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.
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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 ?
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IRR and NPVHP 10B Keystrokes
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Clears registersOne payment per yearPV = -$ 28,371FV = $ 50,000FV in 5 yearsSolve 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 % ?
Clears registersOne payment per year$50,000 future valueDiscount rate = 15%FV in 5 yearsCompute present valueSubtract $28,371
IRR and NPVExample: Yield on an Ordinary Annuity
An investor has the opportunity to invest in real estate costing $28,371today. The investment will provide $445.66 at the end of each month for thenext 8 years. What is the (annual) IRR (compounded monthly) for thisinvestment?
IRR and NPVE x a m p l e : N P V f o r a n O r d i n a r y A n n u i t y
A n i n v e s t o r h a s t h e o p p o r t u n i t y t o i n v e s t i n r e a l e s t a t e c o s t i n g$ 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 ?
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?
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 % ?
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 ?
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 % ?
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 .
IRR and NPVE 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 .