PROBLEM 6-10
1. Purchase.
Time diagrams:
Installments
i = 10%
PV – OA = ?
R =
$350,000 $350,000 $350,000 $350,000 $350,000
Property taxes and other costs
i = 10%
PV – OA = ?
R =
PROBLEM 6-10 (Continued)
Insurance
i = 10%
PV – AD = ?
R =
$27,000 $27,000 $27,000 $27,000 $27,000 $27,000
Salvage Value
i = 10%
PV = ? FV = $500,000
Formula for installments:
PROBLEM 6-10 (Continued)
Formula for property taxes and other costs:
PV – OA = R (PVF – OAn, i)
Formula for insurance:
PV – AD = R (PVF – ADn, i)
Formula for salvage value:
PV = FV (PVFn, i)
PROBLEM 6-10 (Continued)
Present value of net purchase costs:
Down payment………………………………………………..
$ 400,000
Installments ……………………………………………………
Property taxes and other costs ………………………..
Insurance ……………………………………………………….
202,367
Total costs ……………………………………………………..
$2,310,711
Less: Salvage value ……………………………………….
159,315
2. Lease.
Time diagrams:
Lease payments
i = 10%
PV – AD = ?
R =
$270,000 $270,000 $270,000 $270,000 $270,000
Interest lost on the deposit
i = 10%
PV – OA = ?
R =
PROBLEM 6-10 (Continued)
Formula for lease payments:
Formula for interest lost on the deposit:
Interest lost on the deposit per year = $100,000 (10%) = $10,000
Cost for leasing the facilities = $2,023,666 + $68,137 = $2,091,803
Dunn Inc. should lease the facilities because the present value of the
PROBLEM 6-11
(a) Annual retirement benefits.
Jean–current salary
$ 48,000
X 2.56330
(future value of 1, 24 periods, 4%)
annual salary during last year of
work
X .50
retirement benefit %
Colin–current salary
$ 36,000
X 3.11865
(future value of 1, 29 periods, 4%)
annual salary during last year of
work
X .40
retirement benefit %
Anita–current salary
$ 18,000
X 2.10685
(future value of 1, 19 periods, 4%)
37,923
annual salary during last year of
work
X .40
retirement benefit %
$ 15,169
annual retirement benefit
Gavin–current salary
$ 15,000
X 1.73168
(future value of 1, 14 periods, 4%)
25,975
annual salary during last year of
work
X .40
retirement benefit %
PROBLEM 6-11 (Continued)
(b) Fund requirements after 15 years of deposits at 12%.
Jean will retire 10 years after deposits stop.
Colin will retire 15 years after deposits stop.
Anita will retire 5 years after deposits stop.
Gavin will retire the beginning of the year after deposits stop.
PROBLEM 6-11 (Continued)
$165,705
Jean
68,638
Colin
(c) Required annual beginning-of-the-year deposits at 12%:
Deposit X (future value of an annuity due for 15 periods at 12%) = FV
Deposit X (37.27972 X 1.12) = $393,270
PROBLEM 6-12
(a) The time value of money would suggest that NET Life’s discount rate
was substantially higher than First Security’s. The actuaries at NET Life
(b) As the controller of STL, Brokaw assumes a fiduciary role to the
present and future retirees of the corporation. As a result, he is
responsible for ensuring that the pension assets are adequately
(c) If STL switched to NET Life
The primary beneficiaries of Brokaw’s decision would be the corporation
and its many stockholders by virtue of reducing 8 million dollars of
annual pension costs.
If STL stayed with First Security
In the short run, the primary beneficiaries of Brokaw’s decision would
PROBLEM 6-13
Cash Flow Probability
Estimate X Assessment = Expected Cash Flow
2015 $ 2,500 20% $ 500
4,000 60% 2,400
5,000 20% 1,000 X PV
Factor,
n = 1, I = 5% Present Value
$3,900 X 0.95238 = $ 3,714
2017 $ 4,000 30% $1,200
6,000 40% 2,400
PROBLEM 6-14
Cash Flow Probability
Estimate X Assessment = Expected Cash Flow
2015 $ 6,000 40% $ 2,400
9,000 60% 5,400 X PV
2016 $ (500) 20% $ (100)
2,000 60% 1,200