Retirement/Replacement Problems

March 15, 2004

Why consider replacing a physical asset?

• P hysical impairment

• E conomic obsolescence

Determining optimum economic lifetime under steady-state conditions

R

N

M n

I o

I o = $1 0 ,000

M n = 20 0 0 + (n - 1) 1 000

R = 82 6 0

M A RR = 2 0 %

N	0	1	2	3	4	5	6	7	8
I N	64 0 0	32 0 0	16 0 0	80 0	4 0 0	20 0	1 0 0	50	25

(I g nor e effe ct of ta xe s . )

Optimum economic life calculation (contd.)

T w o alter n a t i v e de c i s i on c r ite r ia for choo s i ng opt ima l r e t i r e ment a ge:

( 1 ) M i ni m i z e level i z ed a nnua l c o s t, L A C

LA C = I 0 ( A / P ,20 % , N) Š I N ( A /F , 20 % , N) + 20 00 + 10 0 0 ( A /G,2 0 %, N )

( 2 ) M i ni m i z e pr e s ent wor th of n et r e ceipt s , P W

PW = - I o + I N ( P /F , 20 % , N) + R ( P / A ,2 0 %, N ) Š 2 0 0 0 ( P /A,20 % , N) Š 1 000 ( P/G,

N LA C P W (ne t re ceipt s )

1	1 0 8 00	- 2 118
2	8 2 7 3	- 1 8
3	7 40 5	1 79 5
4	7 06 2	3 10 1
5	69 5 8	38 9 8
6	6 97 6	4 27 3
7	7 0 6 0	43 2 6
8	7 18 1	4 14 3

Que s t i o n: Whi c h o ne of the t w o c r i ter ia g i v e s the c o rr e c t re s u l t ?

Retirement of asset in a changing environment

E x amp le :

Ņ De f ende r Ó Ņ Ch a l l e nge r Ó

B ough t 3 yr s a go fo r $17 0 0 P u r c ha se pr i c e = $2000 E x pe cted l i f e at t h at t i me = 10 yr s E c ono m i c l i f e time = 10 y ear s N S V= 0 N SV = $ 6 0 0

Le v e l i z e d ope r a ting c o s t fo r re m a ining 7 yea r s = $28 1 / yr

M a r k et val u e tod a y = $100 0

A nnua l o per a t ing co st = $ 100. y r

A s s ume:

Weight e d a v er age a fter t a x c o st o f c a p i tal = 1 0 % M a rg ina l t a x rat e = 50 %

Que s t i o n : S h o u l d w e re p l a c e th e defe n der w i th the ch a l l e nger ?

Retirement of asset in changing environment (contd.)

• T wo common mistakes

– # 1: Comparing projects over different time horizons

– # 2: Allowing ‘sunk costs’ to in fluence the investment decision

Asset retirement decision: It is helpful to adopt the perspective of an ‘outsider’

The outsider’s choices:

Choice #1 -- Buy the defender for $1000

S uppo s e the d efend e r tod a y i s exp e cted t o ha ve t h e fo l l ow i n g econo m i c cha r acte r i s t i c s over t he ne x t s e ver a l year s:

Y ear s t o re t i r e m e nt	S a l v ag e V a lu e (I N )	Ope r a tin g C o s t ( l evel i z ed)
1	6 0 0	22 0
2	5 0 j 0	2 3 0
3	4 0 0	24 0
4	3 0 0	25 0
5	2 0 0	26 0
6	1 0 0	27 0
7	0	28 0

F i nd the l i fe time of the d e fende r fo r w h i c h the level i z e d annu a l cost i s m i ni m i z e d

I N

The outsider’s choices:

Choice #1 -- Buy the defender for $1000 (contd.)

F i n d the l i f e t i me of the d e fende r fo r w h i c h the l e v e l i z e d ann u a l c o s t i s m i n i m i z e d

I N

1000

C o n v e r t to m o d i f i ed c a s h f l o w d i a gra m

1000

 D j I N

M j (1 -  )

LAC

de f e nder

  1000 ( A / P , x , N )  I N

( A / F , x , N )   ( 100 0  I N )  M

N L

(1   )

N	L A C de f e n c d e r
3	- 3 0 1
4	- 2 8 8
5	-2 8 1
6	- 2 8 7

The outsider’s choices:

Choice #2 -- Buy the challenger for $2000

Mo di fi ed cas h fl ow di agr am:

 D j

600

LA C

- 2000

  2000 ( A / P ,10 % , 1 0 )  600 ( A / F ,1 0 % , 1 0 )  (1   ) 100     200 0  600  

c h al l eng e r

= -$ 2 6 8

 10 

T h us w e m i ght con c l u d e tha t the cha l l e nge r i s the p r efe r red c h oi c e .

B U T: T h i s w o u l d n ot be c o rr e c t be cau s e we ha v e diffe r en t t i m e ho r i z o n s in t h e t w o cas e s .

The outsider’s choice (contd.)

• A pproaches to achieving consistency in time horizons:

– S ell the challenger at 5 years

– M odify the defender scenario by replacing the defender after 5 years with another challenger and selling the latter off after another 5 years (i.e. at the end of year 10)

– A ssume that t h e defender could be replaced by another 5 year replica of itself