Lycan, Inc., has 8.6 percent coupon bonds on the market that have 9 years left to maturity. The bonds make annual payments.

Lycan, Inc., has 8.6 percent coupon bonds on the market that have 9 years left to maturity. The bonds make annual payments.

Required:

If the YTM on these bonds is 10.6 percent, what is the current bond price? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current bond price

$

rev: 05-02-2011

Explanation:

The price of any bond is the PV of the interest payments, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be:

P = $86({1 – [1/(1 + 0.106)]9} / 0.106) + $1,000[1 / (1 + 0.106)9]

P = $887.52

We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as:

PVIFR,t = 1 / (1 + R)t

which stands for Present Value Interest Factor

PVIFAR,t = ({1 – [1/(1 + R)]t } / R)

which stands for Present Value Interest Factor of an Annuity

These abbreviations are shorthand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in the remainder of the solutions key. The bond price equation for this problem would be:

P = $86(PVIFA10.6%,9) + $1,000(PVIF10.6%,9)

P = $887.52

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

9

10.6%

±$86

±$1,000

N

I/Y

PV

PMT

FV

Solve for

$887.52