Internal Rate of Return (IRR) and Net Present Value (NPV) N etpresentvalue (N PV ): the sum ofthe presentvaluesofall cash inflow sm inusthe sum ofthe presentvaluesofall cash outflow s. The internalrate ofreturn (IR R ): (1) the discountrate that equatesthe sum ofthe presentvaluesofallcash inflow s to the sum ofthe presentvaluesofallcash outflow s; (2)the discountrate thatsetsthe netpresentvalue equalto zero. The internalrate ofreturn m easuresthe investm entyield.
Internal Rate of Return (IRR) and Net Present Value (NPV)
Jan 17, 2016
Internal Rate of Return (IRR) and Net Present Value (NPV). IRR and NPV. IRR and NPV HP 10B Keystrokes. Clears registers One payment per year PV = -$ 28,371 FV = $ 50,000 FV in 5 years Solve for IRR. IRR and NPV. IRR and NPV HP 10B Keystrokes. Clears registers One payment per year - PowerPoint PPT Presentation
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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
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