York is taking out a $10,000,000 two-year loan at a variable rate of LIBOR plus

Question

York is taking out a $10,000,000 two-year loan at a variable rate of LIBOR plus 1.50%. The LIBOR rate will be reset each year at an agreed upon date. The current LIBOR rate is 4.00% per year. The loan has an upfront fee of 1.00%

a) What is the all-in-cost (i.e., the internal rate of return) of the York loan including the LIBOR rate, fixed spread and upfront fee?

b) What portion of the cost of the loan is at risk of changing?

c) If the LIBOR rate jumps to 5.00% after the first year what will be the all-in-cost (i.e. the internal rate of return) for York for the entire loan?

d) If the LIBOR rate falls to 3.00% after the first year what will be the all-in-cost (i.e. the internal rate of return) for York for the entire loan

Explanation / Answer

The All in cost will be 4.00 +1.50 =5.50% + 1% upfront fee will take the total cost to 6.50%. All in cost will be 0.065* 10,000,000 =$ 650,000. 4% of the loan (that is the LIBOR rate) has the chance of risk. If LIBOR changes to 5% the total cost of the loan will be 1.50+5+1 =7.5%. All in cost will be 0.075* 10,000,000 = $750,000 + 650,000 (for year 1) = $1,400,000. So IRR will be 7% on average for 2 years If LIBOR changes to 3% the total cost of the loan will be 1.50+3+1 =5.5%. All in cost will be 0.075* 10,000,000 = $550,000 + 650,000(for year 1) = $1,200,000. So the IRR will be 6% on average for 2 years

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