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Week 5 --tutorial solutions: about stock capital budgeting solutions...

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Extra Problems Incremental IRR and MIRR

Incremental 渐进式 IRR 1. Moulton Industries has two potential projects for the coming year, project B-12 and project F-4. The two projects are mutually exclusive 互斥项目. The opportunity cost of capital for these projects is 10%. Which project should they choose. Calculate the IRRs, the NPVs and the incremental IRR and NPV. The projects have the following cash flows are in 000’s.

Time

0

1

2

3

4

5

B-12

-$4250

$2000

$2000

$2000

$0

$0

F-4

-$3800

$0

$1000

$1500

$2000

$2500

(F-4) – (B-12)

$450

-$2000

-$1000

-$500

$2000

$2500

(B-12) – (F-4)

-450

2000

1000

500

-2000

-2500

NPV project B-12 $723.70. The NPV of F-4 is $1071.75446, so we know the “right” choice is project F-4. The IRR of project B-12 is 19.44% and the IRR of project F-4 is 17.62% so project B-12 looks like the right project (using IRR rule). The IRR of the incremental project is 15.2195% which is greater than the OCC, so we want to do the incremental project. (Note: the IRR is 15.2195% either way, so interpretation of which project is important.)

The NPV of the incremental project (F-4 less B-12) is $348.0465 so it is “worth it” to do the incremental project. Note if we turn it around (difference in CFs between B-12 and F-4), it is a negative NPV so we would not want to do the extra involved in B-12. Choose F-4. 2. You must analyze two projects, X and Y. Each project costs $10,000 and the firm’s WACC is 12 percent. The expected net cash flows are:

0

1

2

3

4

X

-$10000

$6500

$3000

$3000

$1000

Y

-$10000

$3500

$3500

$3500

$3500

a. Calculate each project’s NPV, IRR, and MIRR. b. Which project(s) should be accepted if they are independent? c. Which project should be accepted if they are mutually exclusive? a.

NPVX  10000 

NPV Y  10000 

6500 3000 3000 1000    $966.01 1.12 1.122 1.123 1.124

3500 3500 3500 3500    $630.72 1.12 1.12 2 1.12 3 1.12 4

Alternatively, using a financial calculator, input the cash flows into the cash flow register, enter I/Yr=12, and then press the NPV key to obtain NPVx=966.01 and NPVy=630.72 To solve for IRR, find the rate of return where NPV=0. It is easiest to do this with a financial calculator. Input the cash flows with NPV=0 and solve for I/YR. IRRx will be 18% and IRRy will be 15%. Modified Internal Rate of Return (MIRR): Find each project’s terminal value of cash flows. TVx 6500(1.12)3  3000(1.12) 2  3000(1.12) 1000 17255.23 TVY 3500(1.12)3 3500(1.12)2 3500(1.12) 3500 16727.65

Each project’s MIRR is the discount rate that equates the PV of the TV to each project’s cost, $10000.

MIRRx=14.61% MIRRy=13.73% b. All methods say both project X and Y are good projects. Therefore, accept both projects if they are independent. c. If the projects are mutually exclusive, we can only accept one project. In this case all methods say X is the better project. If the methods were in conflict, we would want the project with the highest NPV, which is project X. If there were a conflict, it is likely due to a project scale issue or due to the reinvestment rate assumption. Since these projects are of similar scale, it would be due to the reinvestment rate assumption. NPV assumes the incoming cash flows are invested at the OCC, IRR assumes they are invested at the IRR. MIRR assumes they are invested at the OCC, thus MIRR is an improvement.

3. A company has a 12 percent WACC and is considering tow mutually exclusive investments (that cannot be repeated) with the following net cash flows:

0

1

2

3

4

5

6

7

A

-$300

-$387

-$193

-$100

$600

$600

$850

-$180

B

-$405

$134

$134

$134

$134

$134

$134

$0

a. b. c. d.

What is each project’s NPV? What is each project’s IRR? What is each project’s MIRR? (Hint: Consider Period 7 as the end of Project B’s life. From you answers in parts a,b, and c, which project would be selected? If the WACC were 18 percent, which project would be selected? e. What is each project’s MIRR at a WACC of 18 percent? a. Using a financial calculator and entering each project’s cash flows into the cash flow registers and entering I/YR = 12, you would calculate each project’s NPV. At WACC = 12%, Project A has the greater NPV, specifically $200.41 as compared to Project B’s NPV of $145.93. b. Using a financial calculator and entering each project’s cash flows into the cash flow registers, you would calculate each project’s IRR. IRR A = 18.1%; IRRB = 24.0%.

c. Here is the MIRR for Project A when WACC = 12%: PV costs = $300 + $387/(1.12)1 + $193/(1.12)2 + $100/(1.12)3 + $180/(1.12)7 = $952.00. TV inflows = $600(1.12)3 + $600(1.12)2 + $850(1.12)1 = $2,547.60. MIRR is the discount rate that forces the TV of $2,547.60 in 7 years to equal $952.00. Using a financial calculator enter the following inputs: N = 7, PV = -952, PMT = 0, and FV = 2547.60. Then, solve for I/YR = MIRRA = 15.10%. Here is the MIRR for Project B when WACC = 12%: PV costs = $405.

