1
Finance School of Management
Chapter 6,Capital Budgeting,
The Basics
Objective
Explain Capital Budgeting and Cost of
Capital,Apply NPV Rule,and
Develop Criteria of Evaluating
Project
2
Finance School of Management
Capital Budgeting
u Any capital budgeting process consists of three
elements,
– coming up with proposals for investment projects
– evaluating them
– deciding which ones to accept and which to
reject
3
Finance School of Management
The Nature of Project Analysis
– Starting point,an idea for increasing
shareholder wealth
– Procedures of project analysis
– Forecasting cash flows,decisions and
events
– Flexibility of decisions in the project’s
life
4
Finance School of Management
Objectives
u Investment projects fall into roughly three
categories,
– Whether to enter a new line of business
– Whether to invest in equipment to reduce costs
– Whether to replace an existing plant
5
Finance School of Management
NPV Rule Revisited
u Invest if the proposed project’s NPV is positive
u Discount rate
u Opportunity cost,the rate of return on comparable
investment opportunities
u Cost of capital
u NPV,the fair market value in competitive and
efficient market
6
Finance School of Management
N P V o f a P r o j e c t
D i s c o u t 10%
Y e a r F l o w PV C u m _ P V
0 - 1 0 0 0 - 1 0 0 0 - 1 0 0 0
1 450 409 - 5 9 1
2 350 289 - 3 0 2
3 250 188 - 1 1 4
4 150 102 - 1 1
5 50 31 20
N P V 20
DCF Payback
7
Finance School of Management
N P V o f a P r o j e c t
D i s c o u t 15%
Y e a r F l o w PV C u m _ P V
0 - 1 0 0 0 - 1 0 0 0 - 1 0 0 0
1 450 391 - 6 0 9
2 350 265 - 3 4 4
3 250 164 - 1 8 0
4 150 86 - 9 4
5 50 25 - 6 9
N P V - 6 9
8
Finance School of Management
N P V o f a P r o j e c t
D i s c o u t 1 1, 0 4 %
Y e a r F l o w PV C u m _ P V
0 - 1 0 0 0 - 1 0 0 0 - 1 0 0 0
1 450 405 - 5 9 5
2 350 284 - 3 1 1
3 250 183 - 1 2 8
4 150 99 - 3 0
5 50 30 0
N P V 0
Internal Rate of Return
9
Finance School of Management
N P V a s a F u n c t i o n o f D i s c o u n t R a t e
- 2 0 0
- 1 5 0
- 1 0 0
- 5 0
0
50
100
150
200
250
0% 5% 10% 15% 20%
D i s c o u n t R a t e
N
P
V
10
Finance School of Management
Example,PC1000 of Compusell Corp,
S al e s
4,000 u n i t s at a p r i c e of $5,000 $20,000,000 p e r ye ar
F i xe d C os t s,
L e as e p aym e n t s $1,500,000 p e r ye ar
P r op e r t y t axe s 200,000
A d m i n i s t r at i on 600,000
A d ve r t i s i n g 500,000
O t h e r 300,000
T ot al F i xe d C os t s $3,100,000
V ar i ab l e C os t s,
D i r e c t l ab or $2,000 p e r u n i t
M at e r i al s 1,000
S e l l i n g e xp e n s e s 500
O t h e r 250
V ar i ab l e c os t p e r u n i t $3,750 p e r u n i t
T ot al V ar i ab l e C os t s f or 4,000 u n i t s $15,000,000 p e r ye ar
F or e c as t of I n i t i al C ap i t al O u t l ay f or P C 100 0
P u r c h as e of E q u i p m e n t $2,800,000
Wor k i n g C ap i t al $2,200,000
T ot al C ap i t al O u t l ay $5,000,000
D e p r e c i at i on $40 0,000
C or p or at e I n c om e T axe s @40%
11
Finance School of Management
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = 1236
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0
T a x e s 600 600 600 600 600 600 600
N e t P r of i t 900 900 900 900 900 900 900
O pe r a t i ng C F 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 3,5 0 0
P V ( N C F,1 5 % ) - 5 0 0 0 1130 983 855 743 646 562 1316
12
Finance School of Management
PC1000,Cash Flows
1.3 1.3 1.3 1.3 1.3 1.3 1.3
-5
1.3 1.3
2.2
? A seven-year coupon bond with an annual coupon
payment of $1.3 million,a face value of $2.2 million,
and a price of $5 million,
13
Finance School of Management
N P V v, D i s c o u n t R a t e
$ 3,0 0 0
$ 2,0 0 0
$ 1,0 0 0
$0
$ 1,0 0 0
$ 2,0 0 0
$ 3,0 0 0
$ 4,0 0 0
$ 5,0 0 0
$ 6,0 0 0
$ 7,0 0 0
0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
R a t e
N
P
V
$
0
0
0
14
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 2 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = - 4 2 9
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0
