Setrakian Industries needs to raise $87.9 million to fund a new project. The company will sell bonds that have a coupon rate of 5.92 percent paid semiannually and that mature in 20 years. The bonds will be sold at an initial YTM of 6.67 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds

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

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