Download - IRR and NPV
Internal Rate of Return (IRR) and Net Present Value (NPV)
Net present value (NPV): the sum of the present values of allcash inflows minus the sum of the present values of allcash outflows.
The internal rate of return (IRR): (1) the discount rate thatequates the sum of the present values of all cash inflowsto the sum of the present values of all cash outflows;(2) the discount rate that sets the net present valueequal to zero.
The internal rate of return measures the investment yield.
IRR and NPV
E x a m p l e : Y i e l d o n a s i n g l e r e c e i p t .
A n i n v e s t o r c a n p u r c h a s e a v a c a n t l o t f o r $ 2 8 , 3 7 1 a n d e x p e c t st o s e l l i t f o r $ 5 0 , 0 0 0 i n 5 y e a r s . W h a t i s t h e e x p e c t e d I R R f o rt h i s i n v e s t m e n t ?
d = 1 2 %
P V F Vd n
1
1( )
$ 2 8 , $ 5 0 ,( )
3 7 1 0 0 01
1 5
d
IRR and NPVHP 10B Keystrokes
50000
CLEAR ALL
P/YR
+ / - PV28371
1
FV
5 N
I/YR
Clears registers
One payment per year
PV = -$ 28,371
FV = $ 50,000
FV in 5 years
Solve for IRR
IRR and NPVE x a m p l e : N P V f o r a s i n g l e r e c e i p t .
A n i n v e s t o r c a n p u r c h a s e a v a c a n t l o t f o r $ 2 8 , 3 7 1 a n d e x p e c t s t o s e l l i t f o r$ 5 0 , 0 0 0 i n 5 y e a r s . W h a t i s t h e e x p e c t e d N P V f o r t h i s i n v e s t m e n t i f t h ei n v e s t o r d i s c o u n t s f u t u r e c a s h f l o w s a t 1 5 % ?
N P V = - $ 2 8 , 3 7 1 + $ 2 4 , 8 5 8 . 8 4 = - $ 3 , 5 1 2 . 1 6
N P V P V F Vd n
1
1( )
N P V
$ 2 8 , $ 5 0 ,( . )
3 7 1 0 0 01
1 0 1 5 5
IRR and NPVHP 10B Keystrokes
CLEAR ALL
1 P/YR
50,000 FV
15 I/YR
5 N
PV +/-
- 28,371 =
Clears registers
One payment per year
$50,000 future value
Discount rate = 15%
FV in 5 years
Compute present value
Subtract $28,371
IRR and NPV
Example: Yield on an Ordinary Annuity
An investor has the opportunity to invest in real estate costing $28,371today. The investment will provide $445.66 at the end of each month for thenext 8 years. What is the (annual) IRR (compounded monthly) for thisinvestment?
PV PMTdk
d
dd
tt
nk
tt
1
1
371 445661
112
1209167%; 110%
1
1
96
( )
$28, .( )
. .
IRR and NPVHP 10B Keystrokes
12
CLEAR ALL
P/YR
28,371 +/- PV
445.66 PMT
8
I/YR
x P/YR
Clears registers
Monthly compounding
PV = - $28,371
Monthly pmt = $445.66
96 months
Compute IRR
IRR and NPVE x a m p l e : N P V f o r a n O r d i n a r y A n n u i t y
A n i n v e s t o r h a s t h e o p p o r t u n i t y t o i n v e s t i n r e a l e s t a t e c o s t i n g$ 2 8 , 3 7 1 t o d a y . T h e i n v e s t m e n t w i l l p r o v i d e $ 4 4 5 . 6 6 a t t h e e n d o fe a c h m o n t h f o r t h e n e x t 8 y e a r s . W h a t i s t h e N P V f o r t h i si n v e s t m e n t i f t h e i n v e s t o r d i s c o u n t s f u t u r e c a s h f l o w s m o n t h l y a t a1 0 % a n n u a l r a t e ?
N P V = - $ 2 8 , 3 7 1 + $ 2 9 , 3 6 9 . 6 6 = $ 9 9 8 . 6 6
N P Vtt
$ 2 8 , .(
.)