T a x e s 600 600 600 600 600 600 600
N e t P r of i t 900 900 900 900 900 900 900
O pe r a t i ng C F 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 3,5 0 0
P V ( N C F) - 5 0 0 0 1040 832 666 532 426 341 734
Was 15%
15
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 3 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = 1860
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0
T a x e s 450 450 450 450 450 450 450
N e t P r of i t 1,0 5 0 1,0 5 0 1,0 5 0 1,0 5 0 1,0 5 0 1,0 5 0 1,0 5 0
O pe r a t i ng C F 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 3,6 5 0
P V ( N C F) - 5 0 0 0 1261 1096 953 829 721 627 1372
Was 40%
16
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 2, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h - 3, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 8, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = - 7 9 7
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 1 9,7 8 8 1 9,5 7 8 1 9,3 7 1 1 9,1 6 5 1 8,9 6 2 1 8,7 6 1
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,3 4 8 3,6 1 6 3,9 0 5 4,2 1 8 4,5 5 5 4,9 1 9
V a r i a b l e c o s t s 1 5,0 0 0 1 4,8 4 1 1 4,6 8 4 1 4,5 2 8 1 4,3 7 4 1 4,2 2 2 1 4,0 7 1
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,1 9 9 879 538 174 - 2 1 4 - 6 2 9
T a x e s 600 480 351 215 70 - 8 6 - 2 5 2
N e t P r of i t 900 719 527 323 104 - 1 2 9 - 3 7 7
O pe r a t i ng C F 1,3 0 0 1,1 1 9 927 723 504 271 23
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,3 0 0 1,1 1 9 927 723 504 271 2,2 2 3
P V ( N C F) - 5 0 0 0 1130 846 610 413 251 117 836
17
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 5, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = 2885
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 1,0 0 0 2 2,0 5 0 2 3,1 5 3 2 4,3 1 0 2 5,5 2 6 2 6,8 0 2
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,7 5 0 1 6,5 3 8 1 7,3 6 4 1 8,2 3 3 1 9,1 4 4 2 0,1 0 1
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,7 5 0 2,0 1 3 2,2 8 8 2,5 7 8 2,8 8 1 3,2 0 0
T a x e s 600 700 805 915 1,0 3 1 1,1 5 3 1,2 8 0
N e t P r of i t 900 1,0 5 0 1,2 0 8 1,3 7 3 1,5 4 7 1,7 2 9 1,9 2 0
O pe r a t i ng C F 1,3 0 0 1,4 5 0 1,6 0 8 1,7 7 3 1,9 4 7 2,1 2 9 2,3 2 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,3 0 0 1,4 5 0 1,6 0 8 1,7 7 3 1,9 4 7 2,1 2 9 4,5 2 0
P V ( N C F) - 5 0 0 0 1130 1096 1057 1014 968 920 1699
Was 0%
18
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 8 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = - 3 7 5 7
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t - 5 0 0 - 5 0 0 - 5 0 0 - 5 0 0 - 5 0 0 - 5 0 0 - 5 0 0
T a x e s - 2 0 0 - 2 0 0 - 2 0 0 - 2 0 0 - 2 0 0 - 2 0 0 - 2 0 0
N e t P r of i t - 3 0 0 - 3 0 0 - 3 0 0 - 3 0 0 - 3 0 0 - 3 0 0 - 3 0 0
O pe r a t i ng C F 100 100 100 100 100 100 100
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 100 100 100 100 100 100 2,3 0 0
P V ( N C F) - 5 0 0 0 87 76 66 57 50 43 865
Was 75%
19
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,5 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = 237
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,5 0 0 3,5 0 0 3,5 0 0 3,5 0 0 3,5 0 0 3,5 0 0 3,5 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,1 0 0 1,1 0 0 1,1 0 0 1,1 0 0 1,1 0 0 1,1 0 0 1,1 0 0
T a x e s 440 440 440 440 440 440 440
N e t P r of i t 660 660 660 660 660 660 660
O pe r a t i ng C F 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 3,2 6 0
P V ( N C F) - 5 0 0 0 922 802 697 606 527 458 1226
Was $3,100,000
20
Finance School of Management
Table 6.4 Project Sensitivity to Sales Volume
S a l e s U n i t s N e t C F O p e r a t i o n s N P V P r o j e c t
2000 200000 5005022
3000 550000 1884708
3604 1003009 0
4000 1300000 1235607
5000 2050000 4355922
6000 2800000 7476237
? 3640 is the NPV break-even point
21
Finance School of Management
S e n s i t i v i t y o f P r o j e c t t o S a l e V o l u m e
$ 5 0 0,0 0 0
$0
$ 5 0 0,0 0 0
$ 1,0 0 0,0 0 0
