Chapter 8

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You are preparing to produce some goods for sale. You will sell them in one year and you will incur costs of $80,000 immediately. If your cost of capital is 6.6%, what is the minimum dollar amount you need to sell the goods for in order for this to be a non-negative NPV?

= PV Costs * (1+ Cost of Capital) = 80,000 * (1+0.066) = 85,280

You are preparing to produce some goods for sale. You will sell them in one year and you will incur costs of $88,000 immediately. If your cost of capital is 7%, what is the minimum dollar amount you need to sell the goods for in order for this to be a non-negative NPV?

= PV Costs * (1+ Cost of Capital) = 88,000 * (1+0.07) = 94,160

Your factory has been offered a contract to produce a part for a new printer. The contract would last for 3 years and your cash flows from the contract would be $5.18 million per year. Your upfront setup costs to be ready to produce the part would be $8.24 million. Your discount rate for this contract is 7.6%. a. What does the NPV rule say you should do?

Compute PV N=3, I/Y=7.6, PMT =5.18 (m/year) PV=13.44630m NPV = -(Invested Cost) + cash flows = -8.24m+13.44630m = 5.2063m The NPV rule says that you should accept the contract because the NPV>0.

The internal rate of return (IRR) rule will agree with the Net Present Value rule even when positive cash flows precede negative cash flows. T/F?

False

Your factory has been offered a contract to produce a part for a new printer. The contract would last for three years, and your cash flows from the contract would be $5.00 million per year. Your upfront setup costs to be ready to produce the part would be $8.00 million. Your discount rate for this contract is 8.0%. a. What is the IRR? b. The NPV is $4.89 million, which is positive so the NPV rule says to accept the project. Does the IRR rule agree with the NPV rule?

Find I/Y: N:3, PV:-8, PMT:5 = 39.45447 = IRR B: The IRR investment rule states: Take any investment opportunity whose IRR exceeds the opportunity cost of capital. Turn down any opportunity whose IRR is less than the opportunity cost of capital. Does the IRR rule agree with the NPV rule? The IRR is 39.45%, which is greater than the cost of capital, 8%, so the project should be accepted. The IRR rule agrees with the NPV rule.

You run a construction firm. You have just won a contract to build a government office complex. Building it will require an investment of $10.2 million today and $4.8 million in one year. The government will pay you $20.5 million in one year upon the building's completion. Suppose the interest rate is 10.2%. a. What is the NPV of this opportunity?

Find PV first. For benefits: FV = 20.5m, I/Y=10.2, N=1 So PV = 18.60254m Then PV of the future cost: FV = 4.8m, I/Y=10.2, N=1 So PV = 4.35572m NPV = PV Benefits - PV Costs = 18.60254m - (10.2m-4.35572m) = $4.04682m

You run a construction firm. You have just won a contract to build a government office complex. Building it will require an investment of $10.1 million today and $4.8 million in one year. The government will pay you $21.5 million in one year upon the building's completion. Suppose the interest rate is 10.6%. a. What is the NPV of this opportunity?

Find PV first. For benefits: FV = 21.5m, I/Y=10.6, N=1 So PV = 19.43942m Then PV of the future cost: FV = 4.8m, I/Y=10.6, N=1 So PV = 4.33996 NPV = PV Benefits - PV Costs = 19.43942m - 10.1m-4.33996m = $4.99946 m

Your storage firm has been offered $97,500 in one year to store some goods for one year. Assume your costs are $95,800, payable immediately, and the cost of capital is 8.7%. Should you take the contract?

Find PV of $97500. I/Y = 8.7, N = 1, FV = $97500 PV = 89,696.41214 Find NPV NPV = PV Benefits - PV Costs = 89,696.41214-95,800 = -6,103.58786 No, you should not take the contract, as the NPV of the contract is negative.

You are evaluating a project that will cost $460,000, but is expected to produce cash flows of $120,000 per year for 10 years, with the first cash flow in one year. Your cost of capital is 11% and your company's preferred payback period is three years or less. b. Should you take the project if you want to increase the value of the company?

Find PV of cash flows N = 10, I/Y=11, PMT=120,000 PV=706,707.84134 NPV = PV of cash flows - initial investment = 706,707.84134 - 460000 = 246,707.84134 If you want to increase the value of the company you will take the project since the NPV is positive.

