FIN 501 Final: FIN 501 Formula Sheet.pdf
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1 | Bond MathΓ’ΒΒAmortizing Loan | |||||
Bank ABC makes a $10,000,000 loan to its customer, XYZ. Bank ABC receives a fee at closing equal to 1% of | ||||||
the principal amount of the loan. The loan has a 5.25% per annum, with interest payable quarterly. Principal | ||||||
is payable quarterly in 20 equal payments on each quarterly interest payment date. The loan closed on | ||||||
May 1, 2017; interest and principal is payable on February 1, May 1, August 1 and November 1 of each year, | ||||||
beginning August 1, 2017. Interest accrues and is payable based on a 30/360 basis. | ||||||
Assume the initial market yield is 5.25%. | ||||||
(a) Show cash flows on the loan and the loan amortization schedule in the table below. | ||||||
Date | Beginning Balance | Interest | Principal | Ending Balance | ||
5/1/17 | ||||||
8/1/17 | ||||||
11/1/17 | ||||||
2/1/18 | ||||||
5/1/18 | ||||||
8/1/18 | ||||||
11/1/18 | ||||||
2/1/19 | ||||||
5/1/19 | ||||||
8/1/19 | ||||||
11/1/19 | ||||||
2/1/20 | ||||||
5/1/20 | ||||||
8/1/20 | ||||||
11/1/20 | ||||||
2/1/21 | ||||||
5/1/21 | ||||||
8/1/21 | ||||||
11/1/21 | ||||||
2/1/22 | ||||||
5/1/22 | ||||||
(b) Assuming that all payments are made on the due date and there are no prepayments, what is the | ||||||
internal rate of return based on quarterly compounding and considering fees, earned by Bank ABC on the loan? | ||||||
(c) What is the internal rate of return calculated in (b) above stated on a semi-annual bond equivalent basis? | ||||||
(d) If the market rate of interest on the loan increases to 5.35% per annum, compounded quarterly, what is the | ||||||
market value of the loan? | ||||||
(e) If the market rate of interest on the loan decreases to 5.15% per annum, compounded quarterly, what is the | ||||||
market value of the loan? | ||||||
(f) What is the average life of the loan assuming no prepayments? | ||||||
years | ||||||
(g) What is the approximate duration of the loan? Use 10bp yield changes. | ||||||
(h) What is the approximate convexity of the loan? Use 10bp yield changes. | ||||||