READING 2 THE TIME VALUE OF MONEY IN FINANCE Flashcards
(32 cards)
When comparing present value (PV) and future value (FV) concepts, which statement is most accurate?
A. Present value increases as the discount rate increases, holding all else constant.
B. Present value decreases as the number of compounding periods increases, holding all else constant.
C. Present value decreases as the discount rate increases, holding all else constant.
Correct Answer: C
Present value decreases as the discount rate increases because future cash flows are discounted more heavily at higher rates. This inverse relationship is fundamental to the time value of money concept.
Option A is incorrect because it states the opposite relationship - higher discount rates lead to lower present values, not higher ones.
Option B is incorrect because, holding the discount rate constant, more compounding periods for the same time horizon would lead to a higher present value, not lower.
Which of the following best describes the key characteristic of a pure discount instrument?
A. It provides periodic interest payments throughout its life.
B. It is sold at a discount to face value and provides no interest payments.
C. It is sold at a premium and pays interest at maturity.
Correct Answer: B
A pure discount instrument (like a zero-coupon bond) is sold at a discount to its face value and makes no periodic interest payments. The investor’s return comes entirely from the difference between the purchase price and the face value received at maturity.
Option A is incorrect because pure discount instruments do not provide periodic interest payments.
Option C is incorrect because pure discount instruments are sold at a discount, not a premium, and they don’t pay separate interest at maturity.
A zero-coupon bond trading at a premium to its face value most likely has:
A. A positive yield to maturity.
B. A negative yield to maturity.
C. A yield to maturity equal to zero.
B. A negative yield to maturity.
When a zero-coupon bond trades at a premium (price above face value), its yield to maturity must be negative. This is because the investor pays more than they will receive at maturity.
Option A is incorrect because a positive yield would indicate the bond is trading at a discount, not a premium.
Option C is incorrect because a zero yield would indicate the bond is trading exactly at face value (neither premium nor discount).
What is the primary difference between discrete and continuous compounding?
A. Discrete compounding occurs at specific intervals, while continuous compounding occurs infinitely many times within a given period.
B. Discrete compounding always results in a higher future value than continuous compounding.
C. Discrete compounding applies only to bonds, while continuous compounding applies only to equities.
Correct Answer: A
Discrete compounding occurs at specific time intervals (annually, semi-annually, etc.), while continuous compounding conceptually occurs at infinitely small intervals, effectively compounding every instant.
Option B is incorrect because continuous compounding actually results in a higher future value than discrete compounding, given the same stated interest rate.
Option C is incorrect because both methods can be applied to any investment type; they are mathematical approaches, not specific to asset classes.
What best describes the relationship between the coupon rate and yield to maturity for a bond trading at par value?
A. The coupon rate is higher than the yield to maturity.
B. The coupon rate equals the yield to maturity.
C. The coupon rate is lower than the yield to maturity.
B. The coupon rate equals the yield to maturity.
When a bond trades at par value (exactly at its face value), its coupon rate exactly equals its yield to maturity. This fundamental relationship exists because the coupon payments provide exactly the market-required return.
Option A is incorrect because if the coupon rate were higher than the yield to maturity, the bond would trade at a premium, not at par.
Option C is incorrect because if the coupon rate were lower than the yield to maturity, the bond would trade at a discount, not at par.
Which of the following statements is most accurate regarding perpetual bonds?
A. Perpetual bonds have an infinite duration.
B. Perpetual bonds have a present value that equals the coupon payment divided by the yield.
C. Perpetual bonds typically offer lower yields than comparable fixed-term bonds.
Correct Answer: B
The present value of a perpetual bond equals the coupon payment divided by the yield (PV = payment/r). This is the mathematical simplification of the infinite series formula for a perpetuity.
Option A is incorrect because although perpetual bonds have no maturity date, their duration is finite (not infinite) due to the time value of money.
Option C is incorrect because perpetual bonds typically offer higher yields than comparable fixed-term bonds to compensate for their greater interest rate risk.
What is the primary characteristic that distinguishes an amortizing bond from a fixed-coupon bond?
A. An amortizing bond pays higher interest rates than fixed-coupon bonds.
B. An amortizing bond includes principal repayment within each periodic payment.
C. An amortizing bond can only be issued by government entities.
Correct Answer: B
In an amortizing bond, each payment includes both interest and a portion of the principal, gradually reducing the outstanding principal over time. This contrasts with fixed-coupon bonds, where the entire principal is paid at maturity.
Option A is incorrect because the interest rate isn’t what defines an amortizing bond; it’s the structure of the payments.
Option C is incorrect because amortizing bonds can be issued by many types of entities, including corporations and municipalities, not just governments.
The yield to maturity of a bond is best described as:
A. The coupon rate adjusted for inflation expectations.
B. The internal rate of return that equates all future cash flows to the current market price.
C. The average of the coupon rate and the current yield.
Correct Answer: B
Yield to maturity is the internal rate of return that equates the present value of all future cash flows (coupons and principal) to the current market price of the bond.
