## Sunday, September 16, 2012

### Present Value of Bond Practice Problem

A company decides to issue bonds payable to finance the acquisition of a new machine. The total bond issue will be \$1,000,000. The bond that will be issued by the company is offering a 10 year term with semi-annual payments of interest at an annual rate of 5%.

At the time of issuance the market rate for a similar offering with similar risk was 8%.

Solve this bond accounting problem and calculate the issue price of the bonds. Also, note if this is a discount or a premium on the face value of the bond.

Present value factors are shown below and are needed to solve this bond problem:

PV of a single sum for 10 periods at 5% is : .614
PV of a single sum for 20 periods at 5% is : .377
PV of a single sum for 10 periods at 8% is : .463
PV of a single sum for 20 periods at 8% is : .215
PV of a single sum for 10 periods at 4% is : .676
PV of a single sum for 20 periods at 4% is : .456

PV of an Annuity for 10 periods at 5% is : 7.722
PV of an Annuity for 20 periods at 5% is : 12.462
PV of an Annuity for 10 periods at 8% is : 6.710
PV of an Annuity for 20 periods at 8% is : 9.818
PV of an Annuity for 10 periods at 4% is : 8.111
PV of an Annuity for 20 periods at 4% is : 13.590

Future Value (FV) = 1,000,000
N = 10 yrs x 2 = 20
Interest = 8%/2 = 4%
PMT = .05/2 x 1,000,000 = 25,000
PV = ?

PV of the 1,000,000 Bond
1,000,000 x .456 = 456,000

PV of the Bond Payments....
25,000 x 13.590 = 339,750

Answer= PV of Bond is 456,000 + 339,750 = \$795,750. Each individual bond is sold at a discount of 795.75

bestuhlung said...

I never understand this kind of measurement, but it's looking interesting here!

Anonymous said...

PV of future cash flows for the coupon \$25000(1-(1/1.04 to 20))/1.04 to 20)would equal \$339,758.16.

PV of the final face value (1000000/(1.04 to the power of 20)) equals \$456,386.95

Total PV should therefore = \$796,145.11 (10000 x \$1000 bonds = \$796.15ea)

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