You have just been offered a contract worth $1.19 million per year for 6 years. However, to take the contract, you will need to purchase some new equipment. Your discount rate for this project is 12.2%. You are still negotiating the purchase price of the equipment. What is the most you can pay for the equipment and still have a positive NPV?

Find PV of cash flows: N=6, I/Y=12.2, PMT =1.19 (m/year) PV = 4.86499m which is the most you should pay for equipment.

You have just been offered a contract worth $1.12 million per year for 7 years. However, to take the contract, you will need to purchase some new equipment. Your discount rate for this project is 11.8%. You are still negotiating the purchase price of the equipment. What is the most you can pay for the equipment and still have a positive NPV?

Find PV of cash flows: N=7, I/Y=11.8, PMT =1.12 (m/year) PV = 5.14399m which is the most you should pay for equipment.

Marian Plunket owns her own business and is considering an investment. If she undertakes the investment, it will pay $4,200 at the end of each of the next 3 years. The opportunity requires an initial investment of $1,050 ,plus an additional investment at the end of the second year of $5,250. What is the NPV of this opportunity if the interest rate is 1.8% per year? Should Marian take it?

Find PV of the cash flows for each of the 3 years. 1st Year: N=1, I/Y=1.8, FV=4200 PV = 4,125.73674 2nd Year: N=2, I/Y=1.8, FV=(4200-5250= -1050) PV = -1,013.19665 3rd Year: N=3, I/Y=1.8, FV=4200 PV = 3,981.12631 NPV = -(Invested Cost) + cash flows = -1050 + 4,125.73674 - 1,013.19665 + 3,981.12631 = 6,043.6664 Yes, Marian should make the investment since it has a positive NPV

You have an opportunity to invest $100,000 now in return for $79,500 in one year and $30,200 in two years. If your cost of capital is 9.3%, what is the NPV of this investment?

Find present values of the first return and the 2nd return separately. For the first: FV = 79500, I/Y = 9.3, N = 1 PV = 72,735.59 For the 2nd: FV = 30200, I/Y=9.3, N=2 PV= 25,279.39 Then compute NPV = PV of Benefits - PV of costs = (72,735.59+25,279.39)-100,000 = -1,985.02

You have been offered a unique investment opportunity. If you invest $10,500 today, you will receive $525 one year from now, $1,575 two years from now, and $10,500 ten years from now. b. What is the NPV of the opportunity if the cost of capital is 2.3% per year? Should you take it now?

Find the PV of each future cash flow if cost of capital is 2.3%. 1st Set: N= 1 Year, I/Y=2.3, FV=525 PV= 513.19648 2nd Set: N= 2 Years, I/Y=2.3, FV=1575 PV= 3rd Set: N= 10 Years, I/Y=2.3, FV=10500 PV= 8,364.36473 Compute net present value = NPV = -(Invested Cost) + cash flows = -10,500 + 513.19648 + 1,504.97502 + 8,364.36473 =-117.46 You shouldn't take this opportunity, NPV is negative.

You have been offered a unique investment opportunity. If you invest $10,500 today, you will receive $525 one year from now, $1,575 two years from now, and $10,500 ten years from now. a. What is the NPV of the opportunity if the cost of capital is 6.3% per year? Should you take the opportunity?

Find the PV of each future cash flow if cost of capital is 6.3%. 1st Set: N= 1 Year, I/Y=6.3, FV=525 PV= 493.88523 2nd Set: N= 2 Years, I/Y=6.3, FV=1575 PV= 1,393.84355 3rd Set: N= 10 Years, I/Y=6.3, FV=10500 PV= 5,699.76111 Compute net present value = NPV = -(Invested Cost) + cash flows = -10,500 + 493.88523 + 1,393.84355 + 5,699.76111 =-2,912.51011 You shouldn't take this opportunity, NPV is negative.

You have been offered a unique investment opportunity. If you invest $10,600 today, you will receive $530 one year from now, $1,590 two years from now, and $10,600 ten years from now. b. What is the NPV of the opportunity if the cost of capital is 2.5% per year? Should you take it now?

