Wk3 and 4 additional homework questions PDF

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Week 3 and 4 Additional Homework Questions Multiple choice questions (2 marks each) 1. What is the NPV of a project that requires an investment of $200,000, returns $80,000 annually for 4 years and the cost of capital is 12%? A. $550,808 B. $149,158 C. $42,984 D. $3,366

2. What should occur when a project's net present value is determined to be negative? A. The discount rate should be decreased. B. The profitability index should be calculated. C. The present value of the project cost should be determined. D. The project should be rejected. 3. Which of the following changes will decrease the NPV of a project? A. A decrease in the discount rate B. A decrease in the size of the cash inflows C. A decrease in the initial investment D. An increase in the number of cash inflows 4. What is the maximum amount that a firm should consider investing in a project that will return $15,000 annually for 5 years if the cost of capital is 10%? A. $33,520 B. $56,862 C. $62,540 D. $75,000

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5. If the IRR for a normal investment project is 11%, then the project's NPV would be: A. negative at a discount rate of 8%. B. positive at a discount rate of 16%. C. negative at a discount rate of 12%. D. positive at a discount rate of 20%.

6. When managers select correctly from among mutually exclusive projects, they: A. prioritise NPV over all other methods. B. prioritise IRR over all other methods. C. prioritise payback period over all other methods. D. prioritise profitability index over all other methods . 7. If the NPV of a project is positive $30,000 when using a discount rate of 7% and negative $80,000 when using a discount rate of 15%, calculate the IRR using linear interpolation? A. 0%. B. 11.8%. C. 11.0% D. 9.2%. 8. Assuming a cost of capital of 8%, what is the minimum cash flow received (rounded to the nearest $10) at the end of year 4 to make the following project "acceptable"? Initial investment = $150,000; cash flows at end of years 1, 2 and 3 = $45,000 each year. A. $25,010 B. $46,300 C. $34,030 D. $35,000

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9. A machine costs $18,000 to purchase and running costs are expected to be $5,000 a year. If the discount rate is 12% and the machine will last for 6 years, what is the equivalent annual cost of the machine to the nearest $? A. $38,557 B. $9,639 C. $9,500 D. $9,378

10. What is the approximate IRR of a project that costs $108,160 and provides cash inflows of $26,380 annually for 5 years? A. 10% B. 0% C. 7% D. 20% 11. A project can in theory have as many different internal rates of return as it has: A. cash inflows. B. cash outflows. C. periods of cash flow. D. changes in the sign of the cash flows.

12. A project with an IRR that is greater than the cost of capital should be: A. rejected for all project types. B. rejected for all lending projects. C. rejected for all borrowing projects. D. accepted for all project types.

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13. If a project's IRR is 13% and the project provides annual cash inflows of $15,000 for 4 years, how much was the initial investment? A. $44,617 B. $52,200 C. $60,000 D. $72,747 14. If the cost of capital is 13% what is the minimum number of years that an investment costing $500,000 must return $65,000 per year in order to be an acceptable investment? A. 8 years B. 14 years C. 17 years D. An infinite number of years 15. Assuming a discount rate of 8%, which of the below statements is incorrect for a project with an initial investment of $30,000 and cash inflows of $7,914 per year for 5 years. A. The payback period is approximately 3.79 years B. The NPV is approximately $1,598 C. The IRR is approximately 10% D. The profitability index is approximately 0.2 16. A project has a payback period of 5 years and the firm has a 10% cost of capital. Which of the following statements is correct concerning this project's discounted payback? A. Discounted payback will exceed 5 years. B. Discounted payback will be less than 5 years. C. Discounted payback will decrease if the project's IRR exceeds 10%. D. Discounted payback will increase if the project's IRR is less than 10%.

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17. In order for a manager to correctly decide to postpone an investment until one year into the future, the NPV of the investment should: A. grow more rapidly than the IRR. B. grow more rapidly than the cost of capital. C. not decrease. D. remain stable. 18. You can lease a new car for $4,700 a year for the next 5 years. Alternatively you can purchase one outright for $16,000 which will last for 5 years and have no scrap value. If r = 13%, which of the below statements is correct? A. Buying the car would be $151 cheaper per year. B. Leasing the car would be $151 cheaper per year. C. Buying the car would be $649 cheaper per year. D. Leasing the car would be $649 cheaper per year

19. Soft capital rationing is imposed upon a firm from _____ sources, while hard capital rationing is imposed from _____ sources. A. internal; external B. internal; internal C. external; internal D. external; external 20. A firm is faced with two mutually exclusive investment projects, both of which have a positive NPV. If no capital rationing has been imposed, which project should be selected? A. Select the project with the higher profitability index. B. Select the project with the lower profitability index. C. Select both projects. D. Select the project with the highest NPV.

