The Time Value of Money Part 2

14) Consider the following timeline: If the current market rate of interest is 8%, then the value as of year 1 is closest to: A) $0 B) $1003 C) $540 D) $77 Answer: D Explanation: D) Two part problem: FV = PV(1 + r)n = 500(1.08)1 = $540 PV = FV/(1 + r)n = -500/(1.08)1 = -$463 So the answer is $540 + -$463 = $77 4.3 Valuing a Stream of Cash Flows 1) Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 8%, then the present value of this stream of cash flows is closest to: A) $22,871 B) $21,211 C) $24,074 D) $26,000 Answer: B Explanation: B) PV = 5000/(1.07)1 + 6000/(1.07)2 + 7000/(1.07)3 + 8000/(1.07)4 = $21,210.72 2) Which of the following statements is FALSE? A) FV = B) PV = C) FV = Cn × (1 + r)n D) Most investment opportunities have multiple cash flows that occur at different points in time. Answer: A 3) Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 8%, then the future value of this stream of cash flows is closest to: A) $11,699 B) $10,832 C) $12,635 D) $10,339 Answer: A Explanation: A) FV = 1000(1.08)4 + 2000(1.08)3 + 3000(1.08)2 + 4000(1.08)1 = $11,699 4) Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 10%, then the present value of this stream of cash flows is closest to: A) $674 B) $600 C) $460 D) $287 Answer: C Explanation: C) PV = 100/(1.10)1 + 100/(1.10)2 + 200/(1.10)3 + 200/(1.10)4 = $460 5) Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 6%, then the future value of this stream of cash flows is closest to: A) $1,723 B) $1,500 C) $1,626 D) $1,288 Answer: A Explanation: A) FV = 100(1.06)5 + 200(1.06)4 + 300(1.06)3 + 400(1.06)2 + 500(1.06)1 = $1723 Use the following timeline to answer the question(s) below. 0 1 $600 2 $1,200 3 $1,800 6) At an annual interest rate of 7%, the future value of this timeline in year 3 is closest to: A) $3,295 B) $3,600 C) $3,770 D) $4,035 Answer: C Explanation: C) FV = PV(1 + i)N = $600(1.07)2 + 1,200(1.07)1 + 1,800 = 3,770.94 7) At an annual interest rate of 7%, the present value of this timeline in year 0 is closest to: A) $3,080 B) $3,600 C) $3,770 D) $4,035 Answer: A Explanation: A) PV = FV/(1 + i)N = $600/(1.07)1 + 1,200/(1.07)2 + 1,800/(1.07)3 = 3,078.21 8) At an annual interest rate of 7%, the future value of this timeline in year 2 is closest to: A) $3,080 B) $3,525 C) $3,770 D) $4,035 Answer: B Explanation: B) FV year 2 = $600(1.07)1 + 1,200 + 1,800/(1.07)1 = 3,524.24 9) Taggart Transcontinental currently has a bank loan outstanding that requires it to make three annual payments at the end of the next three years of $1,000,000 each. The bank has offered to allow Taggart Transcontinental to skip making the next two payments in lieu of making one large payment at the end of the loan's term in three years. If the interest rate on the loan is 6%, then the final payment that the bank will require to make Taggart Transcontinental indifferent between the two forms of payments is closest to: A) $2,673,000 B) $3,000,000 C) $3,184,000 D) $3,375,000 Answer: C Explanation: C) FV = PV(1 + i)N = $1,000,000(1.06)2 + 1,000,000(1.06)1 + 1,000,000 = 3,183,600 Use the information for the question(s) below. Joe just inherited the family business, and having no desire to run the family business, he has decided to sell it to an entrepreneur. In exchange for the family business, Joe has been offered an immediate payment of $100,000. Joe will also receive payments of $50,000 in one year, $50,000 in two years, and $75,000 in three years. The current market rate of interest for Joe is 6%. 10) In terms of present value, how much will Joe receive for selling the family business? Answer: PV = $100,000 + $50,000/(1.06)1 + $50,000/(1.06)2 + $75,000/(1.06)3 = $254,641 4.4 Calculating the Net Present Value Use the following information to answer the question(s) below. Nielson Motors is considering an opportunity that requires an investment of $1,000,000 today and will provide $250,000 one year from now, $450,000 two years from now, and $650,000 three years from now. 1) If the appropriate interest rate is 10%, then the NPV of this opportunity is closest to: A) ($88,000) B) $88,000 C) $300,000 D) $1,300,000 Answer: B Explanation: B) NPV = -1,000,000 + 250,000/(1.10)1 + 450,000/(1.10)2 + 650,000/(1.10)3 = 87,528.17 2) If the appropriate interest rate is 10%, then Nielson Motors should: A) invest in this opportunity since the NPV is positive. B) not invest in this opportunity since the NPV is positive. C) invest in this opportunity since the NPV is negative. D) not invest in this opportunity since the NPV is negative. Answer: A Explanation: A) NPV = -1,000,000 + 250,000/(1.10)1 + 450,000/(1.10)2 + 650,000/(1.10)3 = 87,528.17 Invest since positive NPV 3) If the appropriate interest rate is 15%, then Nielson Motors should: A) invest in this opportunity since the NPV is positive. B) not invest in this opportunity since the NPV is positive. C) invest in this opportunity since the NPV is negative. D) not invest in this opportunity since the NPV is negative. Answer: D Explanation: D) NPV = -1,000,000 + 250,000/(1.15)1 + 450,000/(1.15)2 + 650,000/(1.15)3 = -14,958.49 Do Not Invest since negative NPV 4) Kampgrounds Inc. is considering purchasing a parcel of wilderness land near a popular historic site. Although this land will cost Kampgrounds $400,000 today, by renting out wilderness campsites on this land, Kampgrounds expects to make $35,000 at the end of every year indefinitely. If the appropriate discount rate is 8%, then the NPV of this new wilderness campsite is closest to: A) -$50,000 B) -$37,500 C) $37,500 D) $50,000 Answer: C Explanation: C) NPV = -400,000 + $35,000/.08 = 37,500 5) Wyatt oil is considering drilling a new self sustaining oil well at a cost of $1,000,000. This well will produce $100,000 worth of oil during the first year, but as oil is removed from the well the amount of oil produced will decline by 2%, per year forever. If the Wyatt oil's appropriate interest rate is 8%, then the NPV of this oil well is closest to: A) -$250,000 B) $0 C) $250,000 D) $1,000,000 Answer: B Explanation: B) NPV = -1,000,000 + $100,000/(.08 - (-.02)) = $0 4.5 Perpetuities and Annuities 1) 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 = D) One example of a perpetuity is the British government bond called a consol. Answer: C Explanation: C) PV of a perpetuity = 2) 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: B Explanation: B) A perpetuity never ends. 3) 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. Answer: A 4) Which of the following statements regarding growing annuities is FALSE? A) A growing annuity is a stream of N growing cash flows, paid at regular intervals. B) We assume that g < r when using the growing annuity formula. C) PV of a growing annuity = C × D) A growing annuity is like a growing perpetuity that never comes to an end. Answer: D Explanation: D) An annuity does end. 5) Which of the following statements is FALSE? A) The difference between an annuity and a perpetuity is that an annuity ends after some fixed number of payments. B) Most car loans, mortgages, and some bonds are annuities. C) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever. D) An annuity is a stream of N equal cash flows paid at irregular intervals. Answer: D Explanation: D) annuities are paid at regular intervals. 6) 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: A Explanation: A) PV of a growing annuity = C × Use the information for the question(s) below. Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education. Currently, college tuition, books, fees, and other costs, average $12,500 per year. On average, tuition and other costs have historically increased at a rate of 4% per year. 7) Assuming that costs continue to increase an average of 4% per year, tuition and other costs for one year for this student in 18 years when she enters college will be closest to: A) $12,500 B) $21,500 C) $320,568 D) $25,323 Answer: D Explanation: D) FV = PV(1 + i)N = $12,500(1.04)18 = $25,322.71 8) Assuming that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to: A) $97,110 B) $107,532 C) $101,291 D) $50,000 Answer: A Explanation: A) This is a two step problem. Step #1 determine the cost of the first year of college. FV = PV(1 + i)N = $12,500(1.04)18 = $25,322.71 Step #2 figure out the value for four years of college. PV of a growing annuity due = C × (1 + r) 04 (( 1+. 1+.07 ) ) 4 1− = $25,322.71 × (1 + .07) = $97,110.01