$ 1,5 0 0,0 0 0
$ 2,0 0 0,0 0 0
$ 2,5 0 0,0 0 0
$ 3,0 0 0,0 0 0
$ 2,0 0 0 $ 2,5 0 0 $ 3,0 0 0 $ 3,5 0 0 $ 4,0 0 0 $ 4,5 0 0 $ 5,0 0 0 $ 5,5 0 0 $ 6,0 0 0
S a l e s ( U n i t s )
N
e
t
C
F
f
r
o
m
O
p
e
r
a
t
i
o
n
s
22
Finance School of Management
N P V P r o j e c t
$ 6,0 0 0,0 0 0
$ 4,0 0 0,0 0 0
$ 2,0 0 0,0 0 0
$0
$ 2,0 0 0,0 0 0
$ 4,0 0 0,0 0 0
$ 6,0 0 0,0 0 0
$ 8,0 0 0,0 0 0
$ 1 0,0 0 0,0 0 0
2000 2500 3000 3500 4000 4500 5000 5500 6000
S a l e s ( U n i t s )
N
P
V
23
Finance School of Management
Break-even point
u Cash flow=Net Profit +Depreciation
=0.6(1,250Q-3,500,000)+400,000
=1,003,009
Q=3,604 units per year
n i PV FV PM T r e s u l t
7 15% - 5,0 0 0,0 0 0 2,2 0 0,0 0 0? $ 1,0 0 3,0 0 9, 0 2
24
Finance School of Management
Cost of Capital
u Risk-adjusted discount rate (k)
u The risk of a particular project may be different from
the risk of the firm’s existing assets
u The risk that is relevant in computing a project’s cost
of capital is the risk of the project’s cash flows and not
the risk of the financing instruments (e.g.,stocks,
bonds) the firm issues to finance the project
u The cost of capital should reflect only the market-
related risk of the project (its beta)
25
Finance School of Management
Illustration 1
u 25-year U.S,Treasury bonds paying $100 per year are
selling in the market at $1,000
u A firm has the opportunity to buy $1 million worth of
these bonds for $950 each
u The firm’s overall (average) cost of capital is 16%
u If discounted at 16%,the NPV of the opportunity is -
$340,291
u However,no one will forgo the opportunity
u The correct cost of capital is 10%
26
Finance School of Management
Illustration 2
u An all-equity financed firm with tree divisions,
– An electronics division,30% of the firm’s market value,cost of
capital 22%
– A chemical division,40% of the firm’s market value,cost of capital
17%
– A natural gas transmission division,30% of the firm’s market value,
cost of capital 14%
– The cost of capital for the firm is,3*22%+.4*17%+.3*14%=17.6%
u If 17.6% is adopted as discount rate for all projects,then it is
likely
– to accept projects in the electronics division with negative NPV
– to pass up profitable natural gas transmission
27
Finance School of Management
Illustration 3
u An all-equity financed steel company considering the acquisition of an
integrated oil company that is 60% crude oil reserves and 40% refining
– The market capitalization rate on crude oil investments is 18.6%
and on refining projects is 17.6%
– The market capitalization rate on the oil company shares is 18.2%
– The market capitalization rate for steel projects is 15.3%
u The market price of the oil company’s shares is,fair” ($100,expected
return 18.2%)
u An investment banker reports that all the shares could be acquired for a
tender offer bid of $110 per share
– With 15.3%,the NPV of the acquisition is –110+18.2/.153=$9
– With 18.2%,the NPV of the acquisition is –110+18.2/.182=-$10
28
Finance School of Management
Illustration 4
u Compusell Corporation is planning to finance the
$5 million outlay required to undertake the
PC1000 project by issuing bonds
u Compusell has a high credit rating because it has
almost no debt outstanding and therefore can
issue $5 million worth of bonds at an interest rate
of 6% per year
u It would be a mistake to use 6% as the cost of
capital in computing the NPV of the PC1000
project
29
Finance School of Management
Average Cost of Capital,
Example with 3-Securities
u Let
– ke be the return on equity
– kd be the return on debt
– kp be the return on preferred
– Ve be the market value of issued equity
– Vd be the Market value of issued bonds
– Vp be the market value of issued preferred
F t be the tax rate
30
Finance School of Management Average Cost of Capital,Example
with 3-Securities
u The average cost of capital is also the cost of
capital for each of the firms business divisions
weighted according to their market value
( 1 )e e p p d dk k V k V k V t? ? ? ?