Find the PV of each future cash flow if cost of capital is 6.5%. 1st Set: N= 1 Year, I/Y=2.5, FV=530 PV= 517.07317 2nd Set: N= 2 Years, I/Y=2.5, FV=1590 PV= 1,513.38489 3rd Set: N= 10 Years, I/Y=2.5, FV=10600 PV= 8,280.70306 Compute net present value = NPV = -(Invested Cost) + cash flows = -10,600 + 517.07317 + 1,513.38489 + 8,280.70306 = -288.83888 You shouldn't take this opportunity, NPV is negative.

You have been offered a unique investment opportunity. If you invest $10,600 today, you will receive $530 one year from now, $1,590 two years from now, and $10,600 ten years from now. a. What is the NPV of the opportunity if the cost of capital is 6.5% per year? Should you take the opportunity?

Find the PV of each future cash flow if cost of capital is 6.5%. 1st Set: N= 1 Year, I/Y=6.5, FV=530 PV= 497.65258 2nd Set: N= 2 Years, I/Y=6.5, FV=1590 PV= 1,401.83826 3rd Set: N= 10 Years, I/Y=6.5, FV=10600 PV= 5,646.89598 Compute net present value = NPV = -(Invested Cost) + cash flows = -10,600 + 497.65258 + 1,401.83826 + 5,646.89598 = -3,053.61318 You shouldn't take this opportunity, NPV is negative.

You have an opportunity to invest $49,100 now in return for $60,600 in one year. If your cost of capital is 8.2%, what is the NPV of this investment?

First find the present value of $60,600. N= 1 Year I/Y = 8.2 % FV = 60,600 So PV = NPV=PV (Benefits)−PV(Costs) = $56,007.39372 -$49,100 = $6,907.39372

You have an opportunity to invest $50,000,now in return for $60,700 in one year. If your cost of capital is 8.5%, what is the NPV of this investment?

First find the present value of $60,700. N= 1 Year I/Y = 8.6 % FV = 60,700 So PV = 55,944.70046 NPV=PV (Benefits)−PV(Costs) = $55,944.70046-$50,000 = $5944.70046

Which of the following is NOT a limitation of the payback rule? A. It does not consider the time value of money. B. It cannot be used for projects with non-normal cash flows. C. It is difficult to calculate. D. It does not consider cash flows occurring after the payback period.

It is difficult to calculate.

A convenience store owner is contemplating putting a large neon sign over his store. It would cost $50,000, but is expected to bring an additional $24,000 of profit to the store every year for five years. Would this project be worthwhile if evaluated using a payback period of two years or less and if the cost of capital is 10%?

No, since the value of the cash flows over the first two years are less than the initial investment

Fabulous Fabricators needs to decide how to allocate space in its production facility this year. It is considering the following contracts: Contract - NPV - Use of Facility A - $1.98m- 100% B - $1.02m- 53% C - $1.54m- 47% a. What are the profitability indexes of the projects? b. What should Fabulous Fabricators do?

PI=NPV/Use of facility A: 1.98/100 = 1.98 B: 1.02/53= 1.92 C: 1.54/47= 3.276 Since Fabulous Fabricators has the capacity (% use of facility) to do both B and C and NPVB + NPVC is greater than NPVA, it should do both B and C.

Fabulous Fabricators needs to decide how to allocate space in its production facility this year. It is considering the following contracts: Contract - NPV - Use of Facility A - $2.01m- 100% B - $0.98m- 55% C - $1.52m- 45% a. What are the profitability indexes of the projects? b. What should Fabulous Fabricators do?

PI=NPV/Use of facility A: 2.01/100 = 2.01 B: 0.98/55= 1.78 C: 1.52/45= 3.377 Since Fabulous Fabricators has the capacity (% use of facility) to do both B and C and NPVB + NPVC is greater than NPVA, it should do both B and C.

You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost $5,000 and will be posted for one year. You expect that it will generate additional revenue of $650 a month. What is the payback period?

Payback Period=CF0/CF = 5000/650 = 7.69 months

You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost $5,400 and will be posted for one year. You expect that it will generate additional revenue of $1,026 a month. What is the payback period?

Payback Period=CF0/CF = 5400/1026 = 5.26 months

The NPV rule says that you should accept a project if its NPV>0 because it adds value to the firm equal to the NPV. Therefore, if you take the contract, the value added to the firm will be $5.2063m

The firm can turn this NPV into cash today by borrowing $18.60254 million today and paying it back with 10.2% interest using the $20.5 million it will receive from the government ($18.60254m×1.102=$20.5 million).

