The questions are: An engineering freshman wants to purchase a laptop computer T

Question

The questions are:

An engineering freshman wants to purchase a laptop computer Tor use during the 4 1/2 years that she plans to study engineering at Texas Tech. After looking around a bit, she finds that a well-equipped laptop with software can be purchased for $ 1,800 and that it should have a market value of at least $300 if she wants to sell it when she graduates after 4 Yi years. Assume that maintenance and supplies will cost $100 each six months. Use an interest rate of 12% per year with monthly compounding, and determine the present cost of owning and operating the computer. Hint: i - 12% per year. So, the six month interest rate becomes: k = (1 + 012/12)6 -1 =6.152% A person buys a S 1,000 face value bond 2 years after its issue. He intends to keep it until its maturity7 date, which is 18 years from now. This bond pays 6% annually. What price can he pay now for the bond so that his investment earns 8%? The investor gets the face value back at the maturity. Hint: The price equals the present worth/value of the benefits or income. Stephen Zehnder, ail enterprising engineer, wants to get into business. He is looking at the following two alternatives. He has compiled the cost data for both alternatives as shown in table below. If Stephen wants to have at least a rate of return of 12% on this business investment, which one should he choose? After 20 years, he plans to sell the business at double the initial cost. Two hazardous environment facilities are being evaluated, with the projected life of each facility7 being 10 years. The cash flow's for each facility are shown in the table below. The company uses a MARR of 14%. Based on the rate of return, which is the most desirable alternative?

Explanation / Answer

For 2. There are a few different ways to handle this problem. I am going to take the approach of calculating three different present values. First, the cost of the computer of $1,800 would occur now, so it does not need to be discounted. The $100 can be taken as an annuity. So, on a BAII+ put N = 9, I = 6, PMT = 100, FV = 0 [4.5 years x 2, 12% / 2 because the periods are half years], then press CPT and PV. This should display -$680.17. That is the PV of the maintenance costs. The last present value to calculate is the sale of the laptop for $300. To calculate this with a BAII+ set N = 9, I = 6, PMT = 0, FV = 300 and the CPT and PV again, you should get $177.57. Then simply add these PVs together, -$1,800 - $680.17 + $177.57 = -$2,302.6

Now, the easier way to do this same problem with the BAII+ is this, first hit 2ND then CE/C to make sure you calculator does not have any previous information stored. Then hit CF and again 2ND then CE/C. for CFo, put -$1,800 press ENTER then the down arrow. This should be C01 here put -$100 (This is the cashflow). In F01, the F stands for frequency, meaning how many times we want to repeat. Put 8 here. Go down again, put $200 (i.e. $300 - $100), and F02 should be just 1. Now hit NPV put I = 6 press the down arrow, and hit CPT. You should get exactly what we got before, $2,302.60.

Sometimes the PV or NPV may be the opposite sign you expect. That's OK. You will learn while using this calculator, that the formulas it uses, either the PV or FV will always be negative. So it depends on which one your calculating and how you input the imformation. A simple rule I follow while using this calculator is if I am going to be spending money, put it in as negative. If it is money I will receive, positive. That should keep it in the sign you'd expect to see. This is espcially important when using PMTs.

Luckily, that problem was the most difficult. The others are quite easy.

3. This person wants to purchase a bond that has a face value of $1,000 [Every bond has a face value of $1,000]. The bond pays 6% annually, so he will receive 6% of $1,000 every year, which is $60. Now, the face value is what will be received at the end of 18 years. So here's how to set this up in the BAII+ FV = $1,000, PMT = $60, I = 8%, N = 18. So the PV should come out to be -$812.56. Now notice, I put the FV and PMT as positive, because they are income. The purchase of the bond is an expense, so in real life it would be negative!

NOTE: If you accidentally put the FV as negative and the PMT as positve, you will get a wrong answer of -$312.06, or if you flip flop those, you will get $312.06 which is the wrong sign and number! Please be careful when you have PMTs!

1. This is easy, we will use the CF again on the BAII+. Again, clear your calculator first. For the Convenience Store with Gas put -80,000 for CFo, $12,000 for CF01, 19 for F01, for CF02 put the annual amount $12,000 plus the sale of the business which we are told is double of the intial cost so $160,000. This makes CF02 $172,000. F02 = 1. Then press NPV, set I to 12% and CPT the NPV. You should get $26,220.

Set up the ice cream store the same way. I know you can do it! As a check figure, you should get an NPV of $53,440. Which one would you rather do?

2. This is pretty similar. Use th CF. Clear it out first. Put the intial cost in CFo, Then put the annual benefit in CF01, F01 to 9 and then set CF02 for the annual benefit plus the salvage value. I am not sure if the M&O Cost need to be taken out of the annual benefit, or if the annual benefit already has expenses taken out. Use the 14% for the I on the CF section of your BAII+. This time, however, you are not calculating the NPV. You need the IRR. So press IRR and then CPT. You should get 14.3% for A and 22.67% for B. If you take out the M&O from the annual benefit you should get 9.9% for A and 20.7% for B. The second scenario makes the choice a little more obvious because A does not meet the required 14% MIRR.

Hope that helps!

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