A company can issue commercial paper with an all inclusive rate that reflects a 6.5% annual interest rate, a dealer’s commission of 1/10%, and a backup cost of 1/5%. Its effective annualized cost of borrowing $2 million for three months is closest to: a. 6.5% b. 6.84% c. 6.91% d. 10.37%

Is it D?

C. I still don’t get it. I keep getting ~7.72% when I do it. Don’t know what I’m doing wrong. Stalla answer: [(0.065+0.001+0.002)*(3/12)]/[1-((0.065)*(3/12))]*4 This does not make any sense to me. Can someone please explain.

I so hate working capital!

6.5 is the annual interest, multiplied with period/12 to determine the interest per period 0.001 is the dealer’s commission, multiplied with period/12 to determine the interest per period 0.002 is the backup cost, multiplied with period/12 to determine the interest per period All divided by what’s remaining from the loan, 1- annual interest rate*period/year and the result multiplied with how many 3 month periods are in 1 year. Don’t bother to multiply with the principal of the ammopunt borrowed, it reduces both from the numerator and denominator.

Otherwise: Numerator: (0.065*3/12*2,000,000+0.001*3/12*2,000,000+0.002*3/12*2,000000) Interest expense + dealer’s commission + back-up cost Denominator: (2,000,000 - 0.065*3/12*2,000,000) Total borrowed - interest= net proceeds multiplied with 4 because there are 4 periods of 3 months each in a year.

but aren’t commissions absolute? i.e. I sell $10M in commercial paper and have a 1/10% commission and pay $100K commission right away, no matter duration of the CP, or do I have this wrong? Also what the he*l is backup cost?

I so have no clue, but that’s the formula, on cfai text, volume 4, page 126-127. If the interest rate on the commercial paper is quoted as all inclusive and details the inclusive costs, than it must be commission and backup cost flowing together with the annual interest, each month.

I think Stalla’s formula is wrong because “but aren’t commissions absolute? i.e. I sell $10M in commercial paper and have a 1/10% commission and pay $100K commission right away, no matter duration of the CP, or do I have this wrong? Also what the he*l is backup cost?” So break it down. First, the $2M doesn’t matter if the answers are in % terms. Next, commercial paper is sold on a discount yield basis so the denominator is what we get not if we want to borrow $2M, but what we get if we want to pay back $2M. So if I want to pay back 2M in 3 months at a 6.5% rate I get (1-0.065*3/12)*2M = 1.9675 M But I’m going to have to pay back 2 M - 1.9675 M = $32,500 I’m goin to have to pay 10 bp commission = $2000 and back-up costs of 20 bp = $4000 So total cost = 38,500/1967500 = 1.956% for the quarter. Annualize that and we get some number like OP got. I suppose it’s possible that back-up costs are quoted on an annualized basis but no chance that commissions are. Back-up costs are about a kind of guarantee provided by a bank to pay up on the commercial paper in some circumstances.

Joey, the CFAi text gives that formula. Working Capital is a new little “thing”, about 5 pages lenght, added to the Level I this year in Corporate Finance. Agree it makes no sense.

“Joey, the CFAi text gives that formula.” Doesn’t matter at all if it’s wrong. I’ve never traded commercial paper (someone here does that…plyon maybe?), but it’s really hard to believe that someone says “My commission is 10 bp” and they divide that by the maturity of the paper.

back up cost is the unused line fee a bank charges to the Company on a revolving credit facility. So for example IBM has a $2bn revolving credit facility (basically a large credit card) and every time they draw money on the line they will pay LIBOR + some margin…like L + 100bps (probably a lot lower for an investment grade company like IBM). However, the part of the revolving credit facility that is unused, the bank charges them an ‘unused line fee’ most likely like 15 to 20bps…not margin over LIBOR just 15 to 20bps on the amount of revolver availability / unused amount. So if you are a commercial paper issuer, you have an unused revolver as a ‘back up’ in case you can’t sell the CP and have to draw on the revolver. Large corporation like using CP’s as it is cheaper then the revolver, no investor would lend money to a company that does not have a back up line. Companies like CIT and other financial, non-financial companies have had to draw on their revolver as the CP market has been frozen due to the credit crunch lately and they have had a tough time selling their CP. Hope this helps…

Just thought of something regarding the absolute nature of commission as mentioned above. I think the question is assuming that the company would issue the cp for 3 months, then keep re-issuing after at maturity for 3 more quarters and keep paying 10bps for commission every time around…and thus this way we would get the ‘effective annualized cost of borrowing $2MM for three months’.

Good info up there BlueCollar. Thx. I don’t understand your last point. I also think the commission and the question says 40 bp/year on reissued 3m cp. Stalla’s answer and the formula in CFAI imply 10 bp/year which just can’t be.