31
Finance School of Management
Example,Cost Reducing Project
W i t h ou t W i t h D i f f e r e n c e D u e t o
I n v e s t m e n t I n v e s t m e n t I n v e s t m e n t
1 2 3
R e ve n u e $5,00 0,00 0 $5,00 0,00 0 0
L ab or c os t s 1,00 0,00 0 30 0,00 0 ( $7 00,00 0)
O t h e r c as h e xp e n s e s 2,00 0,00 0 2,00 0,00 0 0
D e p r e c i at i on 1,00 0,00 0 1,40 0,00 0 $4 00,00 0
P r e t ax p r of i t 1,00 0,00 0 1,30 0,00 0 $3 00,00 0
I n c om e t ax e s 33 3,33 3 43 3,33 3 $1 00,00 0
( @ 33
1
/ 3 %)
A f t e r - t ax p r of i t 66 6,66 7 86 6,66 7 $2 00,00 0
N e t c as h f l ow $1,66 6,66 7 $2,26 6,66 7 $6 00,00 0
( A f t e r - t ax p r of i t +
d e p r e c i at i on )
? A firm is considering an investment proposal to automate its
production process to save on labor costs
? Invest $2 million now in equipment (an expected life of 5 years) and
thereby save $700,000 per year in pretax labor costs
? The incremental
cash flows due to
the investment
? At the 10%
discount rate,the
NPV is $274,472
32
Finance School of Management
Project with different lives
u Suppose that there are two different types of equipment with
different economic lives in the previous example,The
longer-lived requires twice the initial outlay but lasts twice
as long,
u An easier approach is called annualized capital cost
n i PV FV P M T R e s u l t
5 10 -2,000,000 0? P M T = $ 5 2 7,5 9 5
n i PV FV P M T R e s u l t
10 10 -4,000,000 0? P M T = $ 6 5 0,9 8 2
Shorter-lived equipment
Long-lived
equipment
33
Finance School of Management
Ranking mutually exclusive projects
u Sometimes two or more projects are mutually
exclusive,
u Rule,This firm should choose the project with the
highest NPV at any cost of capital below 20%,
i n i t i a l o u l a y t e r m c a s h f l o w N PV ( i = 1 5 % ) I R R
o f f i c e b u i l d i n g 2 0 m i l, 1 2 4 m i l, 8 6 9,5 6 5 20%
p a r k i n g l o t 1 0,0 0 0 f o r e v e r 1 0,0 0 0 5 6,6 6 7 100%
34
Finance School of Management
Ranking mutually exclusive projects
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
0.01 0.05 0.1 0.15 0.2 0.25 0.3
Office Building
(mil.)
Parking Lot
(mil.)
