Chapter 6 Review Problems

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[1] For an investment of $15,000 now, a company can receive $9,250 one year from now, and $9,200 two years from now. Check its earnings rate on this deal by comparing it to an account using the following rates. For each part, fill out the following balance sheet

Time (year) Interest Deposit Withdrawal Balance
0 $15,000 $15,000
1 ? $9,250 ?
2 ? 9,200 ?
  1. 10% effective
  2. 20% effective
  3. 15% effective

 

[2] For the investment in the previous problem , find the NPV at each of:

  1. 10% effective
  2. 20% effective
  3. 15% effective.

Relate each value to the results in (a), (b) and (c)

 

[3] A finance company has an opportunity to purchase three promissory notes from a broker for a total of $140,000 cash. The first note would pay $20,000 in one year, the second would pay $70,000 in two years and the third $80,000 in three years. The finance company has set for itself a minimum acceptable rate of return of 10% effective.

  1. Evaluate the net present value of the investment at the company’s MARR.
  2. State your conclusion about the acceptability of the profitability of this deal.

 

[4] A project is to cost $60,000 immediately and to produce net cash inflows of $20,000 at the end of the first year, $30,000 at the end of the second year and $25,000 at the end of the third year. At the end of the third year the business will be sold for $5,000. The company aims at a rate of return of 15% effective.

  1. Show whether or not the company will achieve its objective.
  2. Find the value of the bonus paid at the start which would cause the project to earn exactly 20% effective.

 

[5] Samuels Co. plans to start a repair business. It would provide net returns of $35,000 at the end of the first year, and $50,000 at the end of each of the next three years. The equipment would then be sold for $11,000 and the business terminated. Samuels aims at a rate of return of 15%.  How much should Samuels be willing to invest (now)?

 

[6] Williams Co. has the chance to start a transportation company in the north. It would require $108,000 to start the business and it would provide net returns of $35,000 at the end of the first year, and $40,000 at the end of each of the next two years. The equipment would then be sold for $9,000 and the business terminated. Williams aims at a rate of return of 12%.

  1. Find the NPV at 12% effective, and the IRR. Should Williams Co. start this company?
  2. If the government wanted to subsidize Williams so that it would earn 15% compounded annually, what subsidy paid at the end of the three years would be required?

 

[7] PA Lumber Co. is bidding on the right to cut lumber from a private forest for 10 years. The amount of lumber permitted to be cut each year would allow PA to produce a net cash flow (excluding cost of cutting rights) of $120,000 a year. If PA aims at a rate of return of 12.5%, how much could it afford to bid as a lump sum for the cutting rights?

 

[8]     Iffi Co. plans to install insulation in a building which it plans to use for six years. The insulation and its installation will cost $193,000 and will result in savings of $37,000 a year and will increase the residual value of the building by $90,000. Find the internal rate of return of the planned installation of the insulation.

 

[9] Tessa Quaid has purchased a 10-year video rental franchise for $12,000. She will have to invest another $22,000 in the store immediately. She expects returns of $8,000 a year at the end of each year. Will TQ make a rate of return of at least 15%? What will be the internal rate of return?

 

[10] TW Cable Co. plans to begin operation in a large town and to expand later to a nearby small town. TW estimates its net cash flows to be:

Time (year) Cash Flow
0 -$600,000
1 100,000
2 100,000
3 -50,000 (expansion)
4-9 150,000
10 700,000 (includes sale of business)

Find the net present value at 17% and the internal rate of return.

 

[11] A food concession at an airport has a five year life and costs $130,000. Initial investments in equipment, training and inventory amount to $75,000. The concession’s operation is expected to produce net cash inflows of $50,000 a year and the residual value of equipment and the ending inventory are expected to total $30,000.

  1. Find the NPV at 15% effective.
  2. Find the internal rate of return.

 

[12] The owners of a small business are considering three offers from potential purchasers:

  • Offer #1: $100,000 cash.
  • Offer #2: $80,000 now and $10,000 at the end of each year for five years.
  • Offer #3: $25,000 now and $25,000 at the end of each year for five years.

Which offer is most attractive if money is worth 9% to the owners?

 

[13]     A “10%” Government bond is to pay interest of $100 per year for nine years. Find the price investors  should be willing  to pay for the bond if they want to earn:

  1. 15% effective.
  2. 10% effective.
  3. 5% effective.

