4.5
The future value, FV, of the firm’s investment must equal the $1.5 million pension liability.
FV
= C
0
(1+r)
27
To solve for the initial investment, C
0
, discount the future pension liability ($1,500,000) back 27
years at eight percent, (1.08)
27
.
$1,500,000 / (1.08)
27
= C
0
=
$187,780.23
The firm must invest $187,708.23 today to be able to make the $1.5 million payment.
4.6
The decision involves comparing the present value, PV, of each option.
Choose the option with
the highest PV.
a.
At a discount rate of zero, the future value and present value of a cash flow are always
the same.
There is no need to discount the two choices to calculate the PV.
PV(Alternative 1)
=
$10,000,000
PV(Alternative 2)
=
$20,000,000
Choose Alternative 2 since its PV, $20,000,000, is greater than that of Alternative 1,
$10,000,000.
b.
Discount the cash flows at 10 percent.
Discount Alternative 1 back one year and
Alternative 2, five years.
PV(Alternative 1)
= C / (1+r)
= $10,000,000 / (1.10)
1
=
$9,090,909.10
PV(Alternative 2)
= $20,000,000 / (1.10)
5
=
$12,418,426.46
Choose Alternative 2 since its PV, $12,418,426.46, is greater than that of Alternative
1, $9,090,909.10.
c.