Calculation : the cost of borrowing

CFA Level I Corporate Finance
#1

A firm is looking at borrowing for two months and could issue $500,000 nominal of commercial paper at 7.5%. Dealer’s commission would be 0.25%, and backup line costs would be 0.3% based on the $500,000 issued. The cost of borrowing is closest to:

A) 7.85%

B) 8.05%

C) 8.15%

The equation shows as

Cost=(Interest+Dealer’s commission+Back−upcosts)/Netproceeds×12

And the answer is

[(0.075+0.0025+0.003)×$500,000+2/12]+6

divided by

$500,000−(0.075+$500,000+2/12)=0.0805/0.9875=8.15%

I do not understand the 2/12 and +6 in the equations. Could someone please explain

#2

Hi jgonnz,

The correct formula would be: [(0.075+.0025+.003) * 500,000 * 2/12] * 6

divided by

500,000 - (0.075 * 500,000 * 2/12)

The 2/12 is used because the rates are in an annual basis and you need them in a 2 months basis, therefore you divide them by 6

then the x 6 at the end is used to make the amounts expressed in 2 months basis comparable to an annual basis