 

[14] The Titan Package Co. finds that a $95,000 investment in automated packaging equipment will save it $20,000 a year for the next 10 years. The equipment will have no value at the end of the 10 years. If the company aims at a rate of return of 15% effective should it purchase the equipment? Why/why not?

 

[15] The Fast Food Co. can expand into either of two locations. Location A will need an expenditure of $130,000 now and will result in a yearly net cash inflow of $35,000 (at the end of each year) for 10 years and no other benefits. Location B will need expenditures of $150,000 now and $50,000 in one year. It will then produce  a yearly net cash flow of $45,000 a year for the following 12 years (all at the end of each year). In location B there would also be no other benefits. Which location gives the higher net present value at a required rate of return of 16% effective per year?

 

[16] You are considering a home-based business. You would like to open a kennel. You estimate that your start-up costs will be $250,000 this year and you will need to spend another $10,000 next year. You expect revenues of $35,000 per year for the first two years and $42,000 for the next three years. Your expenses are thought to be $6,000 per year. At the end of five years you plan to sell the kennel and anticipate receiving $255,000. You want to earn a minimum of 14% compounded annually on your investment. All revenue occurs at the end of the year and all expenses are paid at the beginning of the year.

  1. Calculate the payback for this project.
  2. Calculate the net present value for this project. Should you open a kennel?
  3. If you require only 12% effective should you open a kennel? Why or why not?
  4. How much should the start-up costs be reduced by so that you would be willing to open a kennel? Use a MARR of 14%.
  5. Your estimate of the kennel’s selling price may be too low. You think you may be able to sell the kennel for more than $255,000. What is the minimum selling price you must have so that you would be willing to open the kennel? Assume the start-up costs remain unchanged. Round to the nearest $. Use a MARR of 14%.
  6. Calculate the internal rate of return (IRR) for this project. Should you open a kennel if you want to earn at least 14% compounded annually on your investment?

 

[17] You are considering purchasing a home-based business that uses AI to create customized meal plans. You think that you can buy the business from the current owner for $120,000. You expect revenues of $40,000 per year. Your expenses are thought to be $20,000 per year for the first 2 years and $10,000 per year for the last 3 years. At the end of five years you plan to sell the business, retire and move to Las Vegas. You anticipate you could sell it for $130,000. You want to earn at least 16% compounded annually on your investment?

  1. Calculate the payback for this project.
  2. Find the NPV. Should you buy the business?
  3. How high could the purchase price of the business be and still make it worthwhile for you to buy the AI business?
  4. You think you might be overly optimistic in your estimate of the selling price of the business. What is the lowest selling price that you can accept and still be willing to buy the business? Round to the nearest $.
  5. Calculate the internal rate of return (IRR) for this investment. Should you buy the business?
  6. Your accountant tells you that your projected annual revenue is too high. What is the maximum annual decrease in revenue you could withstand and still have this investment be worthwhile?

 

[18] You want to start up a business in a mall selling CFL souvenirs. You plan to spend $80,000 in start up costs. You anticipate that you will break even in the first year and second year, make $20,000 the third, and make $20,000 each year after that. You plan to sell the business for $100,000 at the end of the sixth year. You want to earn at least 15% effective on your investment.

  1. What is the net present value of your business plan?
  2. What is the internal rate of return?
  3. Should you undertake the business plan? Why or why not?
  4. You think you might be overly optimistic in your estimate of the selling price of the business. What is the lowest selling price that you can accept and still undertake the project? Round to the nearest dollar.

 

[19] You are a restaurant owner and are considering expanding your business by buying the recently vacated store next door. The purchase price is $50,000. You will also need to spend an extra $35,000 in re-modeling. The larger dining room is expected to generate net profits of $12,000 a year for the first 4 years and $15,000 a year for the next 6 years. At the end of 10 years, you will retire. You expect to be able to sell the restaurant for $70,000. You want to earn a minimum of 20% on your investment.

  1. What is the net present value?
  2. What is the Internal Rate of Return?
  3. Should you expand the restaurant? Why or why not?
  4. You hear news reports that real estate prices may rise over the next few years and that this is especially true for commercial real estate. You now think you can sell the restaurant for more than $70,000. What is the minimum selling price you must have so that you would be willing to expand the restaurant? Round to the nearest $.

