Question

Problem 5-11

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $55,200 or $161,100, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 4%.

Required:

(a)	If you require a risk premium of 8.5%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)

Price

$

(b)	Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Rate of return

%

(c)	Now suppose you require a risk premium of 11.5%. What is the price you will be willing to pay now? (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)

Price

$

Answer 1

Solution:
a.	Price	96,133
Working Notes:
	Expected Cash flows from the portfolio = sum of (probability x Cash flows )
	Expected Cash flows from the portfolio = 0.5 x $55,200 + 0.5 x $161,100
	Expected Cash flows from the portfolio = $108,150
	Required rate of return = Risk free rate + Risk premium
	Required rate of return = 4% + 8.5%
	Required rate of return = 12.5%
	Let willing to pay value of portfolio be Y
	Y x (1+ Required rate of return) = Expected cash flows from the portfolio
	Y x (1+ 0.125) = $108,150
	Y = $108,150/(1+ 0.125)
	Y =$96,133.3333
	Y=96,133
	Amount willing to be paid for the portfolio = $96,133
b.	Rate of return	12.50	%
Working Notes:
	Since, in given situation required rate of return will be the expected rate of return
	Expected Rate of return = (Expected cash flows - Amount paid )/Amount paid
	Expected Rate of return = (108150 - 96133.33333)/96133.33333
	Expected Rate of return = 0.125
	Expected Rate of return = 12.50%
C.	Price	93,636
Working Notes:
	Expected Cash flows from the portfolio = sum of (probability x Cash flows )
	Expected Cash flows from the portfolio = 0.5 x $55,200 + 0.5 x $161,100
	Expected Cash flows from the portfolio = $108,150
	Required rate of return = Risk free rate + Risk premium
	Required rate of return = 4% + 11.5%
	Required rate of return = 15.5%
	Let willing to pay value of portfolio be Y
	Y x (1+ Required rate of return) = Expected cash flows from the portfolio
	Y x (1+ 0.155) = $108,150
	Y = $108,150/(1+ 0.155)
	Y =$93,636.36364
	Y=93,636
	Amount willing to be paid for the portfolio = $93,636
Please feel free to ask if anything about above solution in comment section of the question.