Chapter 4
NPV and the Time Value of Money
19
6. Plan:
What your aunt and uncle want to know is what is the present value of $100,000 in
six years, discounted at 4% annually. Most likely they do not think of this decision in these
terms and do not use or understand this terminology.
Execute:
6
100,000
PV
1.04
79,031.45
=
=
0
1
2
3
6
PV
=
?
100,000
Evaluate:
Your aunt and uncle would have to invest $79,031.45 today at 4% compounded
annual interest for it to grow in six years into the $100,000 they will need to finance your
cousin’s education.
7. Plan:
Your mom is being offered a choice in how she will take her retirement benefit: either
$250,000 today or $350,000 in five years. If mom wants the alternative that is going to give her
the most wealth, then she should take the alternative with the highest net present value. Your job
is to determine the present values of the $350,000 in five years at different interest rates.
Execute:
0
1
2
3
4
5
PV
=
?
350,000
a.
5
350,000
PV
1.0
350,000
=
=
b.
5
350,000
PV
1.08
238,204
=
=
c.
5
350,000
PV
1.2
140,657
=
=
Evaluate:
a. If the interest rate is zero, an unlikely situation, then your mom should take the 350,000 in
five years. If she takes the $250,000 today and invests it zero percent for five years, she will
have $250,000 in five years. $350,000 is better in five years than $250,000.
b. If the interest rate is 8%, she should take the 250,000 today.
c. If the interest rate is 20%, she should take the 250,000 today.