Fin 300 Ch. 6 Liu

Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $6,600, $11,600, and $17,800 over the next three years, respectively. After that time, they feel the business will be worthless. Marko has determined that a rate of return of 13 percent is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.?

$ 27,261.50 PV = $6,600 / (1 + 0.13) + $11,600 / (1 + 0.13)2 + $17,800 / (1 + 0.13)3 = $27,261.50

Island News purchased a piece of property for $1.36 million. The firm paid a down payment of 12 percent in cash and financed the balance. The loan terms require monthly payments for 10 years at an annual percentage rate of 4.75 percent, compounded monthly. What is the amount of each mortgage payment?

$ 12,548.18 PVA = [$1.36m × (1 - .12)] = C × [(1 - {1 / [1 + (.0475 / 12)](10 × 12)}) / (.0475 / 12)] C = $12,548.18

Your car dealer is willing to lease you a new car for $379 a month for 84 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 4.8 percent, what is the current value of the lease?

$ 27,102.04

What is the effective annual rate of 14.9 percent compounded continuously?

16.07 % EAR = e.149 - 1 = .1607, or 16.07 %

Mr. Miser loans money at an annual rate of 15 percent. Interest is compounded daily. What is the actual rate Mr. Miser is charging on his loans?

16.18 % EAR = [1 + (0.15 / 365)]^365 - 1 = .1618 = 16.18 %

Troy will receive $7,500 at the end of Year 2. At the end of the following two years, he will receive $9,000 and $12,500, respectively. What is the future value of these cash flows at the end of Year 5 if the interest rate is 8 percent?

$ 33,445 FV = $7,500 ×1.083 + $9,000 ×1.082 + $12,500 ×1.08 = $33,445

What is the future value of $700 in 21 years assuming an interest rate of 11 percent compounded semiannually?

$ 6,632.87 For this problem, we simply need to find the FV of a lump sum using the equation: FV = PV(1 + r)t It is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get: FV = $700[1 + (0.11/2)]^42 = $6,632.87

You are scheduled to receive annual payments of $10,800 for each of the next 20 years. Your discount rate is 7 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

$ 8,009 APV = $10,800 × {1 - [1 / (1 + 0.07)20]} / 0.07 = $114,415.35 ADUEPV = $114,415.35 × (1 + 0.07) = $122,424.43 Difference = $122,424.43 - $114,415.35 = $8,009.07 = $8,009 (rounded)

Today, you are retiring. You have a total of $289,416 in your retirement savings. You want to withdraw $2,500 at the beginning of every month, starting today and expect to earn 4.6 percent, compounded monthly. How long will it be until you run out of money?

12.71 years PVA Due = $289,416 = $2,500 × [(1 - {1 / [1 + (.046 / 12)]t }) / (.046 / 12)] × [1 + (.046 / 12)] t = 152.518 months, or 12.71 years

Your local pawn shop loans money at an annual rate of 23 percent and compounds interest weekly. What is the actual rate being charged on these loans?

25.8% EAR = [1 + (.23 / 52)]52 - 1 = .2580, or 25.80 percent

Al's obtained a discount loan of $71,000 today that requires a repayment of $90,000, 3 years from today. What is the APR on this loan?

8.23 % $90,000 = $71,000 ×(1 + r)3 r = ($90,000 / $71,000)1/3 - 1 r = .0823, or 8.23%

Your credit card company charges you 1.14 percent per month. What is the annual percentage rate on your account?

3.68 % APR = .0114 × 12 = .1368 =13.68 %

You grandfather invested $20,000 years ago to provide annual payments of $750 a year to his heirs forever. What is the rate of return?

3.75 % r = $750 / $20,000 = .0375, or 3.75 percent

What is the effective annual rate if a bank charges you an APR of 8.25 percent, compounded quarterly?

8.51 % EAR = [1 + (.0825 / 4)]4 - 1 = .0851, or 8.51 percent

The interest rate that is most commonly quoted by a lender is referred to as?

