On January 1, 2018, OU Company issued 12% bonds with a $20 million face value and a maturity date of December 31, 2019. The market rate is 14%. Coupon payments are due semi-annually and the first coupon payment is due on June 30, 2018. What is the present value of the bond at issuance (i.e., January 1, 2018)

The value of a bond is the sum of the of the cash inflows generated by the bond over its life span discounted at the required rate of return. The required rate of return represents opportunity cost of investing the bond; and it is given as 14% in this question.

The cash inflows are the interest payments and the redemption value.

The present value of these two cash inflows would be computed and added.

Time to maturity = 2 years

Semi-coupon rate = 14% * $12 m × 1/2 =.$1,400,000

Present Value(PV) of Interest payment

Time to maturity = 2 years

Interest payment per 6 months = 14% * $12 m × 1/2 =.$1,400,000

PV =1,400,000 × (1-(1.007)^(-4) - 1)/0.07

= 1,400,000 × 3.3872

= $4,742,095.76

Present Value of redemption value

= 20,000,000 × (1.14)^(-2)

= $15,389,350.57

Present value of the bond issuance

=$4,742,095.76 + $15,389,350.57

= $20,131,446.33

Present value of the bond issuance = $20,131,446.33