Question

Short Term Inc. has issued zero-coupon bonds that mature in one year. The returns from holding these bonds have a beta of 0.25. There is a chance of 70% that the bonds will pay full value, and a chance of 30% that they will only be worth 60 cents for each dollar of face value.Assume that the CAPM holds, that the riskless rate is 5% and that the expected return on the market is 15%.1) What is the current price of the bonds, per $100 face value?2) What is the yield to maturity on the bonds?3) What is the expected return on the bonds?

Answer 1

Answer:

1. Current bonds price = $81.86.

2. Yield to maturity  = 22.16%.

3. 3.  Expected Return = 7.5%.

Explanation:

Required Rate = Rf + beta*MRP

          = 5% + 0.25*(15% - 5%)

       = 5% +0.25*10%

              = 5% + 2.5% = 7.5%

 Required Rate = 7.5%

  Expected Future Value = 70% x $100 + 30% x $60

       = (0.7*$100) + (0.3*$60)

       = $(70+18) = $88

    Expected Future Value = $88

1.  Current bonds price = 88/1.075 = $81.86

2.  Yield to maturity = 100/81.86 - 1 = 1.22159785-1 = 0.22159785 =   22.159785% = 22.16%

3.  Expected Return = 7.5%