 

[20] You have decided to start a business selling vitamin supplements. You estimate that you will have $200,000 in start-up costs. Annual expenses are expected to be $30,000 and revenue is expected to be $50,000 per year for the first 2 years and $75,000 in each of the next 3 years. You plan to sell the business at the end of 5 years for an estimated $250,000. You want to earn at least a 15% rate of return on your investment (MARR is 15%).

  1. Should you invest? What is the IRR?
  2. What is the NPV? Should you invest?
  3. Your accountant tells you that your estimated selling price is too high. What is the minimum selling price you could accept and still have this investment be worthwhile?
  4. One of the supplements you were going to sell has recently been banned. This will cause a substantial decrease in your revenue. What is the maximum annual decrease in revenue you could withstand and still have this investment be worthwhile?

 

[21] You are operations manager for Flatugas, a small natural gas producer in the Peace River Region of British Columbia. You are considering investing in a new technology that captures more of the gas from the wellhead. The technology will cost $1,000,000 and operating costs are estimated at $25,000 per year payable at the beginning of each year. The technology should result in $250,000 in extra natural gas revenue per year and have the added benefit of reducing greenhouse gas emissions. The technology is expected to last for 5 years when it could be sold back to the manufacturer for a guaranteed price of $249,908.70. The company has a 15% MARR and requires a payback period of 4 years or less.

  1. What is the payback period of the investment? Should you invest?
  2. Calculate the IRR for the investment and explain how you would use IRR to make a decision on whether to invest or not.
  3. Calculate the NPV. Should you invest?
  4. The director of finance reviews your analysis and tells you that a MARR of 13% is more appropriate for the project. He also informs you that the company should be able to sell clean air credits under the Paris agreement. What annual revenue would be required from the credits to make this a worthwhile investment at a 13% MARR? (Assume 5 equal payments at the end of the year).

 

[22] The Blue Sky Resort plans to install a new chair lift to serve a new ski area. Construction of the lift is estimated to require an immediate outlay of $190,000. In addition, the company must spend $30,000 today and $30,000 per year for the next 3 years to clear and groom the new area. The life of the lift is estimated to be 11 years with a salvage value of $80,000. Profits from the lift (excluding the cost of grooming and clearing) are expected to be $40,000 per year for the first five years, and $70,000 per year for the next six years. The company wants to earn a minimum of 14% effective on the investment. All revenue occurs at the end of the year and all expenses are paid at the beginning of the year.

  1. Determine the net present value. Should they go ahead with the project? Why or why not?
  2. Determine the internal rate of return. Should they go ahead with the project? Why or why not?
  3. Determine the payback.
  4. You hear on the news that we might be in a recession for the next few years. You now wonder if your salvage value estimate of $80,000 is too high. What is the lowest salvage value you can accept and still undertake the project? Round to the nearest $.

 

[23] A project is to cost $60,000 immediately and to produce net cash flows of $20,000 at the end of the first year, $30,000 at the end of the second year, and $25,000 at the end of the third year. At the end of the third year the business will be sold for $5,000.

  1. If the company requires 15% effective, will it be able to achieve its goal?
  2. Find the value of the bonus paid at the start which would cause the project to earn exactly 20% effective.

 

[24] Due to a restricted capital budget, a company can undertake only one of the following 3-year projects. Both require an initial investment of $650,000 and will have no significant salvage value at the end. Project X is anticipated to have annual profits of $400,000, $300,000, and $200,000 in successive years, whereas Project Y’s only profit, $1.05 million, comes at the end of year three.

  1. Calculate the IRR of each project. On the basis of their IRRs, which project should be selected?
  2. On the basis of NPV, which project should be selected if the firm wants to earn at least 14% effective on their investment?
  3. On the basis of NPV, which project should be selected if the firm wants to earn at least 11% effective on their investment?