The firm can turn this NPV into cash today by borrowing $19.43942 million today and paying it back with 10.6% interest using the $21.5 million it will receive from the government ($19.43942m×1.106=$21.5 million).

Orchid Biotech Company is evaluating several different development projects for experimental drugs. Although the cash flows are difficult to forecast, the company has come up with the following estimates of the initial capital requirements and NPVs for the projects. Given a wide variety of staffing needs, the company has also estimated the number of research scientists required for each development project (all cost values are given in millions of dollars). #1, $10 initial capital, 2 scientists, NPV : 10.1 #2, $15 initial capital, 3 scientists, NPV: 19 #3, $15 initial capital, 4 scientists, NPV:22 #4, $20 initial capital, 3 scientists, NPV:25 $5, $30 initial capital, 12 scientists, NPV:60.2 Suppose that Orchid currently has 12 research scientists and does not anticipate being able to hire more in the near future. How should Orchid prioritize these projects?

To determine the NPV/headcount ratio for each project, use the following formula: = NPV for the project/Number of scientists needed for the project 1: 10.1/2 = 5.1 2:19/3 = 6.3 3:22/4 = 5.5 4:25/3 = 8.3 5:60.2/12=5 If Orchid has a total capital budget of $60 million and currently has only 12 research scientists and does not anticipate being able to hire any more in the near future, the PI rule using the headcount constraint alone selects 4,2,3,1

Orchid Biotech Company is evaluating several different development projects for experimental drugs. Although the cash flows are difficult to forecast, the company has come up with the following estimates of the initial capital requirements and NPVs for the projects. Given a wide variety of staffing needs, the company has also estimated the number of research scientists required for each development project (all cost values are given in millions of dollars). #1, $10 initial capital, 2 scientists, NPV : 10.1 #2, $15 initial capital, 3 scientists, NPV: 19 #3, $15 initial capital, 4 scientists, NPV:22 #4, $20 initial capital, 3 scientists, NPV:25 $5, $30 initial capital, 12 scientists, NPV:60.2 a. Suppose that Orchid has a total capital budget of $60 million. How should it prioritize these projects?

To find the profitability index, use the following formula: PI=NPV/CF0 #1: 10.1m/10m=1.01 #2: 19m/15m=1.27 #3: 22m/15m=1.47 #4: 25m/20m=1.25 $5: 60.2m/30m=2.01 If Orchid has a total capital budget of $60 million, the PI rule selects Projects 5,3,2. These are also the optimal projects to undertake (as the budget is used up fully taking the projects in order).

Net present value (NPV) is the difference between the present value (PV) of the benefits and the present value (PV) of the costs of a project or investment. T/F?

True

The internal rate of return (IRR) is the interest rate that sets the net present value (NPV) of the cash flows equal to zero. T/F?

True

When different investment rules give conflicting answers, then decisions should be based on the Net Present Value rule, as it is the most reliable and accurate decision rule. T/F?

True

he payback rule is based on the idea that an opportunity that pays back its initial investment quickly is a worthwhile opportunity. T/F?

True

You need a particular piece of equipment for your production process. An equipment-leasing company has offered to lease the equipment to you for $10,400 per year if you sign a guaranteed 5-year lease (the lease is paid at the end of each year). The company would also maintain the equipment for you as part of the lease. Alternatively, you could buy and maintain the equipment yourself. The cash flows from doing so are listed below (the equipment has an economic life of 5 years). If your discount rate is 6.5%, what should you do?

compute the net present value of both leasing and buying. PV of leasing: N=5, i/y=6.5, pmt=10400 PV = 43,219.06616 Then, the net present value: NPV = -43,219.06616-0 =-43,219.06616 Cash flow for buying: Year 0 = -40100 Year 1 = -1800 Year 2 = -1800 (continues to year 5) PV of buying: N=5,i/y=6.5,pmt =1800 PV= 7,480.22299 Then find net present value: =-7,480.22299-40100 =-47,580.22299 Leasing is less than buying.

payback period = initial investment/cash flow =460,000/120,000 = 3.833 years

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