Question

2. You have $200,000 to invest in Stock D, Stock E, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 15 percent If D has an expected return of 18 percent and a beta of 1.50, E has an expected return of 15.2 percent and a beta of 1.15, and the risk-free rate is 6 percent, and if you invest $60,000 in Stock D, how much will you invest in Stock E? Brighton, Inc. has bonds outstanding that will mature 12 years from today with a coupon interest rate 3. of 7% paid semi-annually. If investors require 5% YTM for the next 3 years and 6% thereafter, what is the maximum price you are willing to pay?

Answer 1

	2	Portfolio Return =w1R1+w2R2+w3R3
		w1,w2 and w3 are weights of assets1,2 and 3 in the portfolio
		R1,R2 and Re3 are return of assets 1,2 and 3
		R1=Return of stockD=18%
		R2=Return of stock E=15.2%
		R3=Return of risk free asset=6%
		Weight of stock D in the portfolio=w1=60000/200000=	0.3
		w1+w2+w3=1
		w2+w3=1-0.3=0.7….......Equation(1)
		w1*18+w2*15.2+w3*6=Expected Portfolio Return =15%
		0.3*18+w2*15.2+w3*6=15
		15w2+6w3=15-5.4=9.6…....Equation(2)
		Multiplying Equation(1)by 6
		6w2+6w3=6*0.7=4.2….....Equation (3)
		Subtracting (3) from (2)
		9w2=5.4
		w2=5.4/9=	0.6
		w3=1-w2-w3=1-0.3-0.6=0.1
		Amount invested in stock E =w2=0.6*200000=	$120,000
	3
		Fair Price of Bond =Present Value of Future cash flows
		Fair Price at the end of 3 years(after receipt of coupon)
		Semi annual coupon =(1000*7%)/2	$35.00
		Payment at maturity = Par value (assumed to be 1000)
		Present Value of cash flow=Cash Flow/((1+i)^N)
		i=discount rate per period =(6/2)=3%=0.03
		N=Semi annua period of cash flow
		N	A	PV=A/(1.03^N)
		Semi annual Period from end of year3	Cash Flow	Present Value
		1	$35	$33.98
		2	$35	$32.99
		3	$35	$32.03
		4	$35	$31.10
		5	$35	$30.19
		6	$35	$29.31
		7	$35	$28.46
		8	$35	$27.63
		9	$35	$26.82
		10	$35	$26.04
		11	$35	$25.28
		12	$35	$24.55
		13	$35	$23.83
		14	$35	$23.14
		15	$35	$22.47
		16	$35	$21.81
		17	$35	$21.18
	(1000+35)	18	$1,035	$607.95
			SUM	$1,068.77
		Fair Value of the Bond at the end of Year3	$1,068.77
		Fair Value TODAY:
		Discount rate =semi annual YTM =2.5%=0.025
		N	B	PV=B/(1.025^N)
		Semi annual Period from today	Cash Flow	Present Value
		1	$35	$34.15
		2	$35	$33.31
		3	$35	$32.50
		4	$35	$31.71
	(35+1068.77)	5	$35	$30.93
		6	$1,103.77	$951.78
			SUM	$1,114.38
		MAXIMUM PRICE I SHOULD BE WILLING TO PAY	$1,114.38	per $1000 par value