Text:
State Bank and Trust (SBT) is a lender in the floating-rate instrument market, but it has been hurt by recent interest rate decreases. SBT often makes loan commitments for its customers and then accepts the rate in effect on the day the loan is taken out. SBT has avoided floating-rate financing in the past. It takes out a certain amount of fixed-rate financing in advance to cover its loan commitments. One particularly large upcoming loan has it worried. This is a $100 million loan to be made in 65 days at 180-day Libor plus 100 basis points. The loan will be paid back 182 days after being taken out, and interest will be based on an exact day count and 360 days in a year. Current Libor is 7.125 percent, which is the rate it could borrow at now for any period less than 180 days. SBT considers the purchase of an interest rate put to protect it against an interest rate decrease over the next 65 days. The put will have an exercise price of 7 percent and a premium of $475,000
Solution:
First we need to compound the premium for 65 days. This calculation tells us the effective cost of the put as of the time the loan is made:
475,000[1+ ( 0.07125 +0.01 )(65/360)] = 481,968
The outlay will effectively be $100,000,000 + $481,968 = $100,481,968.
My question is, why are they adding 100 basis points to libor in calculating future value? Are we supposed to assume that if they didn’t have to buy this put, they would have effectively loaned this money to someone at current libor plus 1? (I don’t know if I’ll ever be able to think like this in exam )