Option A is incorrect because while inflation expectations influence yield to maturity, YTM isn’t simply an inflation-adjusted coupon rate.
Option C is incorrect because YTM is not calculated as an average of coupon rate and current yield; it’s a distinct measure using discounted cash flow analysis.
Which of the following statements best describes the relationship between a bond’s price and its yield to maturity?
A. The relationship is linear, with price decreasing proportionally as yield increases.
B. The relationship is inverse and convex, with price sensitivity being greater at lower yields.
C. The relationship is direct, with price increasing as yield increases.
Correct Answer: B
The relationship between bond price and yield is inverse (prices fall when yields rise) and convex (not linear). Due to this convexity, bond prices are more sensitive to yield changes at lower yield levels.
Option A is incorrect because the relationship is not linear but convex.
Option C is incorrect because the relationship is inverse, not direct; prices decrease as yields increase.
An annuity is best described as:
A. A series of equal payments at fixed intervals with no definite end date.
B. A series of equal payments at fixed intervals for a specified period.
C. A single payment that grows at a fixed rate indefinitely.
Correct Answer: B
An annuity is defined as a series of equal payments made at regular intervals for a specified period.
Option A is incorrect because it describes a perpetuity, not an annuity. Annuities have a definite end date.
Option C is incorrect because it describes a growing single payment, not a series of payments characteristic of an annuity.
When calculating the present value of a bond, which of the following components must be discounted?
A. Only the coupon payments, as the principal is already expressed in present value terms.
B. Only the principal payment, as coupon payments are already adjusted for the time value of money.
C. Both the coupon payments and the principal payment at maturity.
Correct Answer: C
When calculating a bond’s present value, all future cash flows must be discounted, including both the periodic coupon payments and the principal payment at maturity.
Option A is incorrect because the principal payment occurs in the future and must be discounted to present value terms.
Option B is incorrect because coupon payments are future cash flows that must be discounted; they are not pre-adjusted for time value of money.
From an investor’s perspective, cash outflows and inflows in time value of money calculations are best represented as:
A. Outflows as positive values and inflows as negative values.
B. Outflows as negative values and inflows as positive values.
C. Both outflows and inflows as positive values, distinguished only by timing.
Correct Answer: B
From an investor’s perspective, cash outflows (such as the purchase price of a bond) are typically represented as negative values, while cash inflows (such as coupon payments and principal repayment) are represented as positive values.
Option A is incorrect because it reverses the convention; outflows are typically negative, not positive.
Option C is incorrect because distinguishing between inflows and outflows by sign (+ or -) is standard practice to maintain clarity in financial analysis.
Which of the following best describes the effect of compounding frequency on the future value of an investment, given the same stated annual interest rate?
A. Higher compounding frequency always results in a lower future value.
B. Higher compounding frequency always results in a higher future value.
C. Compounding frequency has no effect on future value if the stated annual interest rate remains constant.
Correct Answer: B
Higher compounding frequency (e.g., monthly vs. annual) will result in a higher future value, given the same stated annual interest rate. This occurs because interest is earned on interest more frequently.
Option A is incorrect because higher compounding frequency increases future value, not decreases it.
Option C is incorrect because compounding frequency does affect future value even when the stated annual interest rate remains constant.
The key difference between the coupon rate and the yield to maturity is that:
A. The coupon rate is the interest rate that equates a bond’s price to the present value of its future cash flows, while yield to maturity is fixed at issuance.
B. The coupon rate determines the periodic payment as a percentage of face value, while yield to maturity is the discount rate that equates cash flows to current market price.
C. The coupon rate varies with market conditions, while the yield to maturity remains fixed throughout the bond’s life.
Correct Answer: B
The coupon rate is fixed at issuance and determines the periodic interest payment as a percentage of the bond’s face value. The yield to maturity is the discount rate that equates all future cash flows to the current market price.
Option A is incorrect because it reverses the definitions; the yield to maturity equates cash flows to price, not the coupon rate.
Option C is incorrect because the coupon rate is typically fixed at issuance, while the yield to maturity changes with market conditions and bond price movements.
A loan payment that includes both interest and principal is characteristic of:
A. An interest-only loan.
B. An amortizing loan.
C. A zero-coupon bond.
Correct Answer: B
An amortizing loan has payments that include both interest and principal components, with the principal portion gradually increasing over the life of the loan.
Option A is incorrect because interest-only loans, by definition, have payments that cover only the interest with no principal reduction until a balloon payment at maturity.
Option C is incorrect because zero-coupon bonds do not make periodic payments; instead, they are sold at a discount and repay face value at maturity.
What distinguishes common stock from preferred stock in terms of dividend characteristics?
A. Common stock pays a fixed dividend, while preferred stock has variable dividend payments.
B. Common stock has no guaranteed dividend, while preferred stock pays a fixed dividend as a percentage of par value.
C. Common stock always pays higher dividends than preferred stock.
Correct Answer: B
Preferred stock has a stated fixed dividend as a percentage of par value, providing more predictable income.