3 7 1 4 4 5 6 61
10 1 0
1 21
9 6
IRR and NPVHP 10B Keystrokes
CLEAR ALL
12 P/YR
445.66 PMT
10 I/YR
8
PV +/-
- 28,371 =
x P/YR
Clears registers
Monthly payments
Monthly pmt = $445.66
Annual discount rate = 10%
96 monthly payments
Compute PV
Subtract $28,371
IRR and NPVExample: What is the IRR for an investment that costs $96,000 today andpays $1028.61 at the end of the month for the next 60 months and then paysan additional $97,662.97 at the end of the 60th month?
d/12 = 1.0921% ; d = 13.10%
PV PMTdk
FVdk
d d
tt
nk
nk
tt
1
1 1
000 028 611
112
662 97
112
1
1
60
60
( ) ( )
$96, $1, .( )
$97, .
( )
IRR and NPVHP 10B Keystrokes
CLEAR ALL
12 P/YR
96,000 +/- PV
1,028.61 PMT
97,662.97 FV
5
I/YR
x P/YR
Clears registers
Monthly payments
PV = -$96,000
Monthly pmt = $1,028.61
FV = $97,662.97
60 months
Compute yield (IRR)
IRR and NPVE x a m p l e : N P V f o r a n o r d i n a r y a n n u i t y w i t h a n a d d i t i o n l u m p
s u m r e c e i p t a t t h e e n d o f t h e i n v e s t m e n t t e r m .
W h a t i s t h e N P V f o r a n i n v e s t m e n t t h a t c o s t s $ 9 6 , 0 0 0 t o d a ya n d p a y s $ 1 0 2 8 . 6 1 a t t h e e n d o f t h e m o n t h f o r t h e n e x t 6 0m o n t h s a n d t h e n p a y s a n a d d i t i o n a l $ 9 7 , 6 6 2 . 9 7 a t t h e e n d o ft h e 6 0 t h m o n t h i f t h e i n v e s t o r d i s c o u n t s e x p e c t e d f u t u r e c a s hf l o w s m o n t h l y a t t h e a n n u a l r a t e o f 1 3 . 1 0 4 7 % ?
N P V = - $ 9 6 , 0 0 0 + $ 9 6 , 0 0 0 = $ 0
N P V P V P M Tdk
F Vdk
N P V
tt
n k
n k
tt
1
1 1
0 0 0 0 2 8 6 11
10 1 3 1 0 4 7
1 2
6 6 2 9 7
10 1 3 1 0 4 7
1 2
1
1
6 0
6 0
( ) ( )
$ 9 6 , $ 1 , .(
.)
$ 9 7 , .
(.
)
IRR and NPVHP 10B Keystrokes
CLEAR ALL
12 P/YR
1,028.61 PMT
97,662.97 FV
5
13.1047 I/YR
PV +/-
- 96,000 =
x P/YR
Clears registersMonthly paymentsMonthly pmt = $1,028.61FV = $97,662.9760 months of paymentsDiscount rate = 13.1047%Compute PV Subtract $96,000
IRR and NPV
E x a m p l e : I R R f o r u n e v e n c a s h f l o w s .
W h a t i s t h e I R R f o r a n i n v e s t m e n t t h a t c o s t s $ 1 0 0 , 0 0 0 t o d a ya n d p a y s $ 2 0 , 0 0 0 o n e y e a r f r o m t o d a y ; $ 3 5 , 0 0 0 t w o y e a r s f r o mt o d a y ; a n d $ 7 5 , 0 0 0 t h r e e y e a r s f r o m t o d a y ?
$ 1 0 0 ,$ 2 0 ,
( )
$ 3 5 ,
( )
$ 7 5 ,
( )
.
0 0 00 0 0
1
0 0 0
1
0 0 0
1
1 1 5 9 %
2 3
d d d
d
IRR and NPVHP 10B Keystokes
CLEAR ALL
1
100,000 +/- CFj
20,000 CFj
35,000 CFj
75,000 CFj
P/YR
IRR/YR
Clears registers
One payment per year
Initial CF = - $100,000
1st CF = $ 20,000
2nd CF = $ 35,000
3rd CF = $ 75,000
Compute yield (IRR)
IRR and NPV
E x a m p l e : N P V f o r u n e v e n c a s h f l o w s .
W h a t i s t h e N P V f o r a n i n v e s t m e n t t h a t c o s t s $ 1 0 , 0 0 0 t o d a y ,$ 8 , 0 0 0 o n e y e a r f r o m t o d a y , $ 5 , 0 0 0 t w o y e a r s f r o m t o d a y a n dp a y s $ 1 5 , 0 0 0 t h r e e y e a r s f r o m t o d a y a n d $ 2 5 , 0 0 0 f o u r y e a r sf r o m t o d a y i f f u t u r e c a s h f l o w s a r e d i s c o u n t e d a t 1 0 % ?
