Econ 134A - Week 5 Section Notes...Econ 134A - Week 5 Section Notes Jaime Ramirez-Cuellar Fall 2018...

Plan Session 4 Review: Investment Rules Equivalent Annual Cost

Econ 134A - Week 5 Section Notes

Jaime Ramirez-CuellarFall 2018

Department of EconomicsUniversity of California, Santa Barbara

November 7, 2018


CONTACT INFORMATION

Email concerns to: ganghua [email protected] hours: M-W 5:00 pm - 6:15 pm (NH 2019)Office hours: Th 10:00 am - 12:30 pm (NH 2051)Office hours: Th 1:00 pm - 2:00 pm (NH 2043)Office hours: Th 2:00 pm - 3:30 pm (NH 2043)


OUTLINE

Plan Session 4

Review: Investment Rules

Equivalent Annual Cost


PLAN

Plan today:

I Review Investment RulesI Examples for Investment RulesI Equivalent Annual Cost


REVIEW: INVESTMENT RULES

I When a firm or an individual want to make an investmentdecision, they need to refer to some rules for them to makea correct decision:

I Net present palue rule (NPV)I Payback periods ruleI Internal rate of return rule (IRR)I Profit index (PI)


REVIEW: INVESTMENT RULES

I NPV is the PV of all cash flows. We invest if it is positiveI Payback periods is the number of periods to compensate

original investmentI Payback periods rule says that a project is better the lower

its payback periodsI Payback periods rule cannot distinguish between two

projects with same payback periods but different NPVI The IRR is the rate that causes the NPV of the project to be

zeroI The IRR is not unique for multiple periods in generalI PI is the ratio between the PV of future cash flows and the

initial investmentI Both IRR and PI suffer from the scale problem


NPV WITH UNCERTAINTY

Suppose that Company A has formulated a new drink, SuperWater.

I If Super Water is a success, the present value of the payoffis $5 million (when the product is brought to the market)

I If the product fails, the present value of the payoff is $2million

I The product goes directly to market, there is a 30% chanceof success and a 70% chance of failure.

I Alternatively, Company A can delay the introduction ofSuper Water by 2 years and spend $300,000 today to testthe market and the product

I Testing the market will improve the product and increasethe chance of success to 60%. The appropriate annualdiscount rate is 5%


NPV WITH UNCERTAINTY

I What is the NPV of going directly to the market (inmillion)?

NPV = .3 × $5 + 0.7 × $2 = $2.9

The NPV is $2.9 millionI What is the NPV of delaying the introduction of Super

Water by 2 years?

NPV = −0.3 +0.6 × $5 + 0.3 × $2

1.052 = $2.965

The NPV is $2.965 millionI If you were advising Company A what to do in 20 words

or less, what would you say? Include any justification foryour advise


IRR

I Selma spent $200,000 today in the development of a newproduct

I and will receive $250,000 five years from nowI Her annual discount rate is 4%I What is her annual internal rate of return for this project?


IRR

I Selma spent $200,000 today in the development of a newproduct

I and will receive $250,000 five years from nowI Her annual discount rate is 4%

NPV = −$200, 000 +$250, 000

1.045 = $5, 481.78

I What is her annual internal rate of return for this project?

0 = −$200, 000 +$250, 000(1 + IRR)5

I IRR = 4.564%


PROFIT INDEX

I T. Cards has an opportunity to develop a new card gameI In order to develop the card game, T needs to spend $5,000

todayI The company receives a positive cash flow of $8,000 two

years from nowI No other cash flows occur with this projectI If the annual discount rate is 14%, what is the profitability

index of this project?


PROFIT INDEX

I T receives $8,000 two years from now in case she takes theopportunity. What is the present value of this cash flow?

PV of future cash flows =$8, 0001.142 = $6, 155.74

I What is the profitability index?

PI =$6, 155.74$5, 000

= 1.23


EQUIVALENT ANNUAL COST

I Suppose a firm must choose between two machines ofunequal lives

I Both machines can do the same job, but they have differentcosts and will last for different time periods

I When confronting with such a problem, we will turn to theEAC approach rather than using NPV

I Why? Because there’s a trade-off between the lower NPVand the longer periods of use

I Machines with lower present value of costs might lastshorter periods than the one with higher present value ofcosts



I Example: One club must choose between two mechanicaltennis ball throwers

I Machine A costs less than machine B but will not last aslong

I The cash outflows from the two machines are shown below

Machine 0 1 2 3 41 $500 $120 $120 $1202 $600 $100 $100 $100 $100

I Assume a discount rate of 10%



I Machine A

$798.42 = $500 +$1201.1

+$1201.12 +

$1201.13

I Machine B

$916.99 = $600 +$1001.1

+$1001.12 +

$1001.13 +

$1001.14



I Better approach: derive equivalent annual cost (EAC) ofeach machine, and choose the one with lower EAC

I Equation (1) means that the cash flows of ($500, $120, $120,$120) are equivalent to a single payment of $8798.42 attime 0

I We want to equate the single payment of $798.42 at date 0with a 3-year annuity:

$798.42 = C[

110%

− 110%(1 + 10%)3

]Solving for C = $321.05



I The payment stream of ($500, $120, $120, $120) isequivalent to annuity payments of $321.05 made at the endof each year for three years

I We refer to $321.05 as the EAC of machine AI Turn to Machine B, to calculate its EAC from

$916.99 = C[

110%

− 110%(1 + 10%)4

]I Solving for C = $289.28I A rational person would choose to pay a lower amount

each period, i.e. machine B is the preferred choice



I You have been asked to analyze the costs of two differentmachines

I If you buy Machine A, you have to pay $1,000 today, andmaintenance costs of $200 in each of years 2, 3, and 4

I If you buy Machine B, you have to pay $1,500 today and$100 in maintenance costs in each years l, 2, 3, 4, and 5

I Machine A lasts 4 years, and Machine B lasts 5 yearsI The effective annual discount rate is 6%



I What is the NPV of all the costs of Machine A?I What is the NPV of all of the costs of’ Machine B?I What is the EAC of Machine A?I What is the EAC of Machine B?I If both machines can be easily replaced in the future,

which machine will you buy? Explain in 15 words or less



I What is the present value for Machine A?

PV = $1, 000 +$2001.062 +

$2001.063 +

$2001.064

I and for Machine B?

PV = $1500 +$100$1.06

+$100$1.062 +

$100$1.063 ++

$100$1.064

$100$1.065



I Machine A

$1, 419.19 = $1, 000 + 0 +$2001.062 +

$2001.063 +

$2001.064

I Machine B

$1, 812.49 = $1500+$100$1.06

+$100$1.062+

$100$1.063+

$100$1.064+

$100$1.065



I What’s the annuity corresponding to Machine A?

$1, 419.19 = C[

10.06

− 10.06(1 + 0.06)3

]I For machine A the annuity is C = $530.93I and for Machine B?

$1, 812.49 = C[

10.06

− 10.06(1 + 0.06)4

]I For machine B the annuity is C = $523.07I A rational person will choose lower payments each period,

i.e., she will choose machine B


WHAT TO READ?

I Corporate Finance: Core Principles & Applications, byRoss, Westerfield, Jaffe (11th ed.)

I This week: Firm value; net present value; payback periodmethods; equivalent annual cost; other investment rulesSections 4.6, 5.1-5.3, and part of 6.4 (p. 188-190)

Date post:	19-Sep-2020
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

Econ 134A - Week 5 Section Notes...Econ 134A - Week 5 Section Notes Jaime Ramirez-Cuellar Fall 2018...

Documents