# Just One, Inc., Has Two Mutually Exclusive Investment Projects, P and Q, Shown Below. Suppose the Market Interest Rate Is 10 Percent.

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

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

Using the IRR method will result in project Q being selected over P due to its higher rate of return. Using the NPV method would result in choosing project P because of its higher NPV. When there are mutually exclusive project, NPV method would be preferred. IRR is misleading because it ignores the absolute amount from the wealth of shareholders which may be increased when the project would be undertaken. It may also be misleading because IRR makes an assumption that interim cash flows are being reinvested at the same equal return rate.

P 3–10: Mr. Jones’s Retirement

Mr. Jones intends to retire in 20 years at the age of 65. As yet he has not provided for retirement in-come, 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 interest per year, how large must his payments be to ensure that after retirement he will be able to draw $30,000 per year from this account until he is 80?

We first compute the present value at the end of the year when he is 65, when he will be required to make 15 annual payments of $30,000.

PMT| -$30,000|

N| 15|

Rate| 4.00%|

| |

PV| $333,551.62|

Then we compute the amount that needs to be added every for 20 years to make future the future value of $333,551.62.

FV| -$333551.62|

N| 20|

Rate| 4.00%|

| |

PMT| $11,201.25|

So, he will have to deposit $11,201.25 every year.

P 3–19: House Mortgage

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

a. What is your annual payment?

b. Assuming you bought the house on January 1, what is the principal balance after one year? After 10 years? 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 costs, 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 of capital.

a.

The annual payment is $21,062. (calculated with a mortgage calculator from yahoo.com)

b.

The principal balance at the end of year 1 is $198,888 and at the end of year 10 is $181,876.

c.

It would not be worth to pay for the mortgage if only living in the house for another 5 years because after the 9 years have passed there would still be 21 years to pay the mortgage and if the house is sold I would be able to recover the total costs I had with it since we have to consider depreciation as well. So, the $3,000 investment would be the better choice.

P 4–6: University Physician Compensation

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 the additional net fees. For example, if $150,000 is billed and collected from 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 $120,000 of fees are collected and $40,000 of expenses are incurred, the...

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