CHAPTER 5
INTRODUCTION TO VALUATION: THE TIME VALUE
OF MONEY
Answers to Concepts Review and Critical Thinking Questions
1.
The four parts are the present value (PV), the future value (FV), the discount rate (
r
), and the life of
the investment (
t
).
2.
Compounding refers to the growth of a dollar amount through time via reinvestment of interest
earned. It is also the process of determining the future value of an investment. Discounting is the
process of determining the value today of an amount to be received in the future.
3.
Future values grow (assuming a positive rate of return); present values shrink.
4.
The future value rises (assuming it’s positive); the present value falls.
5.
It’s a reflection of the time value of money. ScotiaMcLeod gets to use the $29.19 immediately. If
Scotia uses it wisely, it will be worth more than $100 in twenty years.
6.
The key considerations would be: (1) Is the rate of return implicit in the offer attractive relative to
other, similar risk investments? and (2) How risky is the investment; i.e., how certain are we that we
will actually get the $10,000? Thus, our answer does depend on who is making the promise to repay.
7.
The Government of Canada security would have a somewhat higher price because the Government of
Canada is the strongest of all borrowers.
8.
The price would be higher because, as time passes, the price of the security will tend to rise toward
$100. This rise is just a reflection of the time value of money. As time passes, the time until receipt of
the $100 grows shorter, and the present value rises. In 2007, the price will probably be higher for the
same reason. We cannot be sure, however, because interest rates could be much higher, or Canada’s
financial position could deteriorate. Either event would tend to depress the security’s price.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Basic
1.
The simple interest per year is:
$5,000 × .07 = $350
So after 10 years you will have:
$350 × 10 = $3,500 in interest.
The total balance will be $5,000 + 3,500 = $8,500
With compound interest we use the future value formula:
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