IRR and ARR Lecture 8 ppt PDF

Preview

Summary

2018 accounting&finance...

Description

4SSMN135 Lecture 9 Capital investment decisions Dr Dorothy Toh 1

Module outline: 11 weeks • W1: Intro to module, management accounting and cost concepts • W2/T1: Cost volume profit analysis • W3/T2: Relevant costs for decision making • W4/T3: Product Costing Methods: Full (absorption) costing • W5/T4: Activity based costing • W6: Reading week (No lectures/No tutorials) • W7: Mid-term test (No lectures/No tutorials) • W8/T5: Budgeting • W9/T6: Accounting for Control: Variance analysis • W10/T7: Financial management and capital budgeting • W11/T8: Capital budgeting cont; Course review and revision strategy 2

Lecture Outline: Capital investment decision making ▪ Nature and importance of investment decision making ▪ The time value of money ▪ Four main investment appraisal methods ▪ Net present value (NPV) ▪ Payback (PP) ▪ Accounting rate of return (ARR) ▪ Internal rate of return (IRR) ▪ Strengths and weaknesses of each approach

The main investment appraisal methods

Investment appraisal methods

Discounted cash flow methods

Net present value

Internal rate of return

Non-discounted cash flow methods

Accounting rate of return

Payback period

Internal rate of return (IRR)

Internal rate of return (IRR)

Investment appraisal method where you solve for the discount rate which is required in order to achieve a NPV of zero.

Internal rate of return (IRR)

Imagine you have £100 and invest it for a year. You receive £105 at the end of the year. Using: Fn = P(1 + r)n , we can solve for r:

105 = 100 (1 + r) r = 5%

Internal rate of return (IRR)

Now imagine you invest $100 for 2 years and receive $60 for each of year 1 and year 2. What is your rate of return r? ▪ Year 1: $100 today grows to $100(1+r). We then withdraw $60 ▪ Year 2: The remaining 100(1+r) – 60 continues to grow at r

▪ At the end of year 2, we have $(100(1+r) – 60)* (1+r), which is $60

Internal rate of return (IRR): Proof of r  (100(1+r) – 60) (1+r) = 60 Rearrange using algebra:

 100 =

60 1+𝑟

+

60 1+𝑟 2

 r is the return implicit in this investment scheme

At a rate r, the sum of the present value of future cash flows = today’s investment

Internal rate of return (IRR): Proof of r ▪ The internal rate of return equates the present value of future cash flows to today’s investment

▪ Put another way, at a rate of r, the sum of the present value of future cashflows = today’s investment

Internal rate of return (IRR): Example You can purchase a building for £350,000. The investment will generate £16,000 in cash flows (i.e. rent) during the first three years. At the end of the third year, you will sell the building for £450,000. What is the IRR on this investment? 16,000+450,000

0  350,000 

16,000 16,000  466,000  (1  IRR) 1 (1  IRR) 2 (1  IRR) 3 IRR = ???%

The discount rate, which, when applied to the future project cash flows, produces a zero NPV

IRR: Trial and error – try 10% Period Initial Inv

t0 (350,000)

Inflows

t1

t2

t3

16,000

16,000

466,000 0 466,000 0.751

Res Val NCF DF=10%

(350,000) 1.000

16,000 0.909

16,000 0.826

NPV

(350,000)

14,544

13,216

349,966

Net Present Value = 27,726

As NPV is positive the project gives an IRR greater

than 10%.

A higher discount rate gives us a smaller present value. Our objective is to find a rate which gives zero NPV

Present value factor tables To determine the present value of a single payment of £1 received ‘n’ years from the present, with a constant discount rate of x% per year.

Periods 1 2 3 4 5

10% 0.909 0.826 0.751 0.683 0.621

Rate 12% 0.893 0.797 0.712 0.636 0.567

14% 0.877 0.769 0.675 0.592 0.519 Slide 13

IRR: Trial and error – try 14% Period Init Inv Inflows Res Val NCF DF=14% NPV

t0 (350,000)

(350,000) 1.000 (350,000)

t1

t2

16,000

16,000

16,000 0.877 14,032

16,000 0.769 12,304

t3 466,000 0 466,000 0.675 314,550

Net Present Value = (9,114)

As NPV is negative the project gives an IRR less than 14%.

IRR example: interpolation IRR must lie somewhere between 10% and 14%! Use interpolation to estimate IRR £ 36,840 Net present value

£ 27,726

Discount 10% rate

0

IRR

-9,114

14%

IRR example: interpolation The process of estimation shown here is called interpolation.

