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Capital Budgeting: Evaluating Mutually Exclusive Projects, Exercises of Financial Management

Hanoi Open University (HOU)Financial Management

The document evaluates two mutually exclusive projects, A and B, using net present value (NPV) and internal rate of return (IRR) methods. It provides insights into the decision-making process, including identifying the project to undertake based on different discount rates, the discount rate where NPV and IRR yield the same decision, and the problems associated with using IRR in capital budgeting. It also analyzes project K, calculating its NPV, IRR, payback, and discounted payback, and compares projects A and B, examining their NPV profiles, cross-over rate, and decision-making based on different discount rates. Additionally, it evaluates two mutually exclusive air conditioning units, HCC and LCC, using the NPV method.

Typology: Exercises

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61FIN2FIM - FINANCIAL MANAGEMENT
TUTORIAL 8 – CAPITAL BUDGETING
Short Answer Questions
Use the following information to answer question 1 - 10
Projects A and B have the same expected lives and initial cash outflows. However, one project's cash flows
are larger in the early years, while the other project has larger cash flows in the later years. The following
NPV profiles of two mutually exclusive project A and B are provided as below
1. At the discount rate of 10%, which project should be undertaken under NPV criterion?
Project B because it has higher NPV
2. At the discount rate of 13%, which project should be undertaken under NPV criterion?
Project A because it has higher NPV
3. At the discount rate of 10%, which project should be undertaken under IRR criterion?
Project A because it has higher IRR
4. At the discount rate of 13%, which project should be undertaken under IRR criterion?
Project A because it has higher IRR
5. From what discount rate, the NPV and IRR methods yield the same decision?
Greater than 11.5%: project A is selected because it has higher IRR and NPV
6. From what discount rate, the NPV and IRR methods provides conflict decisions?
Less than 11.5%: project A has higher IRR but lower NPV than project B.
7. As a financial manager, you expect that the discount rate of 10% should be used to evaluate the two
projects. Which project should you pick?
Project B is selected because it has higher NPV than project A
8. As a financial manager, you expect that the discount rate of 13% should be used to evaluate the two
projects. Which project should you pick?
Project A is selected because it has higher NPV than project B
9. Which project has larger cash flows in the later years?
10. At what discount rate, the NPV of the two projects are the same?
WACC = 11.5%
11. What are independent projects? Mutually exclusive projects?
Independent projects are projects whose cash flows are not affected by one another. Mutually exclusive projects, on the
other hand, are projects where if one project is accepted, the other must be rejected.
12. What is reinvestment rate used in IRR calculation? NPV calculation?
Reinvestment rate is discount rate used in IRR and NPV calculation. As such, IRR is the reinvestment rate in IRR
calculation and cost of capital (also named WACC or required rate of return) is the reinvestment rate in NPV calculation.
13. Why NPV is superior to IRR?
14. What are some problems of using IRRs in capital budgeting?
- Multiple IRRs exist and No IRR can be found.
15. What criteria are used to measure project’s liquidity and what criteria are used to measure project’s
profitability?
To measure project's liquidity, we use payback and discounted payback.
To measure profitability, we use NPV and IRR.
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61FIN2FIM - FINANCIAL MANAGEMENT

TUTORIAL 8 – CAPITAL BUDGETING

Short Answer Questions Use the following information to answer question 1 - 10 Projects A and B have the same expected lives and initial cash outflows. However, one project's cash flows are larger in the early years, while the other project has larger cash flows in the later years. The following NPV profiles of two mutually exclusive project A and B are provided as below

1. At the discount rate of 10%, which project should be undertaken under NPV criterion? Project B because it has higher NPV 2. At the discount rate of 13%, which project should be undertaken under NPV criterion? Project A because it has higher NPV 3. At the discount rate of 10%, which project should be undertaken under IRR criterion? Project A because it has higher IRR 4. At the discount rate of 13%, which project should be undertaken under IRR criterion? Project A because it has higher IRR 5. From what discount rate, the NPV and IRR methods yield the same decision? Greater than 11.5%: project A is selected because it has higher IRR and NPV 6. From what discount rate, the NPV and IRR methods provides conflict decisions? Less than 11.5%: project A has higher IRR but lower NPV than project B. 7. As a financial manager, you expect that the discount rate of 10% should be used to evaluate the two projects. Which project should you pick? Project B is selected because it has higher NPV than project A 8. As a financial manager, you expect that the discount rate of 13% should be used to evaluate the two projects. Which project should you pick? Project A is selected because it has higher NPV than project B **9. Which project has larger cash flows in the later years?

  1. At what discount rate, the NPV of the two projects are the same?** WACC = 11.5% 11. What are independent projects? Mutually exclusive projects? Independent projects are projects whose cash flows are not affected by one another. Mutually exclusive projects, on the other hand, are projects where if one project is accepted, the other must be rejected. 12. What is reinvestment rate used in IRR calculation? NPV calculation? Reinvestment rate is discount rate used in IRR and NPV calculation. As such, IRR is the reinvestment rate in IRR calculation and cost of capital (also named WACC or required rate of return) is the reinvestment rate in NPV calculation. **13. Why NPV is superior to IRR?
  2. What are some problems of using IRRs in capital budgeting?**
    • Multiple IRRs exist and No IRR can be found. 15. What criteria are used to measure project’s liquidity and what criteria are used to measure project’s profitability? To measure project's liquidity, we use payback and discounted payback. To measure profitability, we use NPV and IRR.

