Question

Montgomery Burns needs $14 million to expand his business. He decides to sell 15-year zero-coupon bonds with a $1,000 face value to finance the expansion. The bonds will be priced to yield 5 percent annually. What is the minimum number of zero-coupon bonds he must sell? Use annual compounding.

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}

= 1000/1.05^15

= 1000/2.07892817941

= $481.02

number of zero-coupon bonds = Amount needed/Value of zero-coupon bond

= 14 million /481.02

= 29,105