Question

6. Bondigo Beverage Inc. is planning to issue two types of 20-year, noncallable bonds to raise a total of $8 million, $4 million from each type of bond. First, 4,000 bonds with a 10% semiannual coupon will be sold at their $1,000 par value to raise $4,000,000. These are called "par" bonds.

Second, Original Issue Discount (OID) bonds, also with a 20-year maturity and a $1,000 par value, will be sold, but these bonds will have a semiannual coupon of only 7.05%. The OID bonds must be offered at below par in order to provide investors with the same effective yield as the par bonds. How many OID bonds must Bondigo issue to raise $4,000,000? Disregard flotation costs, and round your final answer up to a whole number of bonds.

show the calculations

Answer 1

Calculations for OID Bonds

Coupon Rate = 7.05%

YTM = 10% ( because the bonds with 10% coupon are sold at par, which means YTM is 10%. Else, they would also have been sold at premium or discount)

To find the number of bonds to be issued to raise $4,000,000, let's first calculate the price of 1 bond, at which 1 bond can be sold to investors

Price of OID = Present Value of all the coupons to be received + Present Value of the Face value to be received by investors at the end of 20 years

FV = Face Value = Par value = 1000

Here, C = Coupon amount = (7.05% of FV ) to be paid semi-annually = 70.5 / 2 = 35.25

No. of payment periods = 20 years x 2 times a year = 40

YTM = 10% per year

We can calculate the Bond price using excel formula of PV or using the YTM formula using a calculator.

Using excel, the formula is =-PV(0.1/2,40,35.25,1000,0)

Here, Rate is the rate per compounding period, that is, the semi-annual rate, which is 10% / 2 = 0.05

Nper is the number of coupon payment periods = 40

Pmt is the amount of coupon paid = 1000 * 7.05% * 1/2 = 35.25

Type = 0 means that the coupons are paid at the end of the 6 months.

We have used the minus sign in the original formula because the PV formula calculates Present value of investment to be made by us at the end of every 6 months. Bond value is thus exactly opposite of thay. So, we use the opposite sign, that is minus sign.

So, The company can sell an OID bond at $746.90.

It needs to raise $4,000,000 using OID Bonds.

So, No. of bonds to be issued = Amount to be raised / Price of 1 OID Bond = 4,000,000 / 746.90 = 5355.47 = 5356 (rounding off to next number)

Therefore, the company has to issue 5356 OID bond to investors to raise $4,000,000

Note: You may also use the YTM formula to calculate Bond Price. It is explained as below

Bond Price, P = [C x (1 - ((1+(i/2))^-n)) / i/2] + [ FV x (1+(i/2))^-n]

where, C = Coupon amount = 35.25

i = YTM = 10% = 0.10

n = no. of coupons to be paid = 20 years x 2 times a year = 40

FV = Redemption value of bond = 1000

We will get the same answer using this formula too.