You are employed by CGT, a Fortune 500 firm that is a major producer of c plasti

Question

You are employed by CGT, a Fortune 500 firm that is a major producer of c plastics, including plastic grocery bags, styrofoam cups, and fertilizers. You are corporate staff as an assistant to the CFO. This is a position with high visibility and the opportunity for rapid advancement, providing you make the right decisions. Your boss has asked you to estimate the weighted average cost of capital for the company. The balance sheet and some other information about CGT follows below hemicals and Assets Current assets Net plant, property, and equipment Total assets $38,000,000 101,000,000 $139,000,000 Liabilities and equity Accounts payable Accruals Current liabilities Long term debt (bonds) Total liabilities Common stock Retained earnings Total shareholders equity Total liabilities and shareholders equity $ 10,000,000 9.000 S19,000,000 40.000 59,000,000 30,000 50.000.000 80,000,000 $139,000.000 You check The Wall Street Journal and see that CGT stock is currently selling for $4.50 per share and that CGT bonds are selling for $875.00 per bond. The bonds have a $1,000 par value, a 5.25% annual coupon rate, semiannual issued on October 1, 2015 and will expire on October 1, 2035. The book value per share is $3. The yield on a 6-month Treasury bill is 1.50%. CGT is in the 30% tax bracket The annual rate of return for CGG and stock market are given in the below table. are not callable Year GTT stock market 2010 0.0586 0.0556 2011 0.224 0.061052632 2012-0.27070.079365079 2013 0.006 0.182904412 2014-0.0684 0.170940171 20150.33870.142003981 2016-0.0928-0.04706566 1. Estimate the GGT's after-tax cost of debt. 2. Estimate the GGT's cost of external equity 3. Estimate the GGT's cost of capital. 4. Can you assume that the cost of capital would remain constant with using more debt? Please Explain.

Explanation / Answer

1) Cost of Debt = Kd * (1-T)

Selling Price of the bond = $875

Coupon Rate = 5.25% (annual)

Par Value = $1000

Time to Maturity = 20 years

So we need to find the Yield to Maturity for the bond

Selling Price of the bond = (Coupon rate * Face Value of bond)/2 * PVIFA (YTM%/2, n*2 years) + Face Value of bond * PVIF (YTM%/2, n*2 years)

Both Coupon Interest and YTM will be halved and years to maturity be will be doubled since semiannual payments of coupon interest

Again, Coupon Interest for full year = $1000*0.0525 = $52.50

Coupon interest for half year = $26.25

Or, $875 = $26.25 pvifa (r%, 40years) + $1000* pvif (r%, 40 years)

Let us suppose r = 3%

875= 26.25*(23.115) + 1000 * (0.3066) = 913.37

Let us suppose r =4%

875 = 26.25*(19.793) + 1000* (0.2083) = 727.87

Now interpolating the results we get r%

(3-4) %/ (3-r) = 913.37-727.82/ 913.37-875

Or, -1%/ (3-r) = 185.55/38.37

Or, -1*38.37/185.55 = (3-r) %

Or, -0.207 = 3-r

Or, 3.207%

So for the full year YTM will be [{(1+YTM) ^2}-1]*100

Or, [{(1.03207)^2}-1]*100 = 6.5% (approx)

So, cost of debt = 6.5% * (1-Tax rate %)

Or, cost of debt = 6.5%* (1-0.3) = 4.55% (since Tax rate is 30%)

2) Cost of External Equity => rf + Beta* (rm - rf)

Risk Free rate = 1.50%

Market return = (Stock Market return for 2010 + Stock Market return for 2011 + Stock Market return for 2012 + Stock Market return for 2013 + Stock Market return for 2014 + Stock Market return for 2015 + Stock Market return for 2016)/ 7

Or, Marker Return = {0.0556 + 0.061052632 + 0.079365079 + 0.182904412 + 0.170940171 + 0.142003981 + (-0.04706566)}/7 = 0.092257