35
Finance School of Management
Inflation and Capital Budgeting
u Rule,There are two correct ways of
computing NPV,
– Use the nominal cost of capital to discount
nominal cash flows,
– Use the real cost of capital to discount real cash
flows
– Never compare the IRR computed using real
cash flow estimates to a nominal cost of capital,
Finance School of Management
Chapter 6,Capital Budgeting,
The Basics
Objective
Explain Capital Budgeting and Cost of
Capital,Apply NPV Rule,and
Develop Criteria of Evaluating
Project
2
Finance School of Management
Capital Budgeting
u Any capital budgeting process consists of three
elements,
– coming up with proposals for investment projects
– evaluating them
– deciding which ones to accept and which to
reject
3
Finance School of Management
The Nature of Project Analysis
– Starting point,an idea for increasing
shareholder wealth
– Procedures of project analysis
– Forecasting cash flows,decisions and
events
– Flexibility of decisions in the project’s
life
4
Finance School of Management
Objectives
u Investment projects fall into roughly three
categories,
– Whether to enter a new line of business
– Whether to invest in equipment to reduce costs
– Whether to replace an existing plant
5
Finance School of Management
NPV Rule Revisited
u Invest if the proposed project’s NPV is positive
u Discount rate
u Opportunity cost,the rate of return on comparable
investment opportunities
u Cost of capital
u NPV,the fair market value in competitive and
efficient market
6
Finance School of Management
N P V o f a P r o j e c t
D i s c o u t 10%
Y e a r F l o w PV C u m _ P V
0 - 1 0 0 0 - 1 0 0 0 - 1 0 0 0
1 450 409 - 5 9 1
2 350 289 - 3 0 2
3 250 188 - 1 1 4
4 150 102 - 1 1
5 50 31 20
N P V 20
DCF Payback
7
Finance School of Management
N P V o f a P r o j e c t
D i s c o u t 15%
Y e a r F l o w PV C u m _ P V
0 - 1 0 0 0 - 1 0 0 0 - 1 0 0 0
1 450 391 - 6 0 9
2 350 265 - 3 4 4
3 250 164 - 1 8 0
4 150 86 - 9 4
5 50 25 - 6 9
N P V - 6 9
8
Finance School of Management
N P V o f a P r o j e c t
D i s c o u t 1 1, 0 4 %
Y e a r F l o w PV C u m _ P V
0 - 1 0 0 0 - 1 0 0 0 - 1 0 0 0
1 450 405 - 5 9 5
2 350 284 - 3 1 1
3 250 183 - 1 2 8
4 150 99 - 3 0
5 50 30 0
N P V 0
Internal Rate of Return
9
Finance School of Management
N P V a s a F u n c t i o n o f D i s c o u n t R a t e
- 2 0 0
- 1 5 0
- 1 0 0
- 5 0
0
50
100
150
200
250
0% 5% 10% 15% 20%
D i s c o u n t R a t e
N
P
V
10
Finance School of Management
Example,PC1000 of Compusell Corp,
S al e s
4,000 u n i t s at a p r i c e of $5,000 $20,000,000 p e r ye ar
F i xe d C os t s,
L e as e p aym e n t s $1,500,000 p e r ye ar
P r op e r t y t axe s 200,000
A d m i n i s t r at i on 600,000
A d ve r t i s i n g 500,000
O t h e r 300,000
T ot al F i xe d C os t s $3,100,000
V ar i ab l e C os t s,
D i r e c t l ab or $2,000 p e r u n i t
M at e r i al s 1,000
S e l l i n g e xp e n s e s 500
O t h e r 250
V ar i ab l e c os t p e r u n i t $3,750 p e r u n i t
T ot al V ar i ab l e C os t s f or 4,000 u n i t s $15,000,000 p e r ye ar
F or e c as t of I n i t i al C ap i t al O u t l ay f or P C 100 0
P u r c h as e of E q u i p m e n t $2,800,000
Wor k i n g C ap i t al $2,200,000
T ot al C ap i t al O u t l ay $5,000,000
D e p r e c i at i on $40 0,000
C or p or at e I n c om e T axe s @40%
11
Finance School of Management
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = 1236
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0
T a x e s 600 600 600 600 600 600 600
N e t P r of i t 900 900 900 900 900 900 900
O pe r a t i ng C F 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 3,5 0 0
P V ( N C F,1 5 % ) - 5 0 0 0 1130 983 855 743 646 562 1316
12
Finance School of Management
PC1000,Cash Flows
1.3 1.3 1.3 1.3 1.3 1.3 1.3
-5
1.3 1.3
2.2
? A seven-year coupon bond with an annual coupon
payment of $1.3 million,a face value of $2.2 million,
and a price of $5 million,
13
Finance School of Management
N P V v, D i s c o u n t R a t e
$ 3,0 0 0
$ 2,0 0 0
$ 1,0 0 0