Annual Percentage Rate (APR)

Dinero Bank offers you a five-year loan for $56,000 at an annual interest rate of 6.75 percent. What will your annual loan payment be? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

C = $13,566.58 PVA = C({1 − [1 / (1 + r)t]} / r) $56,000 = C{[1 − (1 / 1.06755)] / .0675} We can now solve this equation for the annuity payment. Doing so, we get: C = $56,000 / 4.12779 C = $13,566.58

Which one of the following statements related to annuities and perpetuities is correct? I. An ordinary annuity is worth more than an annuity due given equal annual cash flows for 10 years at 7 percent interest, compounded annually. II. A perpetuity composed of $100 monthly payments is worth more than an annuity of $100 monthly payments; given equal discount rates. III. Most loans are a form of a perpetuity. IV. The present value of a perpetuity cannot be computed but the future value can. Perpetuities are finite but annuities are not.

II. A perpetuity composed of $100 monthly payments is worth more than an annuity of $100 monthly payments; given equal discount rates.

Which one of the following statements concerning interest rates is correct? I. Savers would prefer annual compounding over monthly compounding given the same annual percentage rate. II. The effective annual rate decreases as the number of compounding periods per year increases. III. The effective annual rate equals the annual percentage rate when interest is compounded annually. IV. Borrowers would prefer monthly compounding over annual compounding given the same annual percentage rate. V. For any positive rate of interest, the annual percentage rate will always exceed the effective annual rate.

III. The effective annual rate equals the annual percentage rate when interest is compounded annually.

You are considering five loan offers. The only significant difference between them is their interest rates. Given the following information, which offer should you accept? (Assume a 365-day year.) Offer A: 6.75 percent APR with daily compounding. Offer B: 6.8 percent APR with monthly compounding. Offer C: 7 percent APR with annual compounding. Offer D: 6.825 percent APR with quarterly compounding. Offer E: 6.85 percent APR with semi-annual compounding.

Offer E Offer A: EAR = [1 + (.0675 / 365)]365 - 1 = .0698, or 6.98 percent Offer B: EAR = [1 + (.068 / 12)]12 - 1 = .0702, or 7.02 percent Offer C: EAR = (1 +.07)1 - 1 = .0700, or 7.00 percent Offer D: EAR = [1 + (.06825 / 4)]4 - 1 = .0700, or 7.00 percent Offer E: EAR = [1 + (.0685 / 2)]2 - 1 = .0697, or 6.97 percent

You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 30 years and the payments will increase by 3.9 percent per year. If the appropriate discount rate is 7.9 percent, what is the present value of your winnings? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

PV = $16,950,607.68 We can use the present value of a growing annuity equation to find the value of your winnings today. Doing so, we find: PV = C{[1 / (r - g)] - [1 / (r - g)] × [(1 + g) / (1 + r)]t} PV = $1,000,000{[1 / (.079 - .039)] - [1 / (.079 - .039)] × [(1 + .039) / (1 + .079)]30} PV = $16,950,607.68

You're prepared to make monthly payments of $260, beginning at the end of this month, into an account that pays 6.7 percent interest compounded monthly. How many payments will you have made when your account balance reaches $17,000? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

T= 55.89 Payments FVA = $17,000 = $260[{[1 + (.067 / 12)]t - 1} / (.067 / 12)] Solving for t, we get: 1.00558t = 1 + [($17,000) / ($260)](.067 / 12) t = ln 1.36506 / ln 1.00558 t = 55.89 payments

Which one of these statements related to growing annuities and perpetuities is correct? I. You can compute the present value of a growing annuity but not a growing perpetuity. II. In computing the present value of a growing annuity, you discount the cash flows using the growth rate as the discount rate. III. The future value of an annuity will decrease if the growth rate is increased. IV. An increase in the rate of growth will decrease the present value of an annuity. V. The present value of a growing perpetuity will decrease if the discount rate is increased. References

V. The present value of a growing perpetuity will decrease if the discount rate is increased.