Question: Calculate the FV of your pension plan

Present Value
Present value reflects the current value of a future payment or
receipt.
PV = FVn
{1/(1
+ r
)
n
}
¨
FVn =
the future value of the investment at the end of n years
¨
n =
number of years until payment is received
¨
r =
the interest rate
¨
PV =
the present value of the future sum of money

PV example
¨
What will be the present value of
€
500 to be received 10 years
from today if the discount rate is 6%?
¨
PV =
€
500 x {1/(1+0.06)
10
}
=
€
500 x (1/1.791)
=
€
500 x (0.558)
=
€
279.00

Net Present Value Calculation
Definition:
Present Value is the value of an expected income stream determined as
of the date of valuation.
(how to calculate it
in Excel)
Basic notion:
¨
“An EUR today has a higher value than an EUR tomorrow”.
¨
The
time value of money
describes the greater benefit of receiving
money
now rather than later
.

Customer Lifetime Value
Definition:
The CLV is one application of the NPV calculation. The CLV is is a
prediction of the discounted net profits
attributed to the entire future
relationship with a customer. Thus, the CLV is the NPV of each customer.
The CLV is a long-term concept. It motivates firms to retain clients and
to increase their “share-of-wallet”.
The value of a firm might be calculated multiplying the CLV with the
number of clients.

Annuity
¨
An annuity is a series of equal dollar payments for a specified
number of years.
¨
Ordinary annuity payments occur at the end of each period.

FV
of Annuity
Compound Annuity
¨
Depositing or investing an equal sum of money at the end of each
year for a certain number of years and allowing it to grow.

FV
Annuity - Example
¨
What will be the
FV
of a 5-year,
€
500 annuity compounded at
6%?
¨
FV
5
=
€
500 (1 + 0.06)
4
+
€
500 (1 + 0.06)
3
+
€
500(1 + 0.06)
2
+
€
500 (1 + 0.06) +
€
500
=
€
500 (1.262) +
€
500 (1.191) +
€
500 (1.124)
+
€
500 (1.090) +
€
500
=
€
631.00 +
€
595.50 +
€
562.00 +
€
530.00 +
€
500
=
€
2,818.50

FV of an Annuity – Using the Mathematical Formulas
FV
n
= PMT
{(1 +
r
)
n
–
1/
r
}
¨
FV
n
=
the future of an annuity at the end of the nth year
¨
PMT =
the annuity payment deposited or received at the end of each year
¨
r =
the annual interest (or discount) rate
¨
n =
the number of years

¨
What will
€
500 deposited in the bank every year for 5 years at
6% be worth?
¨
FV
=
PMT
{[(1 +
r
)
n
– 1]/
r
}
=
€
500 (5.637)
=
€
2,818.50
FV of an Annuity – Using the Mathematical Formulas

FV of Annuity: Changing PMT, N, and r
1.
What will
€
5,000 deposited annually for 50 years be worth at
7%?
FV =
€
2,032,644
Contribution =
€
250,000 (= 5000*50)
2.
Change
PMT
=
€
6,000 for 50 years at 7%
FV
=
€
2,439,173
Contribution=
€
300,000 (= 6000*50)

FV of Annuity: Changing PMT, N, and r
3.
Change time = 60 years,
€
6,000 at 7%
FV
=
€
4,881,122
Contribution =
€
360,000 (= 6000*60)
4. Change
r
= 9%, 60 years, $6,000
FV
=
€
11,668,753
Contribution =
€
360,000 (= 6000*60)

Present Value of an Annuity
Pensions, insurance obligations, and interest owed on bonds are all
annuities. To compare these three types of investments we need to
know the present value (
PV
) of each.

PV
of Annuity – Using the Mathematical Formulas
¨
PV
of Annuity
=
PMT
{[1 – (1 +
r
)
–1
]}/
r
= 500 (4.212)
=
€
2,106

PV
of Annuity – Example Pricing Models EA
Compare the following three pricing models and decide, which one

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