FIN CH 5,6,7 Test Review
Sophia and Mallory are the same age. At age 25, Sophia invests $6,000 at 7 percent, compounded annually. At age 30, Mallory invests $6,000 at 7 percent, compounded annually. All else constant, when they both reach age 60:
Sophia will have more money than Mallory.
What is the present value of $1,400 a year at a discount rate of 8 percent if the first payment is received 7 years from now and you receive a total of 25 annual payments?
Annuity * ((1-(1+R)^-N)/R = 1400*((1-(1+0.08)^-25)/0.08 = 9417.69
Which one of the following will decrease the net present value of a project?
Increasing the project's initial cost at Time 0
What is the present value of $12,200 to be received 4 years from today if the discount rate is 5 percent?
12200/(1+0.05)^4 = 10036.97
Your aunt has promised to give you $5,000 when you graduate from college. You expect to graduate three years from now. If you speed up your plans to enable you to graduate two years from now, the present value of the promised gift will:
increase
The internal rate of return:
may produce multiple rates of return when cash flows are conventional. **may be wrong**
If a firm accepts Project X it will not be feasible to also accept Project Z because both projects would require the simultaneous and exclusive use of the same piece of machinery. These projects are considered to be:
mutually exclusive.
Javangula Foods is considering two mutually exclusive projects and has determined that the crossover rate for these projects is 12.3 percent. Given this information, you know that:
the project that is acceptable at a discount rate of 12 percent should be rejected at a discount rate of 13 percent.
Javier and Alex plan on retiring 27 years from today. At that time, they plan to have saved the same amount. Javier is depositing $15,000 today at an annual interest rate of 5.2 percent. How will Alex's deposit amount vary from Javier's if Alex also makes a deposit today, but earns an annual interest rate of 6.2 percent? Alex's deposit will need to be ______ than Javier's. (Assume annual compounding on both accounts.)
$3,381.39 less Javier: Accumulated Value at Retirement = Amount deposited * (1+Annual interest rate)^Time to retirement AVR = 15000*(1.052)^27 = 58954.40 Alex: 58954.40=Amount Deposited * 1.062^27 = 11618.61 15000-11618.61=3381.39 less than Duane
Fifteen years ago, you invested $5,000. Today, it is worth $18,250. What annually compounded rate of interest did you earn?
(FV/PV)^(1/n)-1 (18250/5000)^(1/15) - 1 = 0.09014983 or 9.01%
Your credit card company charges you 1.65 percent interest per month. What is the annual percentage rate on your account?
APR = Periodic rate * number of compounding periods in a year EAR = (1+(APR/Number of compounding periods in a year) ^ number of compounding periods in a year -1 APR = 1.65%*12=19.80%
Jonathan invested $6,220 in an account that pays 11 percent simple interest. How much money will he have at the end of 40 years?
Amount of Interest = Principle * Rate * Time = 6220 * 0.11 * 40 = 27368 = 6220 + 27368 = $33588
Which of the following are advantages of the payback method of project analysis?
Liquidity bias; ease of use
Which one of the following methods predicts the amount by which the value of a firm will change if a project is accepted?
Net present value
Today you paid $351,000 for an investment that provides $12,300 a year forever. What rate of return are you earning on this investment? Assume the first payment is in one year.
Rate of Return = Annual inflows/Current Value =12300/351000 =3.50%
Which one of these statements related to growing annuities and perpetuities is correct?
The present value of a growing perpetuity will decrease if the discount rate is increased.
The interest earned on both the initial principal and the interest reinvested from prior periods is called:
compound interest
You plan to invest $1,140 a year for 5 years at a 7 percent annually? How much will you have in 5 years? Assume the first investment is made in one year.
FV = Annuity(1+rate)^time period -1)/rate =1140(1.07)^5-1)/0.07 =6555.84
You are scheduled to receive $14,000 in two years. When you receive it, you will invest it for eight more years at 9.5 percent per year. How much will you have in ten years?
