FIN 320 chap 4 Time Value of Money: Valuing Cash Flow Streams

6) Which of the following statements regarding growing perpetuities is *FALSE*? A) We assume that r < g for a growing perpetuity. B) PV of a growing perpetuity = C) To find the value of a growing perpetuity one cash flow at a time would take forever. D) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.

A) We assume that r < g for a growing perpetuity.

2) Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r). The present value of Investment X is *$5,000*, while the present value of Investment Y is *$4,000*. Which of the following is true? A) Investment X has a higher growth rate than Investment Y. B) Investment X has a lower growth rate than Investment Y. C) The answer cannot be determined without knowing the interest rate for both investments. D) This makes no sense - with the same initial cash flow and the same interest rate Investment X and Investment Y should have the same present value.

Answer: AA) Investment* X *has a *higher growth rate* than Investment Y.

7) Which of the following formulas is INCORRECT? A) PV of a growing annuity = C × B) PV of an annuity = C × C) PV of a growing perpetuity = D) PV of a perpetuity =

Answer: AA) PV of a growing annuity = C ×

8) Which of the following is *true about perpetuities*? A) Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate. B) Since a perpetuity generates cash flows every period infinitely, each cash flow must be discounted to calculate the present value. C) Since a perpetuity generates cash flows every period infinitely, there is no way to solve for the cash flow given the present value and the interest rate. D) A perpetuity does not generate cash flows every period infinitely.

Answer: AA) Since a perpetuity generates cash flows every period *infinitely*, the cash flow generated equals the *PV times the interest rate*.

2) You are given two choices of investments, Investment A and Investment B. Both investments have the same future cash flows. *Investment A has a discount rate of 4%*, and Investment *B has a discount rate of 5%*. Which of the following is true? A) The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B. B) The present value of cash flows in Investment A is lower than the present value of cash flows in Investment B. C) The present value of cash flows in Investment A is equal to the present value of cash flows in Investment B. D) No comparison can be made - we need to know the cash flows to calculate the present value.

Answer: AA) The *present value of cash flows in Investment A *is *higher* than the present value of cash flows in Investment B.

12) Which of the following statements regarding *annuities is FALSE*? A) PV of an annuity = C × B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. C) An annuity is a stream of N equal cash flows paid at regular intervals. D) Most car loans, mortgages, and some bonds are annuities.

Answer: BB) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.

7) Which of the following statements regarding *perpetuities* is *FALSE*? A) To find the value of a perpetuity one cash flow at a time would take forever. B) A perpetuity is a stream of equal cash flows that occurs at regular intervals and lasts forever. C) PV of a perpetuity = r/C D) One example of a perpetuity is the British government bond called a consol.

Answer: CC) PV of a perpetuity = r/C

9) Which of the following is true about *perpetuities*? A) All else equal, the value of a perpetuity is higher when the periodic cash flow is higher. B) All else equal, the value of a perpetuity is higher when the interest rate is lower. C) If two perpetuities have the same present value and the same interest rate, they must have the same cash flows. D) All of the above are true statements.

Answer: DD) All of the above are true statements.

2) *Trial and error is the only way *to compute the internal rate of return (IRR) when interest is calculated over five or more periods.

Answer: FALSE

4.3 Annuities 1) Cash flows from an *annuity occur every year in the future*.

Answer: FALSE

1) A growing perpetuity where the rate of growth is greater than the discount rate will have an infinitely large present value (PV).

Answer: TRUE

1) The internal rate of return (IRR) is the interest rate that sets the net present value *(NPV) of the cash flows equal to zero*

Answer: TRUE

4.1 Valuing a Stream of Cash Flows 1) The *present value (PV) of a stream of cash flows* is just the sum of the present values of each individual cash flow.

Answer: TRUE