Tutorial exercise 7



Tutorial 8: Answers

Questions

1. Define and explain the Payback Period Method, the Net Present Value (NPV) Method and the Internal Rate of Return (IRR) Method. In your discussion state the criteria for accepting or rejecting an investment under each rule. Discuss the strengths and weaknesses associated with the use of each alternative method.

ANSWER:

Payback Period Method

The payback period is the amount of time required to recover the firm's initial investment in a project. In the case of a mixed stream, the cash inflows are added until their sum equals the initial investment in the project. In the case of an annuity, the payback is calculated by dividing the initial investment by the annual cash inflow.

Criteria: Accept a project if the payback period is less than some preset limit.

Strengths of the payback include:

o It is simple to use and understand

o It is a crude measure of project risk, and

o It is a crude measure of a project's liquidity.

[Note: liquidity here is a measure of how quick it is to exit an investment, and how close is the price you get relative to the initial market price when you start to exit. Projects with shorter payback periods will be more liquid.]

Weaknesses include

o It fails to take into account the time value of money.

o It fails to recognise cash flows that occur after the preset limit

o It assumes cash flows are received on a daily basis

o It fails to select the project that maximises shareholder wealth, etc

[note: here, shareholder wealth is synonymous with the net present value of future cash flows]

Net Present Value Method:

Net Present Value is the sum of the present values of all the cash flows (CF) using the project's cost of capital less the initial investment.

Criteria: Accept if NPV>0 and reject if NPVcost of capital and reject if IRR 0 |IRR > required rate |

For non-mutually exclusive projects, NPV and IRR will usually have similar results:

NPV > 0 means that the project rate of return > required rate

IRR > required rate means project rate of return > required rate

The conflict between NPV and IRR mainly arises for mutually exclusive projects (see below) ]

Problems

1. ABC corporation is attempting to evaluate the feasibility of investing $95000 in a project with five years life. The firm has estimated the associated cash inflows as shown in the following table. The firm has required rate of return 12 percent.

|Year end |Cash inflows ($) |Cumulative CF | |

|1 |20,000 |20,000 | |

|2 |25,000 |45,000 | |

|3 |30,000 |75,000 | |

|4 |35,000 |110,000 | |

|5 |40,000 |150,000 | |

a. Calculate payback period for the proposed investment.

b. Calculate NPV for the proposed investment.

c. Calculate IRR (rounded to the nearest whole per cent) for the proposed investment.

d. Evaluate the acceptability of the proposed investment using NPV and IRR?

ANSWER:

a. Payback period

3 + ($20,000 ( $35,000) = 3.57 years

b. PV of cash inflows

Year CF PVIF12%,n PV

1 $20,000 .893 $ 17,860

2 25,000 .797 19,925

3 30,000 .712 21,360

4 35,000 .636 22,260

5 40,000 .567 22,680

$104,085

NPV = PV of cash inflows - Initial investment

NPV = $104,085 - $95,000

NPV = $9,085

c. [pic]

IRR = 15% (15.36%)

d. NPV = $9,085; since NPV > 0; accept

IRR = 15%; since IRR > 12% cost of capital; accept

The project should be implemented since it meets the decision criteria for both NPV and IRR.

2. Each of following mutually exclusive projects involve an initial cash outlay of $240,000. The estimated net cash flows for the projects are:

|Year |Project A ($) |Project B ($) |

|1 |140000 |20000 |

|2 |80000 |40000 |

|3 |60000 |60000 |

|4 |20000 |100000 |

|5 |20000 |180000 |

a) Calculate the payback period for both projects. Which project should be chosen? Why?

b) The company’s required rate of return is 11 percent. Calculate the NPV and IRR for both projects. Which project should be chosen? Why?

