I am tring to study for my final on my own and I am stuck on a
problem,please help. Here is the question...

Commercial paper usually sold at a discount. Fan Corp. has just sold
an issue of 90-day commercial paper with a face value of $1 million.
THe firm has received initial proceeds of $978,000.

a) What effective annual rate will the firm pay for financing with
commercial paper, assuming that it is rolled over evey 90 days
throughout the year?

b) If a brokerage fee of $9,612 was paid from the initial proceeds to
an investment banker for selling the issue, what effective annual rate
will the firm pay, assuming that the paper is rolled over every 90
days throughout the year?

Thanks!!!

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Clarification of Question by help123-ga on 06 Apr 2005 10:37 PDT

I need this answer by Thursday.

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Request for Question Clarification by omnivorous-ga on 06 Apr 2005 11:42 PDT

Help123 --

This is not a toughy but you've asked it in a fashion that's a bit confusing:
the $978K sounds like it's net of all fees (as they're usually taken
off the top).  But in (b) it sounds as if you're adding $9,612
additional.

Are the brokerage fees additional?  Or included in the discounted proceeds?

Best regards,

Omnivorous-GA

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Clarification of Question by help123-ga on 06 Apr 2005 12:33 PDT

I assumed the brokerage fees are included in the discounted proceeds?

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Request for Question Clarification by omnivorous-ga on 06 Apr 2005 12:48 PDT

Help123 --

I think that makes a) and b) the same, though there might be some
differences in tax assumptions.  The fees would be possibly be
deductible instead of treated as a reduction in principal.

Best regards,

Omnivorous-GA

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Clarification of Question by help123-ga on 06 Apr 2005 17:53 PDT

Omnivorous-GA - 

Part a is calculating the effective interest rate.

Part b is calculating the effective annual return on the paper

Hope you can help, 
Help123

Help123 ?

I was writing this as you posted the last clarification -- and I think
that I've caught the exact response you're seeking.  (B) is the
effective annual return on the commercial paper.

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As you can tell from my clarification requests, portions of this
question were (and still are) confusing me.

It could be that this is meant to highlight the difference between the
price charged investors on the bond and the net to the company ?
called the ?gross spread?:

Comerica
?Glossary ? Gross Spread?
http://www.comerica.com/cma/cda/main/0,00,3_A_1823,00.html

I?m going to make one important assumption here:
?	every time the commercial paper is rolled over the brokerage fees
are paid again, which certainly is realistic

Let?s start with the easy part:

A.	90-DAY INVESTMENT

A $978,000 investment yields $1M, an interest rate of 2.25% to the
firm.  But just as credit cards compound (monthly), you?ll be paying
an additional 2.25% each quarter.  At low interest rates like this,
financial officers might call it a 9% effective annual rate, but it
does compound a little.

There are a couple of ways to figure it but this might be the easiest
to understand.

Q1: $22,000
Q2: $22,000 + 0.0225 * ($22,000)  -- using the $22,000 extra cash you
needed to pay back the bond
Q3: $22,000 +   0.0225 * ($44,000) ? you?re funded 2 quarters of $22,000 extra now
Q4: $22,000 + 0.0225 * ($66,000)?3 quarters where the company has
covered extra cash


TOTAL = $22,000 + $22,495 + $22,990 + $23,485 = $90,970

Interest rate = $90,970 / $978,000 = 9.30% 


B.	BROKERAGE FEES

Brokerage fees reduce the amount that the company receives ? so the
company?s interest rate is higher than the effective rate paid to
INVESTORS.
I know that your question asks about the company ? it?s paying the
SAME rate of 9.30%, as fees are included in its implied interest rate.
 The fees are a current expense.


This problem is made simpler by the fact that the underwriting or
brokerage fees are for the current year.  Were they for a longer
period, they?d have to be capitalized and spread over the expected
life of the bond.  (You have to do the same with points paid on a
mortgage.)

But the investors are paying $987,612 and receiving $1M back after 90
days.  So the interest that they?re receiving is $12,388.

90-day rate: $12,388 / $987,612 = 1.25%

Q1: $12,388
Q2: $12,388 + 0.0125 * ($12,388)  -- using the $22,000 extra cash you
needed to pay back the bond
Q3: $12,388 +   0.0125 * ($24,776) ? you?re funded 2 quarters of $22,000 extra now
Q4: $12,388 + 0.0125 * ($37,164)?3 quarters where the company has
covered extra cash

TOTAL = $12,388 + $12,543 + $12,698 + $12,853 = $50,482

Interest rate = $50,482 / $987,612 = 5.11%

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Again, this 5.11% is the investors? annual yield ? not the company?s. 
But it shows the gross spread ? and shows why investment banking has
always been so lucrative for MBA students.

Google search strategy:
Accounting underwriting fees bonds


Best regards,

Omnivorous-GA