tcdn group 3 (project interactions)

8/2/2019 TCDN Group 3 (Project Interactions)

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Corporate Finance

Group 3

Nguyn Th Phng Hoa

Nguyn Th Mai LinhThn Th Hng Hnh

Nguyn Th QuL Th Vn


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Some Special Cases in Valuing

Projects


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Mutually Exclusive Projects

Projects A & B to be mutually exclusive:Projects A & B to be mutually exclusive:You can only acceptYou can only accept project A or project Bproject A or project B but you can notbut you can not

accept both of themaccept both of them..

Or

Apartment

Cinema


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Cash Flow at

Beginning of Class

Cash Flow at End of

Class (150 mins later)

opportunity 1 -$1 $1.50

opportunity 2 -$10 $11.00


Which would you choose?

Opportunity 1 or Opportunity 2?


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Cash Flow at

Beginning of Class

Cash Flow at End

of Class (150

mins later) NPV IRR

opportunity 1 -$1 $1.50 $0.50 50%

opportunity 2 -$10 $11.00 $1.00 10%

Now,Which would you choose? The reason?

Based on IRR orN

PV?

The answer is to choose Opportunity 2,based onNPV!


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The IRR rule seems to indicate that if you have

to choose, you should go for opportunity 1 since

it has the higher IRR. If you follow IRR rule,

you make the wrong choice.


The problem with IRR is thatit ignores the issues of Scale.


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When you need to choose between

mutually exclusive projects, the decision

rule is to calculate the NPV of each project

and, from that have a positive NPV,

choose the one whose NPV is highest.



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The choice

Should the company save money today by installingCheaper machines that will not last as long?

Should the company save money today by installingCheaper machines that will not last as long?

Long-livedequipment

Short-livedequipment

Long versus Short-lived Equipment


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Example 1: Choose between machine Aand machine B

lasts 3 yearsM

ach

ine A



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lasts 2 yearsMachine B



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Costs, Thousands of Dollars

( the cost of capital is 6%)

Year 0 1 2 3

Machine A 15 4 4 4

Machine B 10 6 6 -



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Because the two machines produce exactly the sameproduct, but with unequal lives the only way to choosebetween them is on the basic ofequivalent annualcost, not on present value of costs.

PV of cost

- Equivalent annual cost (EAC) =

annuity factor



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Annuity Factor

1 1

Annuity Factor = -

r r (1+r)t

* r: Discount rate

* t: Number of periods


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Machine A

4,000 4,000 4,000

- PV of cost = 15,000 + + +

(1+0.06) (1+0.06)2 (1+0.06)3

= 25,690

1 1

- Annuity factor = - = 2.673

0.06 0.06x(1+0.06)3

EAC = 25,690/2.673 = 9.61



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Machine B

6,000 6,000

- PV of cost = 10,000 + + = 21,000

(1+0.06) (1+0.06)2

1 1

- Annuity factor = - = 1.8334

0.06 0.06x(1+0.06)2

EAC = 21,000 / 1.8334 = 11,450



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EAC ($11,450)EAC ($9,610)

Machine BMachine A

M

ach

ine A is better, because its EAC is less

Vs.

PV of cost ($21,000)PV of cost ($25,690) >

Choose to use the old one.


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Should you replace the old machine?

Old New

r = 10%

Last 4 years

operating cost: $7,000/year

Cost: $12,000

r = 10%

Last 2 more years

Operating cost: $11,000/year


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=> You should buy a new machineto replace the old one

Year 0 1 2 3 4 PV at

10%

New machine 12 7 7 7 7 34.19

Equivalent 4-year annuity

--- 10.78 10.78 10.78 10.78 34.19


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And now..For the best answer:

_The modestMercedes_cost of$99,000

& specially, a 5-day tour to Hawaii!


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Workshop 1: Machines F, G are mutually exclusive&have following investment and operating costs:

(Dollars)

Discount rate of10% Which is equivalent annual cost of each investment?

Which one do you choose?

Year

Machine

0 1 2 3

F 10,000 1,100 1,331

G 12,000 1,100 1,331 1,331


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* Machine F:

PV of costs = 10,000 +1,100

(1+0.1)+

1,331

(1+0.1)2= 12,100

Annuity factor =1

0.1-

1

0.1(1+0.1)2= 1.7355

-> EACF =12,100

1.7355= 6,972

SOLUTION


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* Machine G:

PV of costs = 12,000 +1,100

(1+0.1)+

1,331(1+0.1)2

+

1,331

(1+0.1)3= 15,100

Annuity factor =

1

0.1 -

1

0.1(1+0.1)3 = 2.4869

-> EACG=15,1002.4869

= 6,072

SOLUTION


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EACG Machine G is the better buy.


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