Chapter 6 Review Questions Part 1

Theresa adds $1,500 to her savings account on the first day of each year. Marcus adds $1,500 to his savings account on the last day of each year. They both earn 6.5 percent annual interest. What is the difference in their savings account balances at the end of 35 years? A) $12,093.38 B) $12,113.33 C) $12,127.04 D) $12,211.12 E) $12,219.46

A Explanation: FVADue = $1,500[(1.06535 − 1)/.065](1.065) FVADue = $198,145.42 FVA = $1,500[(1.06535 − 1)/.065] FVA = $186,052.04 Difference = $198,145.42 − 186,052.04 Difference = $12,093.38 Difficulty: 2 Medium

Your parents have made you two offers. The first offer includes annual gifts of $5,000, $6,000, and $8,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 6.2 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer? A) $16,707.06 B) $16,407.78 C) $16,360.42 D) $17,709.48 E) $17,856.42

A Explanation: PV = $5,000/1.062 + $6,000/1.0622 + $8,000/1.0623 PV = $16,707.06

Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $218,000, $224,000, and $238,000 over the next three years, respectively. After that time, they feel the business will be worthless. If the desired rate of return is 14.5 percent, what is the maximum Southern Tours should pay today to acquire Holiday Vacations? A) $519,799.59 B) $538,615.08 C) $545,920.61 D) $595,170.53 E) $538,407.71

A Explanation: PVA = $218,000/1.145 + $224,000/1.1452 + $238,000/1.1453 PV = $519,799.59

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

B

You are the recipient of a gift that will pay you $25,000 one year from now and every year thereafter for the following 24 years. The payments will increase in value by 2.5 percent each year. If the appropriate discount rate is 8.5 percent, what is the present value of this gift? A) $416,667 B) $316,172 C) $409,613 D) $311,406 E) $386,101

B Explanation: GAPV = $25,000({1 − [(1.025)/(1.085)]25}/(.085 − .025)) GAPV = $316,172

What is the future value of $8,500 a year for 40 years at 10.8 percent interest, compounded annually? A) $3,278,406.16 B) $4,681,062.12 C) $2,711,414.14 D) $3,989,476.67 E) $4,021,223.33

B Explanation: FVA = $8,500[(1.10840 − 1)/.108] FVA = $4,681,062.12

A perpetuity is defined as: A) a limited number of equal payments paid in even time increments. B) payments of equal amounts that are paid irregularly but indefinitely. C) varying amounts that are paid at even intervals forever. D) unending equal payments paid at equal time intervals. E) unending equal payments paid at either equal or unequal time intervals

D

One year ago, JK Mfg. deposited $12,000 in an investment account for the purpose of buying new equipment four years from today. Today, it is adding another $15,000 to this account. The company plans on making a final deposit of $10,000 to the account one year from today. How much cash will be available when the company is ready to buy the equipment assuming an interest rate of 5.5 percent? A) $43,609.77 B) $45,208.61 C) $44,007.50 D) $46,008.30 E) $47,138.09

D Explanation: FV = $12,000(1.0555) + $15,000(1.0554) + $10,000(1.0553) FV = $46,008.30

You just settled an insurance claim that calls for increasing payments over a 10-year period. The first payment will be paid one year from now in the amount of $5,000. The following payments will increase by 3.5 percent annually. What is the value of this settlement to you today if you can earn 6.5 percent on your investments? A) $42,023.05 B) $36,408.28 C) $34,141.14 D) $41,422.89 E) $38,008.16

D Explanation: GAPV = $5,000{[1 − (1.035/1.065)10]/(.065 − .035)} GAPV = $41,422.89

You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional guaranteed $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why? A) You should accept the $89,500 today because it has the higher net present value. B) You should accept the $89,500 today because it has the lower future value. C) You should accept the first offer as it is a lump sum payment. D) You should accept the second offer because it has the larger net present value. E) It does not matter which offer you accept as they are equally valuable.

D Explanation: Offer A: PV = $89,500 Offer B: PV = $35,000 + $70,000/1.1152 PV = $91,305.17

Project A has cash flows of $4,000, $3,000, $0, and $3,000 for Years 1 to 4, respectively. Project B has cash flows of $2,000, $3,000, $2,000, and $3,000 for Years 1 to 4, respectively. Which one of the following statements is correct assuming the discount rate is positive? (No calculations needed) A) The cash flows for Project B are an annuity, but those of Project A are not. B) Both sets of cash flows have equal present values as of Time 0. C) The present value at Time 0 of the final cash flow for Project A will be discounted using an exponent of three. D) Both projects have equal values at any point in time since they both pay the same total amount. E) Project B is worth less today than Project A.

E

You are comparing two annuities that offer regular payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities? A) These annuities have equal present values but unequal future values. B) These two annuities have both equal present and equal future values. C) Annuity B is an annuity due. D) Annuity A has a smaller future value than annuity B. E) Annuity B has a smaller present value than annuity A.

E

A proposed project has cash flows of $2,000, $?, $1,750, and $1,250 at the end of Years 1 to 4. The discount rate is 7.2 percent and the present value of the four cash flows is $6,669.25. What is the value of the Year 2 cash flow? A) $2,450 B) $2,750 C) $2,500 D) $2,250 E) $2,800

E Explanation: PVCF2 = $6,669.25 − $2,000/1.072 − $1,750/1.0723 − $1,250/1.0724 PVCF2 = $2,436.52 CF2 = $2,436.52(1.0722) CF2 = $2,800