TV inflows = $134(1.12)6 + $134(1.12)5 + $134(1.12)4 + $134(1.12)3 + $134(1.12)2 + $134(1.12) = $1,217.93. MIRR is the discount rate that forces the TV of $1,217.93 in 7 years to equal $405. Using a financial calculator enter the following inputs: N = 7; PV = -405; PMT = 0; and FV = 1217.93. Then, solve for I/YR = MIRRB = 17.03%. d. WACC = 12% criteria: NPV IRR MIRR

Project A $200.41 18.1% 15.1%

Project B $145.93 24.0% 17.03%

The correct decision is that Project A should be chosen because NPVA > NPVB. At WACC = 18%, using your financial calculator enter the cash flows for each project, enter I/YR = WACC = 18, and then solve for each Project’s NPV. NPVA = $2.66; NPVB = $63.68. At WACC = 18%, NPVB > NPVA so Project B would be chosen. e. Here is the MIRR for Project A when WACC = 18%: PV costs = $300 + $387/(1.18)1 + $193/(1.18)2 + $100/(1.18)3 + $180/(1.18)7 = $883.95. TV inflows = $600(1.18)3 + $600(1.18)2 + $850(1.18)1 = $2,824.26. MIRR is the discount rate that forces the TV of $2,824.26 in 7 years to equal $883.95.

Using a financial calculator enter the following inputs: N = 7; PV = -883.95; PMT = 0; and FV = 2824.26. Then, solve for I/YR = MIRRA = 18.05%. Here is the MIRR for Project B when WACC = 18%: PV costs = $405. TV inflows = $134(1.18)6 + $134(1.18)5 + $134(1.18)4 + $134(1.18)3 + $134(1.18)2 + $134(1.18) = $1,492.96. MIRR is the discount rate that forces the TV of $1,492.26 in 7 years to equal $405. Using a financial calculator enter the following inputs: N = 7; PV = -405; PMT = 0; and FV = 1492.26. Then, solve for I/YR = MIRRB = 20.48%.

NPV ($) 1,000

4. A mining company is deciding whether to open a strip mine, which costs $2 million. Net cash inflows of $13 million Project A would occur at the end of Year 1. The land must be Project B returned to its natural state at Co st of Ca pit al (% ) a cost of $12 million, payable at the end of year 2. a. Should the project be accepted if WACC=10%? At WACC=20%? Explain your reasoning. b. Can you think of some other capital budgeting situations in which negative cash flows during or at the end of the project’s life might lead to multiple IRRs? c. What is the project’s MIRR at WACC = 10%? At WACC=20%? Does MIRR lead to the same accept/reject decision for this project as the NPV method? Does the MIRR always lewad to the same accept/reject decision as NPV? (Hint: Consider mutually exclusive projects that differ in size.) 900 800 700 600 500 400 300 200 100

-100

5

10

15

20

25

-200

-300

a.. If WACC = 10%, reject the project since NPV < $0. Its NPV at WACC = 10% is equal to -$99,174. But if WACC = 20%, accept the project because NPV > $0. Its NPV at WACC = 20% is $500,000. b. Other possible projects with multiple rates of return could be nuclear power plants where disposal of radioactive wastes is required at the end of the project’s life.

30

c. MIRR @ WACC = 10%: PV costs = $2,000,000 + $12,000,000/(1.10)2 = $11,917,355. FV inflows = $13,000,000  1.10 = $14,300,000. Using a financial calculator enter the following data: N = 2; PV = -11917355; PMT = 0; and FV = 14300000. Then solve for I/YR = MIRR = 9.54%. (Reject the project since MIRR < WACC.) MIRR @ WACC = 20%: PV costs = $2,000,000 + $12,000,000/(1.20)2 = $10,333,333. FV inflows = $13,000,000  1.20 = $15,600,000.

Using a financial calculator enter the following data: N = 2; PV = -10333333; PMT = 0; and FV = 15600000. Then solve for I/YR = MIRR = 22.87%. (Accept the project since MIRR > WACC.)

Looking at the results, this project’s MIRR calculations lead to the same decisions as the NPV calculations. However, the MIRR method will not always lead to the same accept/reject decision as the NPV method. Decisions involving two mutually exclusive projects that differ in scale (size) may have MIRRs that conflict with NPV. In those situations, the NPV method should be used....