FIN 3601 - 2

What is the present value of $12,750 to be received 2 years from today if the discount rate is 6 percent? $7,650.00 $11,347.45 $12,028.30 $10,076.51 $10,931.07

11,347.45 PV = $12,750/1.062 = $11,347.45

You have just started a new job and plan to save $5,150 per year for 37 years until you retire. You will make your first deposit in one year. How much will you have when you retire if you earn an annual interest rate of 9.61 percent? $1,491,025.31 $1,544,276.22 $1,404,184.12 $1,474,230.17 $1,477,133.77

$1,544,276.22 FV = $5,150[1.096137 − 1)/.0961] = $1,544,276.22

You have just leased a car that has monthly payments of $375 for the next 3 years with the first payment due today. If the APR is 7.08 percent compounded monthly, what is the value of the payments today? $12,130.55 $12,202.12 $12,627.07 $11,092.84 $11,792.18

$12,202.12 PV = $375(1.0059)[(1 −1/1.005936) / .0059] = $12,202.12

Retirement Investment Advisors, Inc., has just offered you an annual interest rate of 5.9 percent until you retire in 35 years. You believe that interest rates will increase over the next year and you would be offered 6.5 percent per year one year from today. If you plan to deposit $17,500 into the account either this year or next year, how much more will you have when you retire if you wait one year to make your deposit? $21,575.82 $18,774.53 $30,771.34 $8,458.82 $29,601.04

$18,774.53 FV = $17,500 × 1.05935 = $130,135.76 FV = $17,500 × 1.06534 = $148,910.29 Difference = $148,910.29 − 130,135.76 = $18,774.53

You need to have $31,500 in 9 years. You can earn an annual interest rate of 5 percent for the first 5 years, and 5.6 percent for the next 4 years. How much do you have to deposit today? $18,877.53 $19,290.14 $20,305.18 $19,734.85 $19,847.62

$19,847.62 PV = $31,500/1.0564 = $25,331.15 PV = $25,331.15/1.0505 = $19,847.62

Marko, Inc., is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $5,200, $10,200, and $16,400 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 14 percent is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.? $23,479.51 $21,442.51 $35,139.00 $25,063.24 $31,800.00

$23,479.51 PV = $5,200/(1 + .14) + $10,200/(1.14)2 + $16,400/(1.14)3 = $23,479.51

One year ago, the Jenkins Family Fun Center deposited $5,100 into an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $6,900 to this account. They plan on making a final deposit of $9,100 to the account next year. How much will be available when they are ready to buy the equipment, assuming they earn a rate of return of 7 percent? $25,784.41 $27,345.40 $26,207.95 $24,767.46 $26,447.10

$27,345.40 FV = $5,100 (1 + 0.07)5 + $6,900 (1 + 0.07)4 + $9,100 (1 + 0.07)3 = $27,345.40

You will receive 24 annual payments of $40,500. The first payment will be received 5 years from today and the interest rate is 6.9 percent. What is the value of the payments today? $502,184.51 $335,680.94 $338,907.21 $358,842.93 $370,804.36

$358,842.93 PV = $40,500[(1 −1/1.069024)/.0690] = $468,613.95PV = $468,613.95/1.06904 = $358,842.93

Gerritt wants to buy a car that costs $30,750. The interest rate on his loan is 5.65 percent compounded monthly and the loan is for 7 years. What are his monthly payments? $441.99 $429.27 $466.27 $453.34 $444.07

$444.07 $30,750 = C[1 − (1/(1 + .0565/12)84)/(.0565/12)] C = $444.07

Your grandparents would like to establish a trust fund that will pay you and your heirs $205,000 per year forever with the first payment one year from today. If the trust fund earns an annual return of 4 percent, how much must your grandparents deposit today? $5,857,142.86 $4,730,769.23 $5,125,000.00 $4,270,833.33 $4,484,375.00

$5,125,000.00 PV = $205,000/.04 = $5,125,000.00

You are going to deposit $4,200 in an account that pays .48 percent interest per month. How much will you have in 5 years? $5,557.21 $5,603.52 $5,597.92 $5,571.18 $5,624.79

$5,597.92 FV = $4,200 × 1.004860 = $5,597.92

Beatrice invests $1,370 in an account that pays 5 percent simple interest. How much more could she have earned over a 6-year period if the interest had been compounded annually? $32.51 $39.01 $329.59 $22.64 $54.93

