The Mongoose Emporium needs to raise $2.8 million for expansion. The firm wants to raise this money by selling 20-year, zero-coupon bonds with a par value of $1,000. The market yield on similar bonds is 6.49 percent. How many bonds must the company sell to raise the money it needs? Assume semiannual compounding. A formula appended to this examination can be applied to the calculation. Keep in mind that the coupon payments are semi-annual.

10,045 bonds

Explanation:

to determine how many bonds Mongoose must sell, we first need to calculate the present value of 1 bond using the present value formula:

present value = future value / (1 + r) ⁿ

future value = $1,000 r = 6.49% / 2 = 3.245% n = 20 years = 40 semiannual periods

present value = $1,000 / (1 + 3.245%) ⁴⁰ = $1,000 / (1 + 3.245%) ⁴⁰ = $1,000 / 3.58724 = $278.765 ≈ $278.77

Each bond can be sold at $278.77, so in order to receive $2,800,000, you need to sell = $2,800,000 / $278.77 = 10,044.12 ≈ 10,045 bonds

10,044 bonds

Explanation:

N=40

I%=6.49/2=3.245

PMT=0

FV=1000

CPT PV = - 278.77

$2,800,000/278.77 = 10,044 bonds