N P V = - $ 1 0 , 0 0 0 - $ 7 , 2 7 2 . 7 3 - $ 4 , 1 3 2 . 2 3 + $ 1 1 , 2 6 9 . 7 2 + $ 1 7 , 0 7 5 . 3 4
= $ 6 , 9 4 0 . 1 0
N P V $ 1 0 ,$ 8 ,
.
$ 5 ,
.
$ 1 5 ,
.
$ 2 5 ,
.0 0 0
0 0 0
1 1
0 0 0
1 1
0 0 0
1 1
0 0 0
1 12 3 4
IRR and NPVHP 10B Keystrokes
CLEAR ALL
1 P/YR
10,000 +/-
+/-
+/-
8,000
CFj
CFj
CFj
CFj
CFj
5,000
15,000
25,000
10 I/YR
NPV
Clear registers
One payment per year
Initial CF = - $ 10,000
1st CF = - $ 8,000
2nd CF = - $ 5,000
3rd CF = $ 15,000
4th CF = $ 25,000
Discount rate = 10%
Compute net present value
IRR and NPV
E x a m p l e : I R R f o r g r o u p e d c a s h f l o w s .
C o m p u t e t h e I R R f o r a n i n v e s t m e n t t h a t c o s t s $ 9 2 , 7 2 5 . 6 0t o d a y a n d i s e x p e c t e d t o p a y $ 1 0 , 0 0 0 a t t h e e n d o f t h e y e a r f o rt h e n e x t t h r e e y e a r s ; $ 1 5 , 0 0 0 a t t h e e n d o f y e a r s 4 a n d 5 ; a n d$ 1 0 0 , 0 0 0 a t t h e e n d o f y e a r 6 .
d = 1 2 %
$ 9 2 , .$ 1 0 ,
( )
$ 1 5 ,
( )
$ 1 0 0 ,
( )7 2 5 6 0
0 0 0
1
0 0 0
1
0 0 0
11
3
4
5
6
d d dtt
tt
IRR and NPVHP 10B Keystrokes
CLEAR ALL
1 P/YR
92,725.60+/- CFj
CFj
CFj
10,000
3
15,000
2
100,000 CFj
IRR/YR
N j
N j
Clears registers
One payment per year
Initial CF = - $ 92,725.60
1st grouped CF = $ 10,000
Occurs three times
2nd grouped CF = $ 15,000
Occurs twice
3rd CF = $ 100,000 (once)
Compute the yield (IRR)
IRR and NPV
E x a m p l e : N P V f o r g r o u p e d c a s h f l o w s .
C o m p u t e t h e N P V f o r a n i n v e s t m e n t t h a t c o s t s $ 9 8 , 0 0 0 t o d a y a n d i se x p e c t e d t o p a y $ 7 9 1 . 3 8 a t t h e e n d o f e a c h m o n t h f o r 1 2 m o n t h s ; $ 8 5 0 . 7 3 a tt h e e n d o f e a c h m o n t h f o r t h e f o l l o w i n g 1 2 m o n t h s ; $ 9 1 4 . 5 4 a t t h e e n d o fe a c h m o n t h f o r t h e f o l l o w i n g 1 1 m o n t h s a n d a b a l l o o n p a y m e n t o f$ 1 0 7 , 4 9 1 . 1 8 a t t h e e n d o f m o n t h 3 6 i f t h e i n v e s t o r d i s c o u n t s f u t u r e c a s hf l o w s m o n t h l y a t a 1 3 % a n n u a l r a t e .
N P V = - $ 5 5 4 . 1 7 = - $ 9 8 , 0 0 0 +
$ 7 9 1 .(
.)
$ 8 5 0 .(
.)
$ 9 1 4 .(
.)
$ 1 0 7 , .
(.
)3 8
1
10 1 3
1 2
7 31
10 1 3
1 2
5 41
10 1 3
1 2
4 9 1 1 8
10 1 3
1 21
1 2
1 3
2 4
2 5
3 5
3 6
tt tt tt
IRR and NPVHP 10B Keystrokes
CLEAR ALL
12 P/YR
98,000 +/- CFj
CFj
CFj
CFj
CFj
I/YR
NPV
791.38
12
850.73
12
914.54
11
107,491.18
13
N j
N j
N j
Clear registersMonthly paymentsInitial CF = - $98,0001st grouped CF = $791.38Occurs 12 times2nd grouped CF = $850.73Occurs 12 times3rd grouped CF = $914.54Occurs 11 times4th CF = $107,491.18 (once)Discount rate = 13%Compute net present value