FV = PV (1+r)^n FV = 14000(1.095)^8 FV = 28936.17
Five years from today, you plan to invest $3,100 for 9 additional years at 5.4 percent compounded annually. How much will you have in your account 14 years from today?
FV = PV * (1+rate)^time 3100*(1+0.054)^9=4976.54
What is the present value of $45,000 to be received 50 years from today if the discount rate is 8 percent, compounded annually?
Future Value / (1+Rate)^Time 45000 / (1.08)^50 = 959.46
Paige wants to have $40,000 for a down payment on a house five years from now. She can either deposit one lump sum today or wait one year and deposit a lump sum then. Assume an interest rate of 3.5 percent, compounded annually. How much additional money must she deposit if she waits for one year rather than making the deposit today?
Future Value Required / (1+I)^n 40000/(1+0.035)^5 33678.92667 End of One Year = 40000 / (1.035)^4 = 34858 33678.93-34858=1179
Kathleen invests $109 with Mr. Madoff, her accountant. Mr. Madoff promises that the account will pay 6 percent simple interest each year. How much money will Kathleen have at the end of 4 years?
I = P * R * T I = 109 * 0.06 * 4 = $26.16 Total value = 109 + 26.16 = $135.16
You are comparing two investment options that each pay 6 percent interest compounded annually. Both options will provide you with $12,000 of income. Option A pays $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each. Which one of the following statements is correct given these two investment options? Assume a positive discount rate. (No calculations needed.)
Option B has a higher present value at Time 0.
What is the future value of $2,928 invested for 8 years at 4.5 percent compounded annually?
P * (1+r) ^n 2928*(1+0.045)^8 = 4163.91
Frodo offers to sell Sam an annuity today for $72,600. The annuity pays $5,100 a year and the annual rate of return is 4 percent. How many years does the annuity last if the first payment is in one year? (Do not round intermediate calculations.)
PV = Annuity * Present Value Factor 72600=5100*(1-(1+r)^-n/r) 14.2352=1-1.04^-n/0.04 (1.04)^-n=0.43058 -n log(1.04) = log (0.43058) n = 21.48
Todd will gain access to his inheritance of $12,450 in exactly 2 years. Todd discounts cash at 6 percent annually. What is the minimum amount Todd would accept today in exchange for his inheritance?
PV = FV / (1+ Rate) ^N PV = 12450 / (1+0.06)^2 = 11080.456
Lionel has to pay a penalty for filing his taxes late. The IRS charges 3% in interest for each month the payment is late. Lionel's original tax bill was $2,000, but he now owes $3,404.87. How many years late is his payment?
PV = Future Value/(1+R)^N (1+R)^N = FV/PV (1+0.03)^N = 3404.87/2000 1.03^N = 1.702435 N = 18 **Wrong answer not sure why**
You are scheduled to receive annual payments of $3,600 for each of the next 12 years. The discount rate is 8 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?
PV = PMT * PVIFA (which is 8% , 12) = 3600*7.5361=27130.01 PV in end mode = 3600*(PVIF(8%,0)+PVIFA(8%,11) =3600*8.1390=29300.4 29300.4-27130.01=2170.39
Which one of the following statements related to the internal rate of return (IRR) is correct?
The IRR is equal to the required return when the net present value is equal to zero.
Which one of the following statements correctly defines a time value of money relationship?
Time and present value are inversely related, all else held constant.
Lionel has to pay a penalty for filing his taxes 30 months late. The IRS charges 30% annual interest on late payments. How much does Lionel owe if his original tax bill was $7,000?
Total Tax = 7000*(1+0.30)^2.5 = 13488.28
Nirav just opened a savings account paying 2 percent interest, compounded annually. After four years, the savings account will be worth $5,000. Assume there are no additional deposits or withdrawals. Given this information, Nirav:
could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest.
