Question

can someone solve step by step, please

ABC Inc. has 10,000 shares of common stock and 3,000 units of debt. Each unit of debt has a face value of $100,6% coupon rate, and 10 years to maturity. The common stock has a standard deviation of return of 30% and a correlation coefficient with S&P 500 return of 0.75. The S&P500 has a return of 12.5% and a standard deviation of return of 20%. The T-bill rate is 3.5%. The debt has a default risk premium of 2% and a maturity risk premium of 1%. The stockholders are expected to receive a dividend of $2 five years hence and a stock price of $105 five years hence. ABC Inc. has a corporate tax rate of 30%. Determine the cost of common stock, and the cost of debt. What is the capital structure of ABC? (How much of the capital is raised by issuing common stock and debt, respectively?) Determine the weighted average cost of capital. If return on an investment is 10%, is the investment acceptable? Explain.

Answer 1

		Cost of Debt
		Risk Free Rate	3.5%
		Default risk premium	2%
		Maturity risk premium	1%
		Before tax cost of debt	6.5%	(3.5+2+1)
	Cd	After tax cost of Debt =6.5*(1-Tax Rate)	4.55%	6.5*(1-0.3)
		Cost of Equity=Ce
		Cost of Equity =Required Return =Rf+Beta*(Rm-Rf)
		Rf=Risk Free Rate=3.5%
		Rm=Market Return=S&P return=12.5%
		Beta=(Covariance of Return of stock & Market)/(Variance of Market Return)
		Covariance (Stock,Market) =Correlation *Standard Deviation of Stock*Standard Devioation of Market
		Correlation (Stock, market)	0.75
		Standard Deviation of Stock	0.3	.(30%)
		Standard Deviation of market (S&P)	0.2	.(20%)
		Covariance (Stock,Market) =0.75*0.3*0.2	0.0450
		Variance of Market Return = (Standard Deviation)^2
		Variance of Market Return = (0.2^2)	0.04
		Beta=0.0450/0.04=	1.125
		Ce=3.5+1.125*(12.5-3.5)=	13.625%
	Ce	Cost of Equity	13.625%
		D5=Dividend in Year 5	$2
		P5=Stock Price in Year 5	$105
		P0=Current Stock Price =Present Value of Future cash flow discounted at cost of equity (13.625%)
		P0=Current Stock Price =2/(1.13625^5)+105/(1.13625^5)
		P0=Current Market Price of stock	$56.50
		Market Value of Equity =10000*56.50	$565,000
		Face value of Bonds	$100
	A	Total Face Value of Debt	$300,000	(3000*100)
	Rate	Before Tax Cost of debt	6.50%	(3.5+2+1)
	Nper	Number of years to maturity	10
	Pmt=(A*6%)	Annual Coupon Payment	$18,000	(6%*300000)
	Fv=A	Payment at maturity	$300,000
	PV	Current Market Value of Debt	$289,217	(Using PV function of excel with Rate=6.5%,Nper=10,Pmt=-18000,Fv=-300000)
		CAPITAL STRUCTURE
	Md	Current Market Value of Debt	$289,217
	Me	Market Value of Common Equity	$565,000
	M=Md+Me	Total Market Value	$854,217
	Wd=Md/M	Weight of Debt	0.34
	We=Me/M	Weight of Equity	0.66
		Weighted Average Cost of Capital (WACC)=(Weight of debt*Cost of Debt)+(Weight of Equity*Cost of Equity)
		Weighted Average Cost of Capital (WACC)=Wd*Cd+We*Ce
		Weighted Average Cost of Capital (WACC)	10.55%	(0.34*4.55+0.66*13.625)
		Investment with return of 10% is not acceptable , because the return is less than cost of capital
							: fe =PV(132,133,-134, 135) F G H I J K L M N O P Q P5=Stock Price in Year 5 $105 PO=Current Stock Price =Present Value of Future cash flow discounted at cost of equity (13.625%) PO=Current Stock Price =2/(1.1362545)+105/(1.1362545) PO=Current Market Price of stock $56.50 Market Value of Equity =10000*56.50 $565,000 Face value of Bonds $100 Total Face Value of Debt $300,000 (3000*100) Before Tax Cost of debt 6.50% (3.5+2+1) Number of years to maturity 10 Annual Coupon Payment $18,000 (6%*300000) Payment at maturity $300,000 Current Market Value of Debt $289,217! (Using PV function of excel with Rate=6.5%,Nper=10, Pmt=-18000,Fv=-300000) CAPITAL STRUCTURE Rate Nper Pmt=(A*6%) Fv=A PV