Common stock dividends are discretionary and determined by management, with no guaranteed payment.
Option A is incorrect because it reverses the dividend characteristics of the two stock types.
Option C is incorrect because dividend levels depend on company performance and policy, not inherent stock type.
What is the fundamental difference between a perpetuity and a constant growth dividend discount model?
A. A perpetuity assumes zero growth in dividends, while the constant growth model assumes a fixed positive growth rate.
B. A perpetuity assumes infinite constant dividends, while the constant growth model assumes increasing dividends.
C. A perpetuity and constant growth model are mathematically identical.
Correct Answer: A
A perpetuity assumes dividends remain constant forever (zero growth), while the constant growth model assumes a fixed positive growth rate in dividends.
The perpetuity formula is a special case of the constant growth dividend discount model when the growth rate is zero.
Option B is incorrect because both models assume constant dividend payments, just with different growth assumptions.
Option C is incorrect because the models have different mathematical formulations due to the growth rate.
What primary constraint exists in the constant growth dividend discount model (Gordon growth model)?
A. The dividend growth rate must be zero.
B. The required return must be greater than the dividend growth rate.
C. The dividend must be exactly equal to the previous period’s dividend.
Correct Answer: B
In the constant growth dividend discount model, the required return (k_e) must be greater than the dividend growth rate (g_e), or the mathematical model breaks down.
This constraint ensures the model remains economically meaningful and prevents infinite valuation.
Option A is incorrect because the model allows for positive growth rates.
Option C is incorrect as the model allows for consistent but growing dividends.
What characterizes a residual claim in the context of common stock ownership?
A. Stockholders receive payments before all other claimants.
B. Stockholders have the first right to a company’s assets in case of bankruptcy.
C. Stockholders are paid after all other claims on a company’s assets have been satisfied.
Correct Answer: C
A residual claim means common stockholders are the last to receive payments, only after all other obligations (debt, preferred stock, etc.) have been met.
This position represents both higher risk and potential for greater rewards.
Option A is incorrect because stockholders are actually last in line for payments.
Option B is incorrect because stockholders have the lowest priority in asset claims during
What fundamental assumption underlies the constant dividend discount model?
A. Dividends will decrease over time.
B. Dividends remain exactly the same in every future period.
C. Dividends will grow at an unpredictable rate.
Correct Answer: B
The constant dividend discount model assumes that dividends remain unchanged in every future period.
This simplifying assumption allows for straightforward valuation when dividend stability is expected.
Option A is incorrect because the model assumes no change in dividend amount.
Option C is incorrect because the model requires a predictable, constant dividend.
How do preferred stocks conceptually differ from bonds in terms of their cash flow characteristics?
A. Preferred stocks have variable dividend payments, while bonds have fixed interest payments.
B. Preferred stocks pay a fixed dividend as a percentage of par value, similar to bond coupon payments.
C. Preferred stocks do not provide any regular income to investors.
Correct Answer: B
Preferred stocks pay a fixed dividend percentage of par value, conceptually similar to bond coupon payments.
Both provide predictable income streams to investors.
Option A is incorrect because preferred stock dividends are fixed, not variable.
Option C is incorrect as preferred stocks do provide regular income.
What distinguishes the implied growth rate in equity valuation?
A. It is a guaranteed future growth rate set by company management.
B. It is calculated as the difference between the required rate of return and the dividend yield.
C. It represents the exact growth rate of a company’s earnings.
Correct Answer: B
The implied growth rate is mathematically derived as the required rate of return minus the dividend yield.
It represents the market’s implicit expectation of future dividend growth.
Option A is incorrect because it is a calculated metric, not a guaranteed rate.
Option C is incorrect as it represents dividend growth, not earnings growth.
What fundamental principle underlies the valuation of preferred stocks using the perpetuity formula?
A. Preferred stocks have a definite maturity date.
B. Preferred stocks can be considered to have an infinite stream of fixed dividends.
C. Preferred stocks never pay dividends.
Correct Answer: B
The perpetuity formula assumes an infinite stream of fixed dividend payments, which matches the characteristics of preferred stocks.
This approach reflects the perpetual nature of preferred stock dividends.
Option A is incorrect because preferred stocks typically do not have a maturity date.
Option C is incorrect as preferred stocks do pay fixed dividends.
Which of the following best describes the relationship between bond price and yield to maturity?
A. When bond price increases, yield to maturity increases.
B. When bond price decreases, yield to maturity decreases.
C. When bond price decreases, yield to maturity increases.
Correct Answer: C
The relationship between bond price and yield to maturity is inverse. When a bond’s price decreases, its yield to maturity increases, and vice versa. This fundamental relationship reflects the fact that if you pay less for the same future cash flows, your rate of return will be higher.
Option A is incorrect because it describes a direct relationship, which is the opposite of the actual inverse relationship between price and yield.
Option B is incorrect because it suggests that both price and yield move in the same direction, which contradicts the inverse relationship that exists between these variables.