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Short answer questions Question 1 Bright plc is considering bringing out a new product. Due to high-tech nature of the industry that Bright operates in, if the product were to be launched then Bright would need to invest $2m in research and development immediately. The expected net cash inflows generated over the next 4 years (the products expected life) are detailed below: Year

1

2

3

4

Cash inflow

$500,000

$750,000

$750,000

$600,000

a) Calculate the internal rate of return (IRR) using the linear interpolation method. (5 marks) b) Assuming that Bright has a cost of capital of 13%, explain whether the investment project should be undertaken. (2 marks) c) Identify and briefly explain the pitfalls of using IRR. (3 marks) Total for the question 10 marks Question 2 a) Explain the difference between hard and soft capital rationing. (2 marks) b) Soft capital rationing imposed by senior management, in some cases, can be an example of an agency cost. Explain this statement. (3 marks) c) NPV is considered to be the “gold standard” of investment appraisal. Explain the NPV approach to investment appraisal. (5 marks) Total for the question 10 marks

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Tutorial 2 – Investment Appraisal Multiple choice solutions 1. What is the NPV of a project that requires an investment of $200,000, returns $80,000 annually for 4 years and the cost of capital is 12%? A. $550,808 B. $149,158 C. $42,984 D. $3,366 NPV = -200,000 + (80,000 x 3.0373) = 42,984 2. What should occur when a project's net present value is determined to be negative? A. The discount rate should be decreased. B. The profitability index should be calculated. C. The present value of the project cost should be determined. D. The project should be rejected.

3. Which of the following changes will decrease the NPV of a project? A. A decrease in the discount rate B. A decrease in the size of the cash inflows C. A decrease in the initial investment D. An increase in the number of cash inflows 4. What is the maximum amount that a firm should consider investing a project that will return $15,000 annually for 5 years if the cost of capital is 10%? A. $33,520 B. $56,862 C. $62,540 D. $75,000 PV inflows = 15,000 x 3.7908 = 56,862 Therefore this is the maximum investment (which would result in an NPV of zero)

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5. If the IRR for a normal investment project is 11%, then the project's NPV would be: A. negative at a discount rate of 8%. B. positive at a discount rate of 16%. C. negative at a discount rate of 12%. D. positive at a discount rate of 20%.

6. When managers select correctly from among mutually exclusive projects, they: A. prioritise NPV over all other methods. B. prioritise IRR over all other methods. C. prioritise payback period over all other methods. D. prioritise profitability index over all other methods . 7. If the NPV of a project is positive $30,000 when using a discount rate of 7% and negative $80,000 when using a discount rate of 15%, calculate the IRR using linear interpolation? A. 0%. B. 11.8%. C. 11.0% D. 9.2%. 𝐼𝑅𝑅 = 7 + (15 − 7) ∗

30,000 = 9.2% 30,000 + 80,000

8. Assuming a cost of capital of 8%, what is the minimum cash flow received (rounded to the nearest $) at the end of year 4 to make the following project "acceptable"? Initial investment = $150,000; cash flows at end of years 1, 2 and 3 = $45,000 each year. A. $25,010 B. $46,300 C. $34,030 D. $35,000 NPV ignoring year 4 cash flow = -150,000 + (45,000 x 2.5771) = -34,030.50 Year 4 cash flow (X):

𝑋 1.084

= 34,030.50, 𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑋 = 34,030.50 ∗ 1.084 = 46,298.12

A cash flow of $46.298.12 received in year 4, and discounted at 8%, would increase the NPV to zero.

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9. A machine costs $18,000 to purchase and running costs are expected to be $5,000 a year. If the discount rate is 12% and the machine will last for 6 years, what is the equivalent annual cost of the machine to the nearest $? A. $38,557 B. $9,639 C. $9,500 D. $9,378 PV of costs = $18,000 + [$5,000 × 4.1114] = $38,557 EAC = 38,557 / 4.1114 = 9,378 10. What is the approximate IRR of a project that costs $108,160 and provides cash inflows of $26,380 annually for 5 years? A. 10% B. 0% C. 7% D. 20% AF 5 years / 7% is 4.1002: PV cash inflows = 26,380 * 4.1002 = 108,163 (approx. = 108,160) 11. A project can in theory have as many different internal rates of return as it has: A. cash inflows. B. cash outflows. C. periods of cash flow. D. changes in the sign of the cash flows. 12. A project with an IRR that is greater than the cost of capital should be: A. rejected for all project types. B. rejected for all lending projects. C. rejected for all borrowing projects. D. accepted for all project types.

