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Aleks04 [339]
3 years ago
14

You have been managing a $5 million portfolio that has a beta of 1.05 and a required rate of return of 9.775%. The current risk-

free rate is 4%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.75, what will be the required return on your $5.5 million portfolio
Business
1 answer:
Lilit [14]3 years ago
6 0

Answer:

9.62%

Explanation:

Re = Rf + (B x Rp)

Re = cost of equity = 9.775%

Rf = risk free rate = 4%

B = beta = 1.05

Rp = risk premium = ?

Rp = (Re - Rf) B = (9.775% - 4%)/1.05 = 5.5%

Re portfolio = Rf + {Rp x [(B₁ x $5/$5.5) + (B₂ x $0.5/$5.5)]}

Re portfolio = 4% + {5.5% x [(1.05 x $5/$5.5) + (0.75 x $0.5/$5.5)]}

Re portfolio = 4% + {5.5% x [0.9545 + 0.0682]}

Re portfolio = 4% + 5.6249% = 9.62%

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An author just signed a lucrative contract with a publisher that offers to pay her the amount of $500 at the end of year 9 when
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Answer:

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Hi, first, let´s bring that $500 to be paid in 9 years to present value, we need to use the following formula.

PresentValue=\frac{FutureValue}{(1+r)^{n} }

Where: r is our discount rate (7%) and n the periods from now when she will receive that $500 amount. This should look like this.

PresentValue=\frac{500}{(1+0.07)^{9} } =271.97

Ok, so the equivalent amount of money today of those $500 in nine years is $271.97, but the author wants $100 today so the remaining amount has to be used to find the equal annual payments to be made in order to be equivalent to re remaining balance ($171.97). We now need to use the following equation.

Present Value=\frac{A((1+r)^{n}-1 )}{r(1+r)^{n} }

And we solve for "A" like this

171.97=\frac{A((1+0.07)^{9}-1 )}{0.07(1+0.07)^{9} }

171.97=\frac{A(0.838459212 )}{0.128692145}

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A=\frac{171.97}{6.515232249} = 26.40

Therefore, the equivalent amount of money of $500 in 9 years is $100 today and $26.40 every year, at the end of the year, for nine years.

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Solution

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