Question

ABC Enterprises issues $400,000 of bonds paying a stated interest rate of 7%. The bonds are due in 10 years, with interest payable annually each year on Jan. 1st. When the bonds are issued, other bonds of similar risk and maturity are paying 11% (i.e. the discount rate or market interest rate is 11%) alculate the issuance (selling) price of this bond (int. payment) (factor)-- Present value of interest payments (annuity portion) Present Value of Bond Principal (single sum value) Total Present Value, or selling price 400,000 (principal)* (factor) Is the bond issued at a premium, discount, or face value (par)?

Answer 1

Answer:

$305,772.29  

The bond was issued at discount

Explanation:

The pv value approach in excel comes handy in determining the price of teh bond.

The formula is stated below:

=-pv(rate,nper,pmt,fv)

rate is the yield to maturity of other bonds of similar risk and maturity at 11%

nper is the number of times that the bond would pay coupon interest to the bondholders ,since the bond is an annual coupon paying bond,it would pay coupon for 10 years

pmt is dollar value of the coupon payable by the bond annually which is 7%*$400,000=$28,000

fv is the face value of the bond at $400,000

=-pv(11%,10,28000,400000)=$305,772.29  

Since the bond was be issued at a price lower than its face value,hence it was issued at a discount

Alternatively

Present value of interest payment = 28000 * 5.8892 = 164,898

Present value of Bond Principal = 400000 * 0.3522 = 140,874.

Total present values                                                        305,772

Answer 2

Answer:

Present value of interest payments = $164,897.83

Present value of bond principal = $140,874.83

Total present value = $305,772.66

The bond was issued at premium.

Explanation:

Face value of the bond = $400,000

Interest rate = 7%

Annual interest payable = 7% of 400000

                    = $28,000

Present value adjusts the value of a future payment into today’s dollars.

We calculate the present value of annual payment of $28,000 for a period of 10years. This is an annuity and we shall calculate using the present value of annuity formula. We also find the present value of bond principal paid at the end of 10years.

$PVA = I [1 - (1+r)^-^n]/r$

Where:

I = annual interest payable = $28,000

r = discount rate or market interest rate = 11%

n = number of years = 10 years

$PVA = 28000[1 - (1+0.11)^-^1^0]/0.11\\ = 28000[1 - (1.11)^-^1^0]/0.11\\\\ = 28000(0.6478)/0.11\\ = 164897.83$

$Present value of principal = P[1+r]^-^n$

Where:

P = Lump sum at maturity = $400000

r = discount rate = 11%

n = maturity period = 10 years

$PV = 400000[1+0.11]^-^1^0\\PV = 400000 * [1.11]^-^1^0\\ = 400000 * 0.3522\\ PV = 140874.83$

Total present value = 164897.83 + 140874.83

Total present value = $305,772.66

Since total present value is less than the face value of the bond of $400,000, it is safe to conclude that the bond was issued at a premium.