Present Value

Table: an asset

YEAR BENEFIT
0 30
1 40
2 50
3 60
4 70

QUESTION 1. How would you set up the calculation to find the value of this asset in period two?
(a) 30(P\G, I=0.1, 4) (1+0.1)2
(b) (1+0.1) 3 (10(P\G, I=0.1, 5)+30(P\A, I=0.1,5))
(c) 30(P\G, I=0.1, 5)(1+0.1)2
(d) (1+0.1) 2 (10(P\G,I=0.1, 4)+30(P\A, I=0.1, 4))
(e) (1+0.1)3 (10(P\G, I=0.1, 4)+30(P\A, I=0.1, 5))

Answer:

The Asset can be divided into a constant serie "Asset(1)", and a gredient serie "Asset(2)", so Asset= Asset(1) + Asset(2)

Asset(1) + Asset(2)
YEAR BENEFIT YEAR BENEFIT
0 30 0 0
1 30 1 10
2 30 2 20
3 30 3 30
4 30 4 40

Conditions:

P2= P2of Asset(1) + P2 of Asset(2)

P2(1)= 30(P\A, I=0.1, 5) (1+0.1)3
P2(2)= 10(P\G, I=0.1, 5) (1+0.1)3


P2 equation:

P2=P2(1)+P2(2)
=30(P\A, I=0.1, 5) (1+0.1)3 + 10(P\G, I=0.1, 5) (1+0.1)3
=(1+0.1)3 [30(P\A, I=0.1, 5) + 10(P\G, I=0.1, 5)]

So, The right answer is "b".

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