$54.93 Balance Year 6 with simple interest = $1,370 + ($1,370 × 0.05 × 6) = $1,781.00Balance Year 6 with compound interest = $1,370 × 1.056 = $1,835.93Additional interest = $1,835.93 - $1,781.00 = $54.93

A project that will last for 9 years is expected to have equal annual cash flows of $103,600. If the required return is 8.5 percent, what maximum initial investment would make the project acceptable? $1,321,028.84 $633,934.89 $545,271.40 $608,679.41 $584,219.36

$633,934.89 NPV = 0 = Time 0 cash flow + $103,600(PVIFA8.5%, 9)Time 0 cash flow = $633,934.89

A project with an initial investment of $449,300 will generate equal annual cash flows over its 10-year life. The project has a required return of 8.9 percent. What is the minimum annual cash flow required to accept the project? $64,435.34 $74,638.31 $69,702.11 $66,657.24 $79,659.56

$69,702.11 NPV = 0 = −$449,300 + C(PVIFA8.9%, 10)C = $69,702.11

Your parents are giving you $205 a month for 4 years while you are in college. At an interest rate of .48 percent per month, what are these payments worth to you when you first start college? $8,331.50 $8,607.09 $8,477.66 $8,770.00 $11,036.25

$8,770.00 PV = $205[(1 −1/1.00484×12)/.0048] = $8,770.00

Five years from today, you plan to invest $4,900 for 8 additional years at 7.8 percent compounded annually. How much will you have in your account 13 years from today? $7,133.29 $9,322.51 $8,936.06 $9,439.74 $13,008.88

$8,936.06 FV = $4,900 × 1.0788 = $8,936.06

A small business has determined that the machinery they currently use will wear out in 16 years. To replace the new machine when it wears out, the company wants to establish a savings account today. If the interest rate on the account is 1.8 percent per quarter and the cost of the machinery will be $295,000, how much will the company have to deposit today? $95,436.95 $221,746.91 $96,274.12 $96,985.20 $94,181.20

$94,181.20 PV = $295,000/1.01816×4 = $94,181.20

You expect to receive a payout from a trust fund in 3 years. The payout will be for $13,400. You plan to invest the money at an annual rate of 5.3 percent until the account is worth $22,600. How many years do you have to wait from today? 11.66 years 9.84 years 10.12 years 13.12 years 11.81 years

13.12 Years $22,600 = $13,400(1.053)tt = 10.12 years Years to wait = 10.12 + 3 = 13.12 years

What is the effective annual rate for an APR of 16.20 percent compounded monthly? 17.46% 17.33% 18.33% 16.35% 17.21%

17.46% EAR = (1 + .1620/12)12 - 1 = .1746, or 17.46%

Mountain Frost is considering a new project with an initial cost of $180,000. The equipment will be depreciated on a straight-line basis to a zero book value over the four-year life of the project. The projected net income for each year is $19,500, $20,400, $24,600, and $16,400, respectively. What is the average accounting return? 20.60% 16.85% 11.24% 22.47% 24.08%

22.47% AAR = [$19,500 + 20,400 + 24,600 + 16,400)/4]/[$180,000 + 0)/2]AAR = .2247, or 22.47%

You have just deposited $9,500 into an account that promises to pay you an annual interest rate of 6.2 percent each year for the next 8 years. You will leave the money invested in the account and 20 years from today, you need to have $27,940 in the account. What annual interest rate must you earn over the last 12 years to accomplish this goal? 4.64% 4.71% 5.74% 5.11% 4.08%

5.11% FV = $9,500 × 1.0628 = $15,371.62 $27,940 = $15,371.62(1 + r)12r = .0511, or 5.11%

One of your customers has just made a purchase in the amount of $14,400. You have agreed to payments of $305 per month and will charge a monthly interest rate of 0.93 percent. How many months will it take for the account to be paid off? 47.21 months 67.26 months 39.32 months 62.46 months 58.29 months

62.46 months $14,400 = $305[(1 − 1/1.0093t) / .0093] t = 62.46 months

When your father was born 51 years ago, his grandparents deposited $275 in an account for him. Today, that account is worth $15,000. What was the annual rate of return on this account? 7.83 percent 8.16 percent 6.09 percent 8.97 percent 7.61 percent

8.16 percent $15,000 = $275(1 + r)51 r = ($15,000/$275)1/51 − 1 r = .0816, or 8.16%