 

 

    1. Final Balance = -$1225, so this investment earns more than 10% effective
    2. Final Balance = $1300, so this investment earns less than 20% effective
    3. Final Balance = $0, so this investment earns exactly 15% effective
    ↵
    1. NPV = $1,012.40
    2. NPV = -$902.78
    3. NPV = $0
    ↵
  3. NPV = -$3,861.76.  The deal does not earn 10% effective MARR. ↵
    1. NPV = -$198.90 at 15% effective. The company does not achieve its objective.
    2. The NPV of the cash flows using i = 20% effective is -$5,138.88. To earn 20%, the NPV must = $0. Therefore the size of the bonus must be $5,138.89 to have a net project cost $54,861.11 instead of $60,000.
    ↵
  5. NPV = $135,994.73 ↵
    1. NPV = -$9,985.01 at 12% effective and IRR = 6.8305% for this three year project.
    2. To earn 15% effective, NPV must = $0. Without the subsidy, the NPV at 15% is -$15,101.18. This is the PV of the required subsidy at the end of the third year. Therefore, the subsidy = future value of this amount at 15% in three years or $22,967.01.
    ↵
  7. NPV = $664,371.70. This is the amount PA can afford to bid. ↵
  8. IRR = 12.7118% ↵
  9. NPV at 15% effective = $6,150.15. TQ will make more than 15% effective. IRR = 19.6004% ↵
  10. NPV = $9,076.27;   IRR = 17.29597% effective. ↵
  11. NPV = $22,476.94 IRR = 10.5635% ↵
  12. NPVs are $100,000, $118,896.51 and $122,241.28 respectively. Offer #3 is the most attractive one at 9% effective. ↵
  13. A 10% bond implies that if the bond is purchased for $1,000, it will generate $100 annual interest, and the bondholder will receive the $1,000 bond investment back at the end of the ninth year. To solve this problem, find the PV of nine annual cash flows of $100 and the $1,000 paid at the end of the ninth year using the target interest rate. a. $761.42 b.         $1,000.00        c.         $1,355.39 ↵
  14. NPV = $5,375.37 Yes, the company should purchase the equipment. ↵
  15. NPV for A is $39,162.96 NPV for B is $8,508.47.  Location A has the higher NPV at 16% effective. ↵
    1. 4+136/297 years = 4.46 years
    2. -$17,152.42 ? No, because the NPV is negative.
    3. The NPV is +$1,111.42 which is above zero so you should open a kennel.
    4. $17,152.42
    5. minimum selling price is $255,000 + $33,025.52 = $288,026
    6. 12.12%, No because the IRR is below the minimum acceptable rate of return of 14%.
    ↵
    1. 4+30/170 = 4.176 years
    2. $16,263.94 Yes buy the business because the NPV is positive (earning more than 16% per year).
    3. Purchase price could increase by up to $16,263.94 to $136,264.
    4. Lowest selling price you could accept is $95,840.
    5. 19.45%/year. This exceeds the required rate of 16%/year so buy business.
    6. Up to a $4,967.16/year decrease in revenue.
    ↵
    1. NPV = +$6408 .24
    2.  IRR = 16.73%
    3. Yes, undertake the business plan because the NPV is positive and the IRR is 16.73% which exceeds the minimum required return of 15%.
    4. $100,000-$14,822.65=$85,177 is the minimum selling price for the business.
    ↵
    1. -$18,573.73
    2. 14.77%
    3. No, because the NPV is negative and the IRR = 14.77% < MARR of 20%.
    4. $70,000 + $115,004 = $185,004 is the minimum selling price.
    ↵
    1. 17.25% > 15% MARR so yes invest.
    2. +$19,413.74. Yes, since the NPV is positive.
    3. $210,952 (rounded to nearest dollar)
    4. $5,791.42/year
    ↵
    1. 4.25 years so no, it is longer than 4 years.
    2. 9.95% is below 15% so no, do not invest.
    3. -$134,086.89 which is below zero, therefore do not invest
    4. $24,000/year
      ↵
    • NPV =+$7,979.31; yes, undertake the project because the NPV is positive
    • IRR = 14.58% exceeds the MARR of 14%
    • 6.57 years
    • $80,000 -\33,722.42 =$46,277.58 is the minimum salvage value.
      ↵
    • NPV = -$198.90; no, the company does not achieve its objective.
    • The bonus must be $5,138.89 to make the NPV equal zero
      ↵
    1. Project X: 20.8%   Project Y: 17.3% Project X has the higher IRR and should be selected.
    2. NPV: Project X: $66,712           Project Y: $58,720 Project X has the higher NPV and should be selected.
    3. NPV:  Project X: $100,085     Project Y: $117,751 Project Y now has the higher NPV and should be selected.
    ↵

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