Session 1 - NPV & IRR Conflict
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Lending or Borrowing Project C K 10% C0 1000 ($0.75) C1 -3600 2% -5.50 C2 4320 5% -2.92 C3 -1728 7.50% -1.57 10% -0.75 NPV (K=10%) ($0.75) 12.50% -0.30 IRR Err:523 15% -0.08 17.50% -0.01 20% 0.00 25% 0.06 30% 0.46 40% 2.92 50% 8.00 60% 15.62 70% 25.44 80% 37.04 0% 10% 20% -10.00 0.00 10.00 20.00 30.00 40.00 N P V
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Transcript of Session 1 - NPV & IRR Conflict
7/21/2019 Session 1 - NPV & IRR Conflict
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Lending or Borrowing
Project C
K 10%
C0 1000 ($0.75)
C1 -3600 2% -5.50C2 4320 5% -2.92
C3 -1728 7.50% -1.57
10% -0.75
NPV (K=10%) ($0.75) 12.50% -0.30
IRR Err:523 15% -0.08
17.50% -0.01
20% 0.00
25% 0.06
30% 0.46
40% 2.9250% 8.00
60% 15.62
70% 25.44
80% 37.04
0% 10% 20%-10.00
0.00
10.00
20.00
30.00
40.00
N P V
7/21/2019 Session 1 - NPV & IRR Conflict
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30% 40% 50% 60% 70% 80% 90%
Discount rate (%)
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Mul!"l# R# &' R#ur
P#r!& 0 1 2 3 4 5
Pr#-* C+ -1000 300 300 300 300 300
,* /# 500 -150 -150 -150 -150
N# C+ -1000 800 150 150 150 150
K 10%NPV 74.9
IRR Err:523
NPV #!# !''#r# r# &' !&u
74.9
-52% -878
-50% 0-25% 952
-10% 480
0% 250
10% 7515% 3
20% -60
25% -116
30% -166
40% -250
50% -319-60% -40%
N P V
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6
-150
-150
-20% 0% 20% 40% 60%
-1000
-500
0
500
1000
1500
Rate of discount (%)
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Mutually Eclusi!e Projects
Project C" C# C$ C C& C' etc
*""" +""" '""" &""" " "
, *""" #-"" #-"" #-"" #-"" #-"" . . .
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Project Project ,
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" &$"" $"" #'-""
5% 10% 15% 20% 25
-10000
-5000
0
5000
10000
15000
20000
Rate of
N P V
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#"%
/RR (%) NPV at #"%
% 01'*$
$"% *"""
$"% +"""
/RR NPV
'&"2.*+
30% 35% 40% 45% 50% 55%
Discount (%)
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K= 10%
Pr&# C0 C1 C2 C3 NPV IRR
-10000 2000 4000 12000 4140 26.5%
-10000 10000 3000 3000 3824 37.6%
4140 38245% 5899 4836
10% 4140 3824
13% 3366 3366
15% 2654 2937
25% 304 1456
30% -633 83335% -1446 273
40% -2157 -233
50% -3333 -1111
60% -4258 -1846
- 0 -8000 1000 9000 $286.87 13.97%
NPV u"!& &u r#-!## r# = K
+NV- 5510+NV- 5090
!''#r## 420
NPV 316
IRR u"!& &u r#-!## r# = IRR
+NV- 0.0E00
+NV- 0.0E00
0% 10% 20% 30% 40
-6000
-4000
-2000
0
2000
4000
6000
8000
Rate of Discoun
N P V
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50% 60% 70%
t (%)
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" #
3 ".#'
Project C
PV/4 ".-+*+
PV/45 ".#'1+ .2-&'
Net cas6 flow (0&"1""") #"""
NPV at #'% 0'12.+$
/RR #*.2%
Benefit cost ratio #.#
P/ ".#
(&"1"""."") "
Modified /RR #2.&&%Project 4
Net cas6 flow (0$"1""") 2"""
NPV at #'% 01-"2."$
/RR $'.$"%
Benefit cost ratio #.#*
P/ ".#*
$""""."" "
Modified /RR $#.--%
5B (0$"1""") 0+1"""
NPV 0#1'++.+"
/RR #+.**%
Modified /RR
Re7lace8ent C6ain (Co88on Life) 577roac6
Project 4
Net Cas6 4low (0$"1""") 2"""
Net Cas6 4low (0$"1""") 021"""
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NPV at #'% 0+1#".$"
/RR $'.$"%
E9ui!alent 5nnual 5nnuity 577roac6
NPV life
Projcet C 0'12.+$ + years
Project 4 01-"2."$ years
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$ & '
".2'+# ".+'2' ".'2#- ".&*2$
-""" #&""" #$""" ##"""
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#""" #$"""
" +$"2.'
(0'1""") 0$1""" 0#$1""" 0##1"""
#""" #$"""
(0$"1""") 2""" #"""
0#1""" (0-1""") 021""" 0#1"""
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PV/45 ".#'1 t 5NPV /nfinite 6ori:on NPV
.2-&' 0#1&#*.* 0*1&++
$.$-$ 0#1++2.& 0##1##+
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+
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Valuation of eico ;toc<
Low End of Range #**+ #**2 #**-
+&r## !!# $1.16 $1.25 $1.34
+&r## & "r!#
Cas6 4lows 0#.#+ 0#.$' 0#.&
/ntrinsic !alue of ;toc< (< = ##%) 0'-.$
/ntrinsic !alue of ;toc< (< = +.-+%) 02"."*
,ig6 End of Range #**+ #**2 #**-
+&r## !!# $1.16 $1.34 $1.55
+&r## & "r!#
Cas6 4lows 0#.#+ 0#.& 0#.''
/ntrinsic !alue of ;toc< (< = ##%) 02*.-'/ntrinsic !alue of ;toc< (< = +.-+%) 0*+.#"
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#*** $"""
$1.44 $1.55
$90.00
0#.&& 0*#.''
#*** $"""
$1.79 $2.07
$125.00
0#.2* 0#$2."2
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!/-,#"#rur# E*r!& &' ;r# <!r&!u
#r 0 1 2 3 4 5
N# I&# 30 30 30 30 30
#"r#!!& 80 80 80 80 80C +l&> -400 110 110 110 110 110
NPV 27.86
IRR 11.65%
?&>-,#"#rur# E*r!& &' ;r# <!r&!u
#r 0 1 2 3 4 5 6 7
N# I&# 28 28 28 28 28 28 28
#"r#!!& 57 57 57 57 57 57 57C +l&> -400 85 85 85 85 85 85 85
NPV 27.80
IRR 11.04%
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