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13. If a project's IRR is 13% and the project provides annual cash inflows of $15,000 for 4 years, how much was the initial investment? A. $44,617 B. $52,200 C. $60,000 D. $72,747

14. If the cost of capital is 13% what is the minimum number of years that an investment costing $500,000 must return $65,000 per year in order to be an acceptable investment?? A. 8 years B. 14 years C. 17 years D. An infinite number of years NPV = ($65,000/.13) - $500,000 NPV = $500,000 -$500,000 NPV = $0 15. Assuming a discount rate of 8%, which of the below statements is incorrect for a project with an initial investment of $30,000 and cash inflows of $7,914 per year for 5 years. A. The payback period is approximately 3.79 years B. The NPV is approximately $1,598 C. The IRR is approximately 10% D. The profitability index is approximately 0.2 Payback period = 30,000 / 7,914 = 3.79 years NPV = -30,000 + (7,914 x 3.9927) = $1,598 Profitability index = 1,598 / 30,000 = 0.05 IRR results in NPV of 0: 30,000 = 7,914 * AF AF = 30,000 / 7,914 = 3.7908 (approx. IRR is 10%)

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16. A project has a payback period of 5 years and the firm has a 10% cost of capital. Which of the following statements is correct concerning this project's discounted payback? A. Discounted payback will exceed 5 years. B. Discounted payback will be less than 5 years. C. Discounted payback will decrease if the project's IRR exceeds 10%. D. Discounted payback will increase if the project's IRR is less than 10%. 17. In order for a manager to correctly decide to postpone an investment until one year into the future, the NPV of the investment should: A. grow more rapidly than the IRR. B. grow more rapidly than the cost of capital. C. not decrease. D. remain stable. 18. You can lease a new car for $4,700 a year for the next 5 years. Alternatively you can purchase one outright for $16,000 which will last for 5 years and have no scrap value. If r=13%, which of the below statements is correct? A. Buying the car would be $151 cheaper per year. B. Leasing the car would be $151 cheaper per year. C. Buying the car would be $649 cheaper per year. D. Leasing the car would be $649 cheaper per year EAA Buying Car = 16,000 / 3.5172 (5 YR AF @ 13%) = $4,549. Therefore buying the car is cheaper by $151 per year. 19. Soft capital rationing is imposed upon a firm from _____ sources, while hard capital rationing is imposed from _____ sources. A. internal; external B. internal; internal C. external; internal D. external; external 20. A firm is faced with two mutually exclusive investment projects, both of which have a positive NPV. If no capital rationing has been imposed, which project should be selected? A. Select the project with the higher profitability index. B. Select the project with the lower profitability index. C. Select both projects. D. Select the project with the highest NPV.

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Short answer questions Question 1 Bright plc is considering bringing out a new product. Due to high-tech nature of the industry that Bright operates in, if the product were to be launched then Bright would need to invest $2m in research and development immediately. The expected net cash inflows generated over the next 4 years (the products expected life) are detailed below: Year

1

2

3

4

Cash inflow

$500,000

$750,000

$750,000

$600,000

a) Calculate the internal rate of return (IRR) using the linear interpolation method. NPV of the project using a discount rate of 5% (A): NPVa = -2m + (0.5m x 0.9524) + (0.75m x 0.9070) + (0.75m x 0.8638) + (0.6m x 0.8227) = 0.3m

NPV of the project using a discount rate of 15% (B): NPVb = -2m + (0.5m x 0.8696) + (0.75m x 0.7561) + (0.75m x 0.6575) + (0.6m x 0.5718) = - 0.16m IRR = 5 + (15-5) x 0.3m / 0.3m + 0.16m = 11.5 Note: if you used different discount rates then you may well have got a slightly different answer, this is not a problem! As long as you used a discount rate that gave a positive NPV and another that have a negative NPV then full marks would have been gained.

b) Assuming that Bright has a cost of capital of 13%, explain whether the investment project should be undertaken.

Bright’s cost of capital of 13% represents the rate of return required to satisfy its investors. The IRR calculated of 11.5% is below this figure, therefore it can be concluded that this project should be rejected as it does not generate the returns needed. An alternative way to think of the IRR is that it is the discount rate that would result in an NPV of zero, given that the actual cost of capital higher than this, the project would have a negative NPV. Bright should seek out alternative investments where the IRR exceeds the cost of capital. c) Identify and briefly explain the pitfalls of using IRR.

Students would be expected to briefly explain: 1. Lending vs borrowing projects 2. Mutually exclusive projects 3. Multiple IRRs

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Question 2 a) Explain the difference between hard and soft capital rationing. Answers would be expected to explain: Soft capital rationing: internally imposed restriction Hard capital rationing: due to an actual shortage of funds (cash) available b) Soft capital rationing imposed by senior management, in some cases, can be an example of an agency cost. Explain this statement. Answers would be expected to explain:  

Definition of an agency cost (decision made by management which is not in best interests of shareholders) If soft capital rationing results in projects with a positive NPV not going ahead then it is to the detriment of shareholder wealth

c) NPV is considered to be the “gold standard” of investment appraisal. Explain the NPV approach to investment appraisal. Answers would be expected to explain the below:

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