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Wednesday Oct 15:

Moving money through time and

present value calculations

Friday Oct 17:

MARR, IRR and ERR

Monday Oct 20:

Depreciation, bathtub curves and replacement analysis

Mr Smith has a small brewing company. In 2006 he

bought a shed for $10,000, then in 2007 he bought a

brewing machine for $15,000. The shed depreciates

in value by 10% per year, while the machine depreciates

by 30% per year. Starting in January 2006, Mr Smith

paid an annual fire-insurance premium of $2,000.

In December 2009, the shed burns down, destroying

the machine. Under the terms of the insurance policy,

the insurance company will now pay for a new shed

and a new machine.

Regarding the insurance payments as an investment

and the difference between the value of the depreciated

property and its new replacements as income, what is

Mr Smith’s IRR on his insurance policy?

The heating system in Jacob’s building has worn out and

he has to get a new one. All the alternatives are gas-fired

furnaces, but they vary in efficiency. Model A is leased

at $500/year. It has installation charges of $500, and

saves $200 a year compared with his previous system.

Model B is purchased for $3600, including installation.

After 10 years it will have a salvage value of $1000.

It saves $500 a year compared with the old system.

Model C is purchased at a total cost of $8000, half paid

now, half paid in two years time. It has a salvage value

of $1000 after ten years, and saves $1000/year compared

with the current system. Assuming an MARR of 12%

and using the IRR method, which furnace should Jacob get?

Now consider whether Jacob wants to upgrade

to Option C. Construct the cash-flow diagram

for the upgrade.

You can make monthly deposits into a savings account that pays interest at a nominal rate of 18% per

year, compounded monthly.

How much should you deposit each month if you want to have $5,000 in five years time?

Your company is considering purchasing a new machine.

It will take three years to put into operation,

but at the end of the third year it will increase company income by $10,000, increasing by $1,000 per

year for the following five years.

At the end of the eighth year it will be worn out and have no scrap value.

If the cost of capital to the company is 15%, what is the most it is worth paying for the machine now?

I take out a $100,000 mortgage on a warehouse, at 5% annual

interest, to be paid back over 5 years.

What is my annual payment?

How much of my payment in the second year is interest, and

how much is repayment of principal?

(This will turn out to be important when we come to look at

taxes.)

(From APEGBC Exam, May 2003, #1)

Northern Mining Company plans to develop a new copper mine in New Caledonia.

The anticipated cash flow for this project is given below:

- The MARR for the company is y. Determine:
- PV of cashflow if X=6 and y= 12%, quarterly compounding
- The value of X if the future value of the cashflow (Year 5) is $3.9M and y = 12%
- annual compounding
- c) The payback period if X = 9
- d) The internal rate of return if X=5
- e) The external rate of return if X=5 and y=10% annual compounding

(From APEGBC Exam, Dec 2003, #2)

Two proposals are submitted for constructing a new toll road. The financial information

related to the projects is as shown on the following table, in millions of dollars:

Find: a) the B/C ratio for Project A

b) The B – C value of Project B

c) Which project, if either, should the government choose?

Assume an interest rate of 5%

(From APEGBC Exam, May 2004, #2)

The operating and maintenance costs of the air cleaning, air supply and exhaust system

for a silver mine in New Mexico are $300,000 in the first year of operation, and are expected

to increase by 10% in each subsequent year. The initial cost of the system, including installation,

is $900,000, and the physical life of the system is 5 years. Its salvage value is zero and it would

cost $100,000 to remove it.

The company’s MARR is 8%.

Determine: a) the annual cost of the system if it is replaced after three years of use

b) the economic life of the system

c) the yearly saving if the system is replaced at the end of its economic life,

rather than after three years.

Either

Or

Wednesday Oct 15, 1 hour:

Moving money through time and

present value calculations

Friday Oct 17, 1 hour:

MARR, IRR and ERR

Monday Oct 20, 1 hour:

Depreciation, bathtub curves

and replacement analysis

Wednesday Oct 15, 1 hour:

Moving money through time and

present value calculations

Friday Oct 17, 2 hours:

MARR, IRR and ERR; Depreciation,

bathtub curves and replacement analysis

Monday Oct 20:

Lecture on TAXES

(Everyone preferred the 3-exam option)

(From APEGBC Exam, Dec 2004, #2)

A company is considering three mutually exclusive alternatives for upgrading its mining

equipment. The cashflows associated with each proposal, in $M, are shown below. Equipment

salvage values are zero. The company’s MARR is y%.

Determine: a) the equivalent uniform annual savings if we choose Option 2 and y = 10%

b) the preferred alternative using the future worth method, y = 10%

c) the preferred alternative using the IRR method, y = 8%

Your company needs to make a $2,800,000 purchase of capital equipment. This can be financed either by a 5-year bank loan for the whole amount, or by $1,200,000 of your company’s own money plus a three-year loan of $1,600,000 from a trust company. If you take the bank loan, you will be charged 12% nominal annual interest, compounded half-yearly, and you will pay the loan off in ten equal half-yearly payments. If you take the loan from the trust company, you will be charged x% annual interest. At the end of Years 1 and 2, you pay back the interest accumulated to date, and at the end of the third year you pay back the $1,600,000 plus any additional interest. Your pre-tax MARR is 21%.

a) What is the present value of the bank loan? (5 points)

b) What is the present value of the trust loan if x=10%? (5 points)

c) For what value of x are the two options economically equivalent? (10 points)

You have $20,000 to invest, and you have a choice between three investment opportunities. One of these involves an immediate cost of $10,000 and a return of $14,400 in two years time. The second involves an immediate cost of $20,000, with a return of $26,500 in two years time. The third alternative is putting money in the bank, where it will earn 9% annual interest.

- What is the IRR of the first option? (7 points)
- What is the IRR of the second option? (7 points)
- What is the incremental IRR of upgrading from the first option to the second option? (10 points)
- Which option should you choose? (6 points)

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