after-tax cost of debt

[kaia_p]

Valence Industries issues a bond to finance a new project. It offers a 10-year, 5 percent semi-annual coupon bond. Upon issue, the bond sells at $1,025. What is Valence’s before-tax cost of debt? If Valence’s marginal tax rate is 35 percent, what is Valence’s after-tax cost of debt?
Solution:
Given:
PV = $1,025
FV = $1,000 PMT =5 percentof1,000÷2=$25
n = 10 × 2 = 20 ⎛20 $25 ⎞ $1,000
$1,025 = ⎜∑ t ⎟ + 20 ⎝t=1(1+i)⎠ (1+i)

how was the FV derived in the Solution?
Thanks!
K.

 

[S2000magician]

You wrote some weird stuff there.

• PV = -1,025
• FV = 1,000
• PMT = 25
• n = 20
• Solve for i = 2.3420% as the semiannual rate

So the effective annual rate is (1.02342)² – 1 = 4.7389%. Thus, the after-tax cost of debt is 4.7389% × (1 – 35%) = 3.0803%.
Note that you use the effective annual rate, not the bond equivalent rate.

 

[kaia_p]

S2000magician wrote:
You wrote some weird stuff there.

• PV = -1,025
• FV = 1,000
• PMT = 25
• n = 20
• Solve for i = 2.3420% as the semiannual rate

So the effective annual rate is (1.02342)² – 1 = 4.7389%. Thus, the after-tax cost of debt is 4.7389% × (1 – 35%) = 3.0803%.
Note that you use the effective annual rate, not the bond equivalent rate.

Cheers- I think the format might have shifted a bit after copying. Sorry still fail to understand how did you calculate the FV since it was not given in the data

 

[S2000magician]

Unless stated otherwise, bonds have a par (face) value of 1,000 (dollars, euro, pounds, Francs, whatever). The only (common) exception is bonds denominated in yen, which have, I believe, a value of JPY10,000.

 

[MrSmart]

kaia_p wrote:

S2000magician wrote:
You wrote some weird stuff there.

• PV = -1,025
• FV = 1,000
• PMT = 25
• n = 20
• Solve for i = 2.3420% as the semiannual rate

So the effective annual rate is (1.02342)² – 1 = 4.7389%. Thus, the after-tax cost of debt is 4.7389% × (1 – 35%) = 3.0803%.
Note that you use the effective annual rate, not the bond equivalent rate.

Cheers- I think the format might have shifted a bit after copying. Sorry still fail to understand how did you calculate the FV since it was not given in the data

$1,000 or sometimes $100 is the default face value of bonds.
If a bond is issued at a disconut of $650, then it must have a face value of $1,000.
If a bond is issued at a premium of $109, then it’s FV is $100.

 

[kaia_p]

Makes sense Thanks for that-cheers!