Question

In: Finance

1. Assume the economy can either be booming or in recession. The probability of a boom...

1. Assume the economy can either be booming or in recession. The probability of a boom is 65%. If the economy is booming, a certain stock has an expected return of 20%. If the economy is in recession, the expected return of that same stock is 4%. What is the long term expected return of the stock?

2. Over the last year you observe that a certain company had a stock return of 24%, while the market had a return of 12%, and the risk-free rate was 2%. What would be your estimate of the firm's beta?

3. Assume a corporation is expecting the following cash flows in the future: $-4 million in year 1, $8 million in year 2, $21 million in year 3. After year 3, the cash flows are expected to grow at a rate of 4% forever. The discount rate is 12%, the firm has debt totaling $39 million, and 10 million shares outstanding. What should be the price per share for this company?

4. Stock A has a beta of 1.4, and stock B has a beta of 1.2. You invest 0.8% of your capital in stock A, and the rest in stock B. What is the beta of the resulting portfolio?

5. As with most bonds, consider a bond with a face value of $1,000. The bond's maturity is 19 years, the coupon rate is 5% paid semiannually, and the discount rate is 17%.

What is the estimated value of this bond today?

6. As with most bonds, consider a bond with a face value of $1,000. The bond's maturity is 16 years, the coupon rate is 8% paid annually, and the discount rate is 13%.

What is this bond's coupon payment?

Solutions

Expert Solution

1)Probability of recession = 100-65= 35%

long term expected return of the stock =[Er of boom* probabiliy of boom]+[Er of recession*Probability of recession]

     =[20*.65]+[4*.35]

   = 13+1.4

    = 14.4%

2)Return on stock =Rf+ [beta*(Return on market -Rf)]

      24= 2+ [B(12-2)]

     24-2 = 10 B

   B(beta) = 22/10 = 2.2

3)Terminal value at year3 =CF3(1+g)/(Rs-g)

      = 21(1+.04)/(.12-.04)

     = 21 *1.04 / .08

        = 273

Value of firm =[PVF12%,1*CF1]+[PVF12%,2*CF2]+.....[PVF12%,3*TV]

    =[.89286*-4]+[.79719*8]+[.71178*21]+[.71178*273]

   = -3.5714+ 6.3775+ 14.9474+ 194.3159

    = 212.0694

Value of equity = 212.0694 - 39

     = 173.0694

price per share= value of equity /shares outstanding

              = 173.0694/10

            = $ 17.30694 or 17.31 per share

4)Beta of portfolio =[Beta of a*Weight a]+[Bb*Wb]

      = [1.4*.8]+[1.2*.20]

        = 1.12+ .24

         = 1.36

**weight of B = 1-.80 = .20

jeff jeffy answered 2 years ago
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