FINC409/609 - Fixed Income Seccurities: Lecture 04 Quiz

Question 1

Which statement best describes the present value (PV) of a cash flow?

It is the value in the future of an amount invested today at the market interest rate. It is the value today of a future cash flow after discounting at the appropriate market interest rate. It is always strictly less than the future cash flow, regardless of the interest rate. It is the sum of all coupon payments that a bond will pay.

Question 2

A bond will pay a single $100 cash flow in 5 years. If the market discount rate increases, what happens to the bond’s present value (all else equal)?

The present value increases because investors earn more interest. The present value decreases because the future cash flow is discounted more heavily. The present value stays the same; only the future value changes. The effect is ambiguous; it can increase or decrease.

Question 3

Consider two risk‑free cash flows: $100 in 1 year and $100 in 3 years. The interest rate is positive and the same for both. Which has the higher present value?

$100 in 1 year has the higher present value. $100 in 3 years has the higher present value. They have the same present value. It depends on the compounding frequency.

Question 4

Which statement correctly distinguishes an annuity from a perpetuity?

An annuity pays a fixed amount forever; a perpetuity pays for a fixed number of periods. Both an annuity and a perpetuity pay a fixed amount forever. An annuity pays a fixed amount for a finite number of periods; a perpetuity pays the same amount forever. Both an annuity and a perpetuity pay a fixed amount for a finite number of periods.

Question 5

For a growing perpetuity with first cash flow $C_1$, discount rate $r$, and growth rate $g$, the usual formula is $PV = \dfrac{C_1}{r - g}$. Which condition must hold for this formula to make economic sense?

The growth rate must be strictly less than the discount rate: $g < r$. The growth rate must be greater than the discount rate: $g > r$. The growth rate must equal the discount rate: $g = r$. There is no restriction on the relationship between $g$ and $r$.

Question 6

You invest $1,000 for 5 years at a stated annual rate of 5%. Which compounding convention gives the highest future value?

Annual compounding (once per year). Semi‑annual compounding (twice per year). Quarterly compounding (four times per year). Continuous compounding.

Question 7

A U.S. Treasury bond with $100 face value has a 6% annual coupon and 5 years to maturity. Coupons are paid semi‑annually. Which approach correctly describes how to compute its present value?

Treat it as paying $6 once a year for 5 years and discount at the annual yield. Treat it as paying $3 every six months for 10 periods plus $100 at maturity, and discount each cash flow using the semi‑annual yield (annual yield divided by 2). Treat it as paying $12 once a year for 5 years and discount at half the annual yield. Any of the above will give the same present value.

Question 8

What is the effective annual rate (EAR) associated with a quoted nominal rate that is compounded more than once per year?

It is always equal to the quoted nominal rate. It is the nominal rate divided by the number of compounding periods per year. It is the single annual rate that, when compounded once per year, gives the same future value as the quoted nominal rate with its compounding frequency. It is the rate that ignores compounding altogether.

Question 9

You are given a 4% rate compounded semi‑annually and you want the equivalent quarterly‑compounded rate. Conceptually, how should you do this?

Simply divide 4% by 4 to get 1% per quarter. Multiply 4% by 2 to get an 8% quarterly rate. Equate the future value of a $1 investment after one year under both compounding conventions and solve for the unknown quarterly rate. It is impossible to convert between compounding frequencies.

Question 10

Which statement about continuous compounding is correct?

With continuous compounding, interest is added only once per year. With continuous compounding, interest is added at every instant, and the future value is $FV_T = PV \cdot e^{rT}$. Continuous compounding always gives the same future value as annual compounding. Continuous compounding cannot be used in financial models.

FINC409/609 - Fixed Income Securities

Prof. Matt Fleckenstein

Lecture 4 - Quiz