ANSWER:

a)

|Cumulative cash inflows: |

|Year |Project A |Project B |

|1 |140000 |20000 |

|2 |220000 |60000 |

|3 |280000 |120000 |

|4 |300000 |220000 |

|5 |320000 |400000 |

PBPA = 2 + (240000-220000) / 60000 = 2 + .3333 = 2.33 years

PBPB = 4 + (240000-220000) / 180000 = 4 + .1111 = 4.11 years

Decision: Project A is better than project B

b) NPV

NPVA = [pic]

= $20 000 (to nearest thousand)

NPVB = [pic]

= $27 000 (to nearest thousand)

Using the NPV method, project B should be selected.

IRR

IRRA = 16% (rounded)*

IRRB = 14% (rounded)

Using the IRR method, project A should be selected.

This suggests a ranking conflict between the NPV and IRR methods.

To maximise the value of the company, the NPV method should be used and therefore project B should be selected.

[

Note: There are several reasons why NPV and IRR may conflict for mutually exclusive projects (e.g. )

]

3. Projects with Unequal Lives– Annualised Net Present Value (ANPV) Approach

ABC firm is considering to invest in one of three mutually exclusive projects X, Y and Z. The initial investment and annual net cash inflows over the life of each project are shown in the following table:

| |Project X |Project Y |Project Z |

|Initial investment |$78,000 |$52,000 |$66,000 |

|Year |Net cash flows |

|1 |$17,000 |$28,000 |$15,000 |

|2 |$25,000 |$38,000 |$15,000 |

|3 |$33,000 |------ |$15,000 |

|4 |$41,000 |------ |$15,000 |

|5 |------ |------ |$15,000 |

|6 |------ |------ |$15,000 |

|7 |------ |------ |$15,000 |

|8 |------ |------ |$15,000 |

All the projects have equal risk and firm’s required rate of return for these projects is 14%.

a. Calculate the NPV for each project over its life. Rank the projects in descending order based on NPV.

b. Calculate the Equivalent Annual Value (EAV) for each project over its life. Rank the projects in descending order based on EAV.

c. Compare and contrast your findings in a & b above. Which project would you recommend the firm to purchase? Why?

a. Project X

Year CF PVIF14%,n PV

1 $ 17,000 .877 $ 14,909

2 25,000 .769 19,225

3 33,000 .675 22,275

4 41,000 .592 24,272

$ 80,681

NPV = $80,681 - $78,000 = $2,681

Calculator solution: $2,698.32

Project Y

Year CF PVIF14%,n PV

1 $ 28,000 .877 $ 24,556

2 38,000 .769 29,222

$ 53,778

NPV = $53,778 - $52,000

NPV = $1,778

Calculator solution: $1,801.17

Project Z

PVn = PMT x (PVIFA14%,8 yrs.)

PVn = $15,000 x 4.639

PVn = $69,585

NPV = PVn - Initial investment

NPV = $69,585 - $66,000

NPV = $3,585

Calculator solution: $3,582.96

Rank Project

1 Z

2 X

3 Y

b. [pic]

Project X

EAV = $2,681 ( 2.914 (14%,4 yrs.)

EAV = $920.04

Project Y

EAV = $1,778 ( 1.647 (14%,2 yrs.)

EAV = $1,079.54

Project Z

EAV = $3,585 ( 4.639 (14%, 8 yrs.)

EAV = $772.80

Rank Project

1 Y

2 X

3 Z

c. Project Y should be accepted. The results in a and b show the difference in NPV when differing lives are considered.

[Note: Projects with long-dated lives will likely have higher NPVs than shorter-dated projects.

The Annualised Net Present Value approach (or Equivalent Annuity approach) recognises the fact that the longer-dated project will ‘tie up’ capital for a longer period compared to the shorter-dated project - the shorter-dated project allows the investor to get back their original investment faster, which then allows them to reinvest in another project.

The Annualised NPV approach expresses each project as an equivalent annual cashflow (EAC) having the same total NPV as the project. This allows the equivalent annual cashflows to be compared between projects – see below.]

[pic]

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