 34,810,000 + 0. 1 * 285610000
= 39762000 + 5000 + 6962000 + 28561000
= 75290000
Standard Deviation = Square Root (Variance) = (7529000)^1/2 = 8676.9810 or 8676.98 (rounded off)
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