Answer:
Minimum number of units to be issued = 45,791.4 units
Step-by-step 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