Chapter 4: Net Present Value
Concept Questions - Chapter 4
4.1 ∙ Define future value and present value.
Future value is the value of a sum after investing over one or more periods.
Present value is the value today of cash flows to be received in the future.
∙How does one use net present value when making an investment decision?
One determines the present value of future cash flows and then subtracts the cost of the investment. If this value is positive, the investment should be undertaken.
If the NPV is negative, then the investment should be rejected.
4.2 ∙ What is the difference between simple interest and compound interest?
With simple interest, the interest on the original investment is not reinvested.
With compound interest, each interest payment is reinvested and one earns
interest on interest.
∙What is the formula for the net present value of a project?
T
NPV = -C0 + ∑ C t /(1+I)t
t=1
4.3 ∙ What is a stated annual interest rate?
The stated annual interest rate is the annual interest rate without consideration of compounding.
∙ What is an effective annual interest rate?
An effective annual interest rate is a rate that takes compounding into account.
∙ What is the relationship between the stated annual interest rate and the
effective annual interest rate?
Effective annual interest rate = (1 + (r/m) )m - 1.
∙Define continuous compounding.
Continuous compounding compounds investments every instant.
4.4 ∙ What are the formulas for perpetuity, growing-perpetuity, annuity, and
growing annuity?
Perpetuity: PV = C/r
Growing Perpetuity: PV = C/(r-g)
Annuity: PV = (C/r) [1-1/(1+r)T]
Growing Annuity: PV = [C/(r-g)] [1-((1+g) / (1+r))T ] ∙What are three important points concerning the growing perpetuity formula?
1.The numerator.
2.The interest rate and the growth rate.
3.The timing assumption.
∙What are four tricks concerning annuities?
1. A delayed annuity.
2.An annuity in advance
3.An infrequent annuity
4.The equating of present values of two annuities.
Answers to End-of-Chapter Problems
Questions And Problems
Annual Compounding
4.1 Compute the future value of $1,000 compounded annually for
a. 10 years at 5 percent.
b. 10 years at 7 percent.
c. 20 years at 5 percent.
d. Why is the interest earned in part c not twice the amount earned in part a?
4.1 a. $1,000 ⨯ 1.0510 = $1,628.89
b. $1,000 ⨯ 1.0710 = $1,967.15
c. $1,000 ⨯ 1.0520 = $2,653.30
d. Interest compounds on the interest already earned. Therefore, the interest earned
in part c, $1,653.30, is more than double the amount earned in part a, $628.89.
4.2 Calculate the present value of the following cash flows discounted at 10 percent.
a. $1,000 received seven years from today.
b. $2,000 received one year from today.
c. $500 received eight years from today.
4.2 a. $1,000 / 1.17 = $513.16
b. $2,000 / 1.1 = $1,818.18
c. $500 / 1.18 = $233.25
4.3 Would you rather receive $1,000 today or $2,000 in 10 years if the discount rate is 8 percent?
96 Part II Value and Capital Budgeting
14The following conventions are used in the questions and problems for this chapter.
If more frequent compounding than once a year is indicated, the problem will either state: (1) both a stated annual interest rate and a compounding period, or (2) an effective annual interest rate.
If annual compounding is indicated, the problem will provide an annual interest rate. Since the stated annual interest rate and the effective annual interest rate are the same here, we use the simpler annual interest rate.
4.3 You can make your decision by computing either the present value of the $2,000 that you
can receive in ten years, or the future value of the $1,000 that you can receive now.
Present value: $2,000 / 1.0810 = $926.39
Future value: $1,000 ⨯ 1.0810 = $2,158.93
