Question

A bank uses its mortgage loans of $500 million as collateral to issue two different trenches of securities (CMOs) in mortgage markets, Trench A and Trench B. The information is given below. Assume the coupon payment is made annually.

Loan value: $500 million

Interest rate: 6.5%

Maturity: 10 years

CMOs: Par value & Interest rate

Trench A $350 million 4.5%

Trench B $250 million 6.25%

a) Please estimate the profits from the CMO.

b) The bank would like to make a profit of $20 million from the CMO by adjusting the interest rate for Trench B. Please estimate what should be the new interest rate.

Answer 1

a

Loan value	500,000,000
Interest rate	6.50%
Maturity Yrs	10
Annual interest payment	32,500,000
= 500 M* 6.5%
Trench A
Face value	350,000,000
Interest rate	4.50%
Maturity Yrs	10
Annual interest payment	15,750,000
= 350 M* 4.5%
Trench B
Face value	250,000,000
Interest rate	6.25%
Maturity Yrs	10
Annual interest payment	15,625,000
= 250 M* 6.25%

Year	1	2	3	4	5	6	7	8	9	10	10
Cash flows
From Loan	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	500,000,000
To tranche A	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(350,000,000)
To tranche B	(15,625,000)	(15,625,000)	(15,625,000)	(15,625,000)	(15,625,000)	(15,625,000)	(15,625,000)	(15,625,000)	(15,625,000)	(15,625,000)	(250,000,000)
Net profit to Bank	1,125,000	1,125,000	1,125,000	1,125,000	1,125,000	1,125,000	1,125,000	1,125,000	1,125,000	1,125,000	(100,000,000)
PV of cash flows discounted at loan interest rate	1,056,338	991,867	931,330	874,488	821,116	771,001	723,944	679,760	638,272	599,317	(53,272,604)
NPV	(45,185,170)

b
Cash flows from loan and to tranche A remain the same
Loan value	500,000,000
Interest rate	6.50%
Maturity Yrs	10
Annual interest payment	32,500,000
= 500 M* 6.5%
Trench A
Face value	350,000,000
Interest rate	4.50%
Maturity Yrs	10
Annual interest payment	15,750,000
= 350 M* 4.5%

Since the cashflows are over 10 years, it is easier to arrive at the interest rate for tranche B by trial and error. We have to find a value for cash flow to tranche B such that the NPV of cash flows over 10 years comes to be $20M

Trench B
Face value	250,000,000
Maturity Yrs	10
Annual interest payment	6,557,430
Interest rate	2.62%
=interest payment/ tranche face value

Year	1	2	3	4	5	6	7	8	9	10	10
Cash flows
From Loan	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	32,500,000	500,000,000
To tranche A	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(15,750,000)	(350,000,000)
To tranche B	(6,557,430)	(6,557,430)	(6,557,430)	(6,557,430)	(6,557,430)	(6,557,430)	(6,557,430)	(6,557,430)	(6,557,430)	(6,557,430)	(250,000,000)
Net profit to Bank	10,192,570	10,192,570	10,192,570	10,192,570	10,192,570	10,192,570	10,192,570	10,192,570	10,192,570	10,192,570	(100,000,000)
PV of cash flows discounted at loan interest rate	9,570,488	8,986,374	8,437,910	7,922,920	7,439,362	6,985,316	6,558,982	6,158,669	5,782,787	5,429,847	(53,272,604)
NPV	20,000,052

The interest rate for tranche B is very small since the face values of tranches A & B combined are 20% higher than the loan value.