sive projects, on the ent rate in IRR e in NPV calculation. re project’s

Part 2 - Problems

1. Project K costs $52,125, its expected cash inflows are $12,000 per year for 8 years, and its WACC is 12%. A. Calculate the project’s NPV. B. Calculate the project’s IRR. C. Calculate the project’s payback. D. Calculate the project’s discounted payback. E. Should the project be undertaken? Hints A. NPV = -52,125 + 12,000/12%[1 - 1/(1+12%)^8] = $7,486. B. Set NPV = 0 and solve for discount rate 52,125 = 12,000/IRR[1 - 1/(1 + IRR)^8] So IRR = 16% C. $52,125/$12,000 = 4.34 years D. Period CF Discounted CF Cummulative 0 -$52,125 -$52,125 -$52, 1 $12,000 $10,714 -$41, 2 $12,000 $9,566 -$31, 3 $12,000 $8,541 -$23, 4 $12,000 $7,626 -$15, 5 $12,000 $6,809 -$8, 6 $12,000 $6,080 -$2, 7 $12,000 $5,428 $2, 8 $12,000 $4,847 $7, The discounted payback period is 6 + $2,788.11/$5,428.19 years, or 6.51 years. E. Based on NPV: this project should be undertaken because it has positive NPV. Based on IRR: this project should be undertaken because its IRR (16%) is more than its cost of capital (Wacc=12%). There is no set criteria for payback or discounted payback, thus no decision based on these two methods can be made. 2. Your division is considering two projects with the following cash flows (in millions): 0 1 2 3 Project A (^) -$25 $5 $10 $ Project B (^) -$20 $10 $9 $ A. What are the projects’ NPVs assuming the WACC is 5%? 10%? 15%? B. What are the projects’ IRRs at each of these WACCs? C. Draw NPV profiles for the two projects. D. Calculate the cross-over rate. E. Based on the examination of NPV profile and given that the WACC was 5% and A and B were mutually exclusive, which project would you choose? What if the WACC was 10% or 15%? Hints A) WACC 5% 10% 15% NPV(A) $3.52 $0.58 -$1. NPV(B) $2.87 $1.04 -$0. B) WACC 5% 10% 15% IRR(A) 11.10% 11.10% 11.10% IRR(B) 13.18% 13.18% 13.18%

C)

NPV PROFILE

Discount rate NPV(A) NPV(B) 0% $7.00 $5. 5% $3.52 $2. 10% $0.58 $1. 11% $0.00 $0. 13.18% -$1.05 $0. 15% -$1.91 -$0. D) Cross over rate Rate 7.81% NPV(A) $ NPV(B) $ E) (^) WACC 5% 10% 15% Desicion A B B (always prioritize project with higher positive NPV) 0% 2% 4% 6% -$4. -$2. $0. $2. $4. $6. $8.

NPV PRO

NPV(A) Discou NPV

0% 2% 4% 6% 8% 10% 12% 14% 16% 0 0 0 0 0 0 0

NPV PROFILE

NPV(A) NPV(B) Discount rate

  1. A firm with a 14% WACC is evaluating two projects for this year’s capital budget. After-tax cash flows, including depreciation, are as follows: 0 1 2 3 4 5 Project A (^) -$6,000 $2,000 $2,000 $2,000 $2,000 $2, Project B (^) -$18,000 $5,600 $5,600 $5,600 $5,600 $5, A. Calculate NPV, IRR, payback, and discounted payback for each project. B. Assuming the projects are independent, which one(s) would you recommend? C. If the projects are mutually exclusive, which would you recommend? Hints A. NPV, IRR, Payback period, and discounted payback for two projects are presented in the below table: Criteria Project A Project B NPV $866.16 $1,225. IRR 19.86% 16.80% Payback 3 years 3.21 years Discounted payback 4.17 years 4.58 years B. Two projects are independent: Using NPV method: Both projects should be accepted because their NPVs are positive. Using IRR method: Both projects should be accepted because their IRRs are greater than WACC. C. Two projects are mutually exclusive, use NPV as the most appropriate method of evaluation. Select project B at the WACC of 14%. 4. Kim Inc. must install a new air conditioning unit in its main plant. Kim must install one or the other of the units; otherwise, the highly profitable plant would have to shut down. Two units are available, HCC and LCC (for high and low capital costs, respectively). HCC has a high capital cost but relatively low operating costs, while LCC has a low capital cost but higher operating costs because it uses more electricity. The costs of the units are shown here. Kim’s WACC is 7%. 0 1 2 3 4 5 HCC -$600,000 -$50,000 -$50,000 -$50,000 -$50,000 -$50, LCC (^) -$100,000 -$175,000 -$175,000 -$175,000 -$175,000 -$175, A. Which unit would you recommend? Explain. B. If Kim’s controller wanted to know the IRRs of the two projects, what would you tell him? Hints WACC 7% A) NPV HCC -$805,009. LCC -$817,534. I personally would reject both of them, but we can not tell further Cash flow, maybe positive, so we could try pro B) unable to find IRR since all the values are negative A. Two projects are mutually exclusive so we will apply NPV criterion for project evaluation. Even cash flows of the two p NPV (HCC) = -$805,009.87 (at WACC =7%) NPV (LCC) = -$817,534.55 (at WACC=7%) Since NPV (HCC) is greater than that of LCC, we select HCC project.

he other of the HCC and LCC erating costs, he costs of the tive, so we could try project HCC with higher NPV and pray for good luck :D cash flows of the two projects are all negative, but the firm must install one, as such we will select a higher NPV project.