Wzory na kolokwium z Zarządzania Procesami Inwestycyjnymi.

Stopy Procentowe:

( r − i) ⋅ 100

r

a

=

a

100 + i

r = r ⋅ 1

( − T )

f

n

r

r

ef =

1

[( +

) n

n

− ]

1 ⋅ 100

Odsetki proste:

FV = PV ⋅ 1

( + r ⋅ t) FV

PV = 1(+ r ⋅ t) I = PV ⋅ r ⋅ t FV = PV ⋅ 1

( + r ⋅ t + r ⋅ t + ... + r ⋅ t ) 1

1

2

2

n

n

Odsetki złożone (z kapitalizacją): t

FV = PV ⋅ 1

( + r)

1

PV = FV

t

1

( + r)

I = PV ⋅ 1

( + r i−1

) ⋅ r

t

t

t

1

2

n

FV = PV ⋅ 1

( + r ) ⋅ 1

( + r ) ⋅ ...⋅ 1

( + r )

1

2

n

1

CO =

t

t

1

( + k)

Kredyt i Leasing:

r

r

1

( +

) n ⋅

KR = SK ⋅

m

m

0

r

1

( +

) n − 1

m

r

r

1

( +

) t−1 ⋅

m

m

K

SK

t =

⋅

0

r

1

( +

) n − 1

m

k =

KK

EF

(

0 ) − 1

FK

KR = K + O

t

t

Ocena projektów inwestycyjnych: I

O

=

Zw

CF

skumulo

e

wan NCF

O

= n +

n

Zw

NCFn+1

= Z

ROI

n ⋅

%

100

I

1 ∑ n Z

n

n

t= 0

ROI

⋅

%

100

I

= CF

ROI

t ⋅

%

100

I

n

n

n

CF

I

NCF

NPV = ∑

t

−

t

∑

t

=

t

∑

t

t

t= 0 1

( + k)

t= 0 1

( + k)

t= 0 1

( + k)

NPV

NPVR = PVI

n

NCFt

∑

= 0 ⇒ k = IRR

t

t= 0 1

( + k)

+

−

+

+

NPV ⋅ ( k −

)

IRR = k +

k

+

−

NPV + NPV

n

+

∑ NCFt t

t= m+ 1 1

( + )

PI =

k

m

−

∑ NCFt t

t= 0 1

( + k)