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# Annual Payment and Principal Balance

P 3-4
Just One, Inc, has two mutually exclusive investment projects, P and Q, shown below. Suppose the market interest rate is 10 percent?

Project Initial Investment Year 1 Year 2 IRR NPV (r = 10%)
P -\$200.00 \$140.00 \$128.25 22.4% \$33.26
Q -100.00 80.00 56.25 25.0 19.21

The ranking of projects differs, depending on the use of IRR or NPV measures. Which project should be selected? Why is IRR ranking misleading?

3-10
Mr. Jones intends to retire in 20 years at the age of 65. As yet he has not provided for retirement income, and he wants to set up a periodic savings plan to do this. If he makes equal annual payments into a savings account that pays 4 percent per year, how larges must his payments be to ensure that after retirement he will be able to draw \$30,000 per year until he is 80?

You have just purchased a house and have obtained a 30-year, \$200,000 mortgage with an interest rate of 10 percent.

a. What is your annual payment?

b. Assuming you bought the house January 1, what is the principal balance after one year?

c. After four years, mortgage rates drop to 8 percent for 30-year fixed-rate mortgages. You still have the old 10 percent mortgage you signed four years ago and you plan to live in the house for another five years. The total cost to refinance the mortgage is \$3,000, including legal fees, closing cost, and points. The rate on a five-year CD is 6 percent. Should you refinance your mortgage or invest the \$3,000 in a CD? The 6 percent CD rate is your opportunity cost capital.

4-6
Physicians practicing in Eastern University's hospital have the following compensation agreement. Each doctor bills the patient(or Blue Cross Blue Shield) for his or her services. The Doctor pays for all direct expenses incurred in the clinic, including nurses, medical malpractice insurance, secretaries, supplies, and equipment. Each doctor has a stated salary target(e.g., \$100,000). For patient fees collected over the salary target, less expenses, the doctor retains 30 percent of additional net fees. For example, if \$150,000 is billed and collected form patients and expenses of \$40,000 are paid, then the doctor retains #3,000 of the excess net fees [30 percent of \$150,000-\$40,000-\$100,000)] and Eastern University receives \$7,000. If \$120,000of fees are collected and \$40,ooo of expenses are incurred, the physician's net cash flow is \$80,000 and Eastern University receives none of the fees.

Critically evaluate the existing compensation plan and recommend any changes.

4-20
Coase Farm grow soybeans near property owned by Taggart Railroad. Taggart can build zero, one, or two railroad tracks adjacent to Coase Farm, yielding a net present value of \$0, \$9 million, or \$12 million.

(in millions)
as a Function of the
Number of Train Tracks
(before any damages)

Zero tracks \$0
One Track 9
Two tracks 12

Coase Farm can grow soybeans on zero, one, or two fields, yielding a net present value of \$0, \$15 millions, or \$18 million before any environmental damages inflicted by taggart trains. Environmental damages inflicted by Taggart's trains are \$4 million per field per track. Coase Farm's payoffs as a function of the number of fields it uses to grow soybeans and the number of tracks the Taggart builds are shown below.

Value of Coase Farm (in millions)
As a function of the number of fields planted
And the number of train tracks

Zero fields One field Two fields
Zero tracks \$0 \$15 \$18
One track 0 11 10
Two tracks 0 7 2

It is prohibitively expensive for taggart Railroad and Coase Farm to enter into a long-term contract regarding either party's use of its land.

a. Suppose Taggart Railroad cannot be held liable for the damages its tracks inflict on Coase Farm. Show that Taggart Railroad will build two tracks and Coase Farm will plant soybeans on one field.

b. Suppose Taggart Railroad can be held fully liable for the damages that its tracks inflict on
Coase Farm. Show that Taggart Railroad will build one track and Coase Farm will plant soybeans on two fields.

c. Now suppose Taggart Railroad and Coase farm merge. Show that the merge firm will build one track and plant soybeans on one field.
d. What are the implications of the merger for the organizational architecture of the newly merged from firm in terms of decision rights, performance measurement, and employee compensation?

#### Solution Summary

The annual payment and principal balance for Just One, Inc is examined.

\$2.19