Answer:
47,884.79 units of bonds
Explanation:
The units to be sold to arise $87.9 million will be equal to the
$87.9 million / divided by the bond price
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 = 5.92/2 = 2.96%
Interest payment =2.96%× 2,000= 59.2
Semi annual yield = 6.67%/2 = 3.335
PV of interest payment
= A ×(1- (1+r)^(-n))/r
= 59.2× (1-(1.03335)^(-2×20))/0.03335)
= 1,297.22
Step 2
PV of redemption value
PV = FV× (1+r)^(-n)
= 2,000 × (1+0.03335)^(-2× 20)
= 538.43
Step 3
Price of bond =
= 1297.22 + 538.43
= $1835.65
Step 4
Units to be used
= $87.9 million/ $1,835.65
= 47,884.79 units
Answer:
47,885 bonds
Explanation:
In determining the number of bonds that must be sold to raise $87.9 million to fund the project , the current price per bond can computed which can thereafter be used to divide the expected proceeds from the issue in order to determine the number of bonds to be issued.
The current price of the bond can be calculated using the pv formula in excel which is given as:
=pv(rate,nper,pmt,fv)
rate is the yield to maturity divided by 2 since interest is paid twice a year
that is 6.67%/2
nper is the time to maturity of the bond multiplied by 2;20*2
pmt is the six month interest receivable by investors 5.92%/2*$2000=$59.2
fv is the face value at $2000
=pv(6.67%/2,40,59.2,2000)
pv=$1835.66
The number of bonds=$87,900,000/$1835.66
=47885 bonds
