Problem set 1 – solution
zhipeng Yan
Problem Set 1: Present Value
Solution
1. (a) The PV of the project is
10
1
17000
(1 14%)
t
t
=
+
∑
=
)
)
14
.
0
1
(
1
1
(
14
.
0
17000
10
+
−
(use annuity
formula ) = $886, 739.66
(b) At the end of 5 years, there will be 5 more years of income from the project,
Therefore it will be worth
∑
=
+
5
1
)
14
.
0
1
(
170000
t
t
= $583, 623.76 (This is the PV at the end of 5
th
year, if you want to get PV now, you have to discount it again )
2. An annuity of $1 over the next 12 years is worth
12
11
[1
]
8%
(1 8%)
−
+
= $7.536
Therefore, Basset can buy 20,000/7.536 = 2653.90 units of $1 annuity and receive
$2563.90 every year. Or, equivalently, you can use the annuity formula directly:
Solve
12
1
]
20,000
8%
(1 8%)
x
−=
+
Get x = 2653.9.
In Excel, you should use function PMT(rate, Nper, Pv), where rate = 8%, Number of
periods = 12, and PV = 20,000.
However, since you cannot use Excel in the exams, you’d better learn how to use
formulas I gave you.
3. Value of this year’s production = $14*100,000 = $1,400,000
The growth rate of income= 1.02* 0.96
−
1 =
−
2.080%
Using the annuity with growth formula, the PV of the oil well is =
18
1,400,000*(1 2.08%)
1 2.08%