$0
$ 1,0 0 0
$ 2,0 0 0
$ 3,0 0 0
$ 4,0 0 0
$ 5,0 0 0
$ 6,0 0 0
$ 7,0 0 0
0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
R a t e
N
P
V
$
0
0
0
14
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 2 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = - 4 2 9
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0
T a x e s 600 600 600 600 600 600 600
N e t P r of i t 900 900 900 900 900 900 900
O pe r a t i ng C F 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 1,3 0 0 3,5 0 0
P V ( N C F) - 5 0 0 0 1040 832 666 532 426 341 734
Was 15%
15
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 3 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = 1860
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0 1,5 0 0
T a x e s 450 450 450 450 450 450 450
N e t P r of i t 1,0 5 0 1,0 5 0 1,0 5 0 1,0 5 0 1,0 5 0 1,0 5 0 1,0 5 0
O pe r a t i ng C F 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 1,4 5 0 3,6 5 0
P V ( N C F) - 5 0 0 0 1261 1096 953 829 721 627 1372
Was 40%
16
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 2, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h - 3, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 8, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = - 7 9 7
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 1 9,7 8 8 1 9,5 7 8 1 9,3 7 1 1 9,1 6 5 1 8,9 6 2 1 8,7 6 1
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,3 4 8 3,6 1 6 3,9 0 5 4,2 1 8 4,5 5 5 4,9 1 9
V a r i a b l e c o s t s 1 5,0 0 0 1 4,8 4 1 1 4,6 8 4 1 4,5 2 8 1 4,3 7 4 1 4,2 2 2 1 4,0 7 1
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,1 9 9 879 538 174 - 2 1 4 - 6 2 9
T a x e s 600 480 351 215 70 - 8 6 - 2 5 2
N e t P r of i t 900 719 527 323 104 - 1 2 9 - 3 7 7
O pe r a t i ng C F 1,3 0 0 1,1 1 9 927 723 504 271 23
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,3 0 0 1,1 1 9 927 723 504 271 2,2 2 3
P V ( N C F) - 5 0 0 0 1130 846 610 413 251 117 836
17
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 5, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = 2885
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 1,0 0 0 2 2,0 5 0 2 3,1 5 3 2 4,3 1 0 2 5,5 2 6 2 6,8 0 2
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,7 5 0 1 6,5 3 8 1 7,3 6 4 1 8,2 3 3 1 9,1 4 4 2 0,1 0 1
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,5 0 0 1,7 5 0 2,0 1 3 2,2 8 8 2,5 7 8 2,8 8 1 3,2 0 0
T a x e s 600 700 805 915 1,0 3 1 1,1 5 3 1,2 8 0
N e t P r of i t 900 1,0 5 0 1,2 0 8 1,3 7 3 1,5 4 7 1,7 2 9 1,9 2 0
O pe r a t i ng C F 1,3 0 0 1,4 5 0 1,6 0 8 1,7 7 3 1,9 4 7 2,1 2 9 2,3 2 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,3 0 0 1,4 5 0 1,6 0 8 1,7 7 3 1,9 4 7 2,1 2 9 4,5 2 0
P V ( N C F) - 5 0 0 0 1130 1096 1057 1014 968 920 1699
Was 0%
18
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,1 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 8 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = - 3 7 5 7
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0 3,1 0 0
V a r i a b l e c o s t s 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0 1 7,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t - 5 0 0 - 5 0 0 - 5 0 0 - 5 0 0 - 5 0 0 - 5 0 0 - 5 0 0
T a x e s - 2 0 0 - 2 0 0 - 2 0 0 - 2 0 0 - 2 0 0 - 2 0 0 - 2 0 0
N e t P r of i t - 3 0 0 - 3 0 0 - 3 0 0 - 3 0 0 - 3 0 0 - 3 0 0 - 3 0 0
O pe r a t i ng C F 100 100 100 100 100 100 100
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 100 100 100 100 100 100 2,3 0 0
P V ( N C F) - 5 0 0 0 87 76 66 57 50 43 865
Was 75%
19
Finance School of Management
A s s u m p t i o n s ( T a b l e i n $ ' 0 0 0 )
C o s t o f c a p i t a l 1 5, 0 0 %
T a x r a t e 4 0, 0 0 %
U n i t s a l e s i n y e a r 1 $ 4,0 0 0
S a l e s g r o w t h r a t e 0, 0 0 %
U n i t p r i c e $ 5,0 0 0
U n i t P r i c e G r o w t h 0, 0 0 %
Fi x e d S t a r t 3,5 0 0,0 0 0
Fi x e d G r o w t h 0, 0 0 %
V a r i a b l e p c e n t 7 5, 0 0 %
D e p r e c i a t i o n s c h e d u l e 4 0 0,0 0 0 N P V = 237