Beta = Covariance (Stock, Market)/ Variance of Market

Variance of the Market = {(Stock Market return for 2010 – Overall Marker Return)^2 + (Stock Market return for 2011 – Overall Marker Return)^2 +(Stock Market return for 2012 – Overall Marker Return)^2 +(Stock Market return for 2013 – Overall Marker Return)^2 +(Stock Market return for 2014 – Overall Marker Return)^2 +(Stock Market return for 2015 – Overall Marker Return)^2 +(Stock Market return for 2016 – Overall Marker Return)^2 }/ (N-1)

It’s (N-1) because of the degrees of freedom;

Or, Variance of Market = {(0.0556-0.092257)^2 + (0.061052632 – 0.092257) ^2 + (0.079365079 - 0.092257) ^2 + (0.182904412 - 0.092257) ^2 + (0.170940171 - 0.092257) ^2 + (0.142003981-0.092257)^ 2 +(-0.04706566-0.092257)^2}/ (7-1)

Variance of Market = {0.001271 + 0.000974 + 0.000166 + 0.008217 + 0.006191 + 0.002475 + 0.019411}/ (7-1) = 0.006451

Covariance of (Stock, Market) = {(Stock Market return for 2010 – Overall Marker Return) * (Stock’s Return for 2010 – Overall return for GTT) + {(Stock Market return for 2011 – Overall Marker Return) * (Stock’s Return for 2011 – Overall return for GTT) +{(Stock Market return for 2012 – Overall Marker Return) * (Stock’s Return for 2012 – Overall return for GTT) +{(Stock Market return for 2013 – Overall Marker Return) * (Stock’s Return for 2013 – Overall return for GTT) +{(Stock Market return for 2014 – Overall Marker Return) * (Stock’s Return for 2014 – Overall return for GTT) +{(Stock Market return for 2015 – Overall Marker Return) * (Stock’s Return for 2015 – Overall return for GTT) +{(Stock Market return for 2016 – Overall Marker Return) * (Stock’s Return for 2016 – Overall return for GTT) }/ (N-1)

Overall Return of GTT = (0.0586 + 0.224 -0.2707 + 0.006 -0.0684 + 0.3387 -0.0928)/7 = 0.0279143

Covariance of (stock, market) = {(0.0566-0.092257)*(0.0586-0.027914) + (0.061052632-0.092257)*(0.224-0.027914) + (0.079365079-0.092257)*( -0.2707-0.027914) + (0.182904412-0.092257)* (0.006-0.027914) + (0.170940171-0.092257)*( -0.0684-0.027914) + (0.142003981-0.092257)* (0.3387 -0.027914)+ (-0.04706566-0.092257)* (-0.0928-0.027914)}/(7-1)

Or, Covariance = {(-0.00109) + (-0.00612) + (0.00385) + (-0.00199) + (-0.00758) + (0.015461) + (0.016818)}/ (7-1) = 0.003225

So, Beta = 0.003225/0.006451 = 0.50

Again cost of external equity = 0.015 + 0.50* (0.092257-0.015) = 5.35%

3) GTT’s cost of capital = Weight of equity * cost of equity + weight of debt* cost of debt

Total No. of equity shares outstanding = Total Book Value of Equity / Book Value per share

Or, Total No. of equity shares outstanding = 80,000,000/3 = 26,666,667

Total Market Value of equity = Total No. of equity shares outstanding * Current Selling Price

Or, total Market Value of equity = 26,666,667*4.50 = 120,000,000

Total Market Value of Debt = Book value of Debt/ Par Value of bond * Selling Price per bond

Total Market Value of Debt = 40,000,000/1000*875 = 35,000,000

So, Weight of Equity = 120,000,000/ (120,000,000 + 35,000,000) = 77.42%

Weight of Debt = 35000000/ (120,000,000 +35000000) = 22.58%

Or, Cost of capital = 0.7742* 0.0535 + 0.2258*0.0455 = 5.17%

4) No cost of capital would not remain constant if more debt is used. It will decrease the cost of capital if the weight of debt increases. It has be kept in mind that if the debt increases without changing the market value of equity it will automatically increase the total market value and hence the weight of equity and cost of equity will be diluted thereby bringing down the cost of overall capital.

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