Formula for IRR interpolation: Lower of the pair of discount rates +

( Difference between the NPVs × Difference in rates) % NPV at lower rate

IRR example: interpolation 27,726  36,840

10% +

 4 % 

= 13%

£ 36,840 Net present value

£ 27,726

Discount 10% rate

0

IRR

-9,114

14%

IRR: using Excel Enter all the cash flows and then let Excel find the IRR.

1 2 3 4 5 6 7

A B T ime CF 0 -350,000 1 16,000 2 16,00 0 3 IRR

466,000 13%

The IRR formula used: IRR(B2:B5)

IRR decision rule IRR Rule is to accept projects with IRR’s higher than the opportunity cost of capital and reject projects with IRRs lower than the opportunity cost of capital.

IRR > Cost of Capital  Accept IRR < Cost of Capital  Reject Cost of capital = required return for making an investment

The relationship between NPV and IRR IRR > cost of capital  Accept  NPV > 0 

200,000 150,000

100,000

NPV

50,000

IRR < cost of capital  Reject  NPV < 0 

0 -50,0000% 5% 10% 15% 20% 25% 30% 35% 40% -100,000

IRR

-150,000

-200,000 OpportunityCostof Capital

Evaluation of IRR: Advantages ▪ Percentages make more sense to most people. ▪ It is a very simple way to communicate the value of a project (via % return) ▪ If the IRR is high enough, you may not need to estimate the cost of capital, which is often difficult

Evaluation of IRR: Disadvantages

▪ Projects with non-conventional cash flows lead to multiple IRRs ▪ Cannot handle multiple discount rates ▪ Can lead to wrong decision when projects are mutually exclusive ▪ Mutually exclusive projects are those where when one is chosen, the others must be turned down.

Evaluation of IRR: Pitfalls – multiple rates of return ▪ Certain (non-standard) cash flows can generate NPV=0 at two different discount rates. ▪ The following cash flows generate NPV=0 at both 6% and 31%. Project A

C0 -62

C1 100

C2 25

C3 -65

Which rate should be used?

IRR 6% 31%

Evaluation of IRR: Pitfalls – can lead to wrong decision Project

C0

C1

A B

-5 -350

10 16

C2 16

C3

I RR

NPV@ 7%

466

100% 13%

4.35 59.32

▪ Based solely on IRR would lead you to choose project A ▪ But this is not the option which would maximise shareholder’s wealth ▪ When making decisions with projects which are mutually exclusive, select the one with the highest NPV

Accounting rate of return (ARR)

Accounting rate of return (ARR)

Investment appraisal method which measures the average accounting profit (as opposed to cash flows) expressed as a % of the average investment.

Accounting rate of return (ARR)

Average Annual Profit* Accounting rate = of return

Average investment to earn that profit

* Where profit is profit after depreciation but before taxes

Accounting rate of return (ARR) You have put forward an investment proposal based on an initial investment of 12,000 and accounting profits as follows. At the end of year 4, the residual value of the original investment is estimated to be £1,000. Year 0 Year 1 Year 2 Year 3 Year 4

(12,000) 4,000 1,000 1,000 1,000

Calculating ARR Project with a Residual Value

1. Calculate the average investment: Avg Investment = (Cost+ Residual Value )/ 2 = (12,000 + 1,000) / 2 = 6,500 2. Calculate the average accounting profit:

Average annual profit

= (4,000+1,000+1,000+1,000)/4 = 7,000/4 =1,750

Calculating ARR 3. Calculate the ARR: ARR

= 1,750/6,500 = 26.9%

Average Annual Profit

Accounting rate = of return

Average investment to earn that profit

Evaluation of ARR as a method Advantages

Limitations

▪ Easy to calculate ▪ Easily understood produces a Return On Investment figure (ROI) which is popular ▪ Aligns with financial statement analysis

▪ Uses concept of accounting profit, which are inherent with measurement problems ▪ Ignores timing of cash flows ▪ Ignores time value of money

Appraisal techniques

Methods which are used in practice

Desirable characteristics of investment appraisal methods ▪ It should account for the timing of the project’s expected cash flows ▪ It should account for the risk of the project’s expected cash flows ▪ Overall, it should measure the value created by taking on the project

Only NPV satisfies all these criteria… Advantages ▪ is a direct measure of value creation ▪ adjusts for timing of the project’s expected cash flows ▪ adjusts for risk of the project’s expected cash flows ▪ includes ALL cash flows over the life of the project Disadvantages ▪ requires estimation of cash flows for entire life of the project ▪ requires estimation of a discount rate

END OF EXAMINABLE MATERIAL

4SSMN135 Lecture 10 Course review Dr Dorothy Toh 36...