S t a r t w o r k i n g c a p t 2,2 0 0,0 0 0
I n v e s t m e n t s c h e d u l e 2,8 0 0,0 0 0
C a p i t a l m o v e m e n t s s c h 0
D i v i d e n d 1,0 0 0,0 0 0
W o r k i n g C a p S c h 2,2 0 0,0 0 0
Y e a r 0 1 2 3 4 5 6 7
C F Fo r e c a s t
S a l e s r e v e n u e 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0 2 0,0 0 0
E x pe ns e s
Fi x e d C o s t s ( c a s h ) 3,5 0 0 3,5 0 0 3,5 0 0 3,5 0 0 3,5 0 0 3,5 0 0 3,5 0 0
V a r i a b l e c o s t s 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0 1 5,0 0 0
D e p r e c i a t i o n 400 400 400 400 400 400 400
O pe r a t i ng P r of i t 1,1 0 0 1,1 0 0 1,1 0 0 1,1 0 0 1,1 0 0 1,1 0 0 1,1 0 0
T a x e s 440 440 440 440 440 440 440
N e t P r of i t 660 660 660 660 660 660 660
O pe r a t i ng C F 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0
W o r k i n g c a p m o v e 2200 - 2,2 0 0
I n v e s t m e n t i n P & E 2,8 0 0 0 0 0 0 0 0
I nv e s t C F 5,0 0 0 0 0 0 0 0 0 - 2,2 0 0
N e t C F - 5,0 0 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 1,0 6 0 3,2 6 0
P V ( N C F) - 5 0 0 0 922 802 697 606 527 458 1226
Was $3,100,000
20
Finance School of Management
Table 6.4 Project Sensitivity to Sales Volume
S a l e s U n i t s N e t C F O p e r a t i o n s N P V P r o j e c t
2000 200000 5005022
3000 550000 1884708
3604 1003009 0
4000 1300000 1235607
5000 2050000 4355922
6000 2800000 7476237
? 3640 is the NPV break-even point
21
Finance School of Management
S e n s i t i v i t y o f P r o j e c t t o S a l e V o l u m e
$ 5 0 0,0 0 0
$0
$ 5 0 0,0 0 0
$ 1,0 0 0,0 0 0
$ 1,5 0 0,0 0 0
$ 2,0 0 0,0 0 0
$ 2,5 0 0,0 0 0
$ 3,0 0 0,0 0 0
$ 2,0 0 0 $ 2,5 0 0 $ 3,0 0 0 $ 3,5 0 0 $ 4,0 0 0 $ 4,5 0 0 $ 5,0 0 0 $ 5,5 0 0 $ 6,0 0 0
S a l e s ( U n i t s )
N
e
t
C
F
f
r
o
m
O
p
e
r
a
t
i
o
n
s
22
Finance School of Management
N P V P r o j e c t
$ 6,0 0 0,0 0 0
$ 4,0 0 0,0 0 0
$ 2,0 0 0,0 0 0
$0
$ 2,0 0 0,0 0 0
$ 4,0 0 0,0 0 0
$ 6,0 0 0,0 0 0
$ 8,0 0 0,0 0 0
$ 1 0,0 0 0,0 0 0
2000 2500 3000 3500 4000 4500 5000 5500 6000
S a l e s ( U n i t s )
N
P
V
23
Finance School of Management
Break-even point
u Cash flow=Net Profit +Depreciation
=0.6(1,250Q-3,500,000)+400,000
=1,003,009
Q=3,604 units per year
n i PV FV PM T r e s u l t
7 15% - 5,0 0 0,0 0 0 2,2 0 0,0 0 0? $ 1,0 0 3,0 0 9, 0 2
24
Finance School of Management
Cost of Capital
u Risk-adjusted discount rate (k)
u The risk of a particular project may be different from
the risk of the firm’s existing assets
u The risk that is relevant in computing a project’s cost
of capital is the risk of the project’s cash flows and not
the risk of the financing instruments (e.g.,stocks,
bonds) the firm issues to finance the project
u The cost of capital should reflect only the market-
related risk of the project (its beta)
25
Finance School of Management
Illustration 1
u 25-year U.S,Treasury bonds paying $100 per year are
selling in the market at $1,000
u A firm has the opportunity to buy $1 million worth of
these bonds for $950 each
u The firm’s overall (average) cost of capital is 16%
u If discounted at 16%,the NPV of the opportunity is -
$340,291
u However,no one will forgo the opportunity
u The correct cost of capital is 10%
26
Finance School of Management
Illustration 2
u An all-equity financed firm with tree divisions,
– An electronics division,30% of the firm’s market value,cost of
capital 22%
– A chemical division,40% of the firm’s market value,cost of capital
17%
– A natural gas transmission division,30% of the firm’s market value,
cost of capital 14%
– The cost of capital for the firm is,3*22%+.4*17%+.3*14%=17.6%
u If 17.6% is adopted as discount rate for all projects,then it is
likely
– to accept projects in the electronics division with negative NPV
– to pass up profitable natural gas transmission
27
Finance School of Management
Illustration 3
u An all-equity financed steel company considering the acquisition of an
integrated oil company that is 60% crude oil reserves and 40% refining
– The market capitalization rate on crude oil investments is 18.6%
