Question

Cincinnati Exporters wants to raise $40 million to expand its business. To accomplish this, it plans to sell 22-year, $1,000 face value, semiannual coupon bonds. The bonds will be priced to yield 6.85 percent and coupon rate of 5.72 percent. What is the minimum number of bonds it must sell to raise the money it needs

Answer 1

Answer:

Minimum number of units to be issued = 45,791.4 units

Explanation:

The units of the bonds to be sold to raise the money equals to the price of the bonds divided by the sum to be raised

The price of a bond is the present value (PV) of the future cash inflows expected from the bond discounted using the yield to maturity.

These cash flows include interest payment and redemption value

The price of the bond can be calculated as follows:

Step 1

PV of interest payment

Semi-annual coupon rate = 5.72/2 = 2.86 %

Semi-annual Interest payment =( 2.86 %×$1000)= $28.6

Semi annual yield = 6.85%/2 = 3.42%

PV of interest payment  

= A ×(1- (1+r)^(-n))/r

A- interest payment, r- yield -3.42%, n- no of periods- 2 × 22 = 44 periods

= 28.6× (1-(1.0342)^(-44)/0.0342)= 645.82

 

Step 2  

PV of redemption value (RV)

PV = RV × (1+r)^(-n)

RV - redemption value- $1000, n- 7, r- 4.5%  

= 1,000 × (1+0.0342)^(-2×22)

= 1000 × 1.0342^(-44)= 227.7

Step 3

Price of bond = PV of interest payment + PV of RV

645.82 + 227.7= 873.525

Minimum number of units to be issued = $40 million/873.5= 45,791.4 units

 

Minimum number of units to be issued = 45,791.4 units