Question

Roberts Co.'s zero coupon bonds mature in 22 years and have a yield to maturity of 12%. Each zero has a face value of $1,000 and there are 2,000 of the bonds outstanding. If the market value of Roberts' equity is $1,000,000, what capital structure weight for debt would you use in calculating the WACC, assuming Roberts' only debt consists of the zeros? .

Answer 1

Price of a zero-coupon bond is the present value of future cashflows discounted at required rate of return. As far as a zero-coupon bond is concerned, it does not pay any coupon payments, it pays only a lump sum amount on its maturity.

Value of zero-coupon bond = Face vale / (1+required return)^{time to maturity}

= 1000/1.12^22

= 1000/12.1003100562

= 82.6425

market value of debt = Value of zero-coupon bond*bonds outstanding

= 82.6425*2000

= 165285

Weight of for calculating WACC = 165285/(165285+1000000)

= 165285/1165285

= 14.18%