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What is the duration of this bond?

Chapter 15 — Working Capital Management
PROBLEM 1
On a typical day, Park Place Clinic writes $1,000 in checks. It
generally takes four days for those checks to clear. Each day the
clinic typically receives $1,000 in checks that take three days to
clear. What is the clinic’s average net float?

PROBLEM 2
Drugs ‘R Us operates a mail order pharmaceutical business on the
West Coast. The firm receives an average of $325,000 in payments
per day. On average, it takes four days for the firm to receive
payment, from the time customers mail their checks to the time the
firm receives and processes them. A lockbox system that consists of
ten local depository banks and a concentration bank in San
Francisco would cost $6,500 per month. Under this system,
customers’ checks would be received at the lockbox locations one
day after they are mailed, and the daily total would be wired to
the concentration bank at a cost of $9.75 each. Assume that the
firm can earn 10 percent on marketable securities and that there
are 260 working days and hence 260 transfers from each of the ten
lockbox locations per year.

What is the total annual cost of operating the lockbox
system?
What is the dollar benefit of the system to Drugs’R Us?
Should the firm initiate the lockbox system?

PROBLEM 3
Suppose one of the suppliers to Seattle Health System offers
terms of 3/20, net 60.

When does the system have to pay its bills from this
supplier?
What is the approximate cost of the costly trade credit offered
by this supplier? (Assume 360 days per year.)

Chapter 18 — Financial Risk Management
PROBLEM 1
Pleasant View Nursing Home estimates that its building will last
another ten years and then it will need to be replaced. The home
estimates that the capital cost of a new building in ten years will
be $10 million. The home plans to set aside a portion of an
endowment fund in government bonds to ensure it has sufficient
funds to pay for the replacement of the building. If we assume that the
yield curve is horizontal, the current interest rate on all
Treasury securities is 9 percent, and the type of security used for
the building fund is Treasury bonds, then the present value of $10
million discounted back ten years at 9 percent is $4,224,108.
Suppose interest rates change from the current 9 percent rate
immediately after the nursing home has bought the Treasury bonds.
What would be the value of the bonds at the end of ten years under
each of the following situations? (For simplicity, assume annual
coupons).

The home buys $4,224,108 of 9 percent, ten-year maturity bonds;
rates fall to 7 percent immediately after the purchase and remain
at that level; rates rise to 12 percent.
The home buys $4,224,108 of 9 percent, 40-year maturity bonds;
rates fall to 7 percent immediately after the purchase and remain
at that level; rates rise to 12 percent.

PROBLEM 2
Pleasant View Nursing Home has decided to immunize its portfolio
against interest rate and reinvestment rate risk by buying a bond
that has a duration equal to the years until the funds will be
needed (approximately ten years from today). The home is
considering a 20-year, 9 percent annual coupon bond bought at its
par value of $1,000.

What is the duration of this bond?
If the nursing home purchases $4,224,000 worth of this bond,
what would be the value of the bonds at the end of the duration
period if interest rates fall to 7 percent immediately after the
purchase and remain at that level? If interest rates rise to 12
percent?