and on refining projects is 17.6%
– The market capitalization rate on the oil company shares is 18.2%
– The market capitalization rate for steel projects is 15.3%
u The market price of the oil company’s shares is,fair” ($100,expected
return 18.2%)
u An investment banker reports that all the shares could be acquired for a
tender offer bid of $110 per share
– With 15.3%,the NPV of the acquisition is –110+18.2/.153=$9
– With 18.2%,the NPV of the acquisition is –110+18.2/.182=-$10
28
Finance School of Management
Illustration 4
u Compusell Corporation is planning to finance the
$5 million outlay required to undertake the
PC1000 project by issuing bonds
u Compusell has a high credit rating because it has
almost no debt outstanding and therefore can
issue $5 million worth of bonds at an interest rate
of 6% per year
u It would be a mistake to use 6% as the cost of
capital in computing the NPV of the PC1000
project
29
Finance School of Management
Average Cost of Capital,
Example with 3-Securities
u Let
– ke be the return on equity
– kd be the return on debt
– kp be the return on preferred
– Ve be the market value of issued equity
– Vd be the Market value of issued bonds
– Vp be the market value of issued preferred
F t be the tax rate
30
Finance School of Management Average Cost of Capital,Example
with 3-Securities
u The average cost of capital is also the cost of
capital for each of the firms business divisions
weighted according to their market value
( 1 )e e p p d dk k V k V k V t? ? ? ?
31
Finance School of Management
Example,Cost Reducing Project
W i t h ou t W i t h D i f f e r e n c e D u e t o
I n v e s t m e n t I n v e s t m e n t I n v e s t m e n t
1 2 3
R e ve n u e $5,00 0,00 0 $5,00 0,00 0 0
L ab or c os t s 1,00 0,00 0 30 0,00 0 ( $7 00,00 0)
O t h e r c as h e xp e n s e s 2,00 0,00 0 2,00 0,00 0 0
D e p r e c i at i on 1,00 0,00 0 1,40 0,00 0 $4 00,00 0
P r e t ax p r of i t 1,00 0,00 0 1,30 0,00 0 $3 00,00 0
I n c om e t ax e s 33 3,33 3 43 3,33 3 $1 00,00 0
( @ 33
1
/ 3 %)
A f t e r - t ax p r of i t 66 6,66 7 86 6,66 7 $2 00,00 0
N e t c as h f l ow $1,66 6,66 7 $2,26 6,66 7 $6 00,00 0
( A f t e r - t ax p r of i t +
d e p r e c i at i on )
? A firm is considering an investment proposal to automate its
production process to save on labor costs
? Invest $2 million now in equipment (an expected life of 5 years) and
thereby save $700,000 per year in pretax labor costs
? The incremental
cash flows due to
the investment
? At the 10%
discount rate,the
NPV is $274,472
32
Finance School of Management
Project with different lives
u Suppose that there are two different types of equipment with
different economic lives in the previous example,The
longer-lived requires twice the initial outlay but lasts twice
as long,
u An easier approach is called annualized capital cost
n i PV FV P M T R e s u l t
5 10 -2,000,000 0? P M T = $ 5 2 7,5 9 5
n i PV FV P M T R e s u l t
10 10 -4,000,000 0? P M T = $ 6 5 0,9 8 2
Shorter-lived equipment
Long-lived
equipment
33
Finance School of Management
Ranking mutually exclusive projects
u Sometimes two or more projects are mutually
exclusive,
u Rule,This firm should choose the project with the
highest NPV at any cost of capital below 20%,
i n i t i a l o u l a y t e r m c a s h f l o w N PV ( i = 1 5 % ) I R R
o f f i c e b u i l d i n g 2 0 m i l, 1 2 4 m i l, 8 6 9,5 6 5 20%
p a r k i n g l o t 1 0,0 0 0 f o r e v e r 1 0,0 0 0 5 6,6 6 7 100%
34
Finance School of Management
Ranking mutually exclusive projects
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
0.01 0.05 0.1 0.15 0.2 0.25 0.3
Office Building
(mil.)
Parking Lot
(mil.)
35
Finance School of Management
Inflation and Capital Budgeting
u Rule,There are two correct ways of
computing NPV,
– Use the nominal cost of capital to discount
nominal cash flows,
– Use the real cost of capital to discount real cash
flows
– Never compare the IRR computed using real
cash flow estimates to a nominal cost of capital,
