Finance review questions topic 3

Larry's Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $26,000 per year forever. Assume the required return on this investment is 7.8 percent. How much will you pay for the policy?

26,000/.078= 333,333.33

For each of the following annuities, calculate the annual cash flow. Cash Flow Present Value $32,200, $29,35086, $156,500,$227,100 Years 6, 8, 18, 25 Interest Rate 8%, 6%, 11%, 10%

Calculator Solution N=6 I/Y=8% PV=-32200 FV=0 PMT= 6,965.36 N=8 I/Y=6 PV=-29,350 FV=0 PMT=4,726.40 N=18 I/Y=11 PV=-156500 FV=0 PMT=20320.41 N=25 I/Y=10% PV=227,100 FV=0 PMT=25,019.17

Find the APR, or stated rate, in each of the following cases Number of Times Compounded: semiannually, monthly, weekly, daily Effective Rate (EAR) 16.00 %, 12.00%, 9.00%, 7.00%

EAR = [1 + (APR/m)]m - 1 EAR = .1600 = [1 + (APR/2)]2 - 1 APR = 2[(1.1600)1/2 - 1]= .1541, or 15.41% EAR = .1200 = [1 + (APR/12)]12 - 1 APR = 12[(1.1200)1/12 - 1]= .1139, or 11.39% EAR = .0900 = [1 + (APR/52)]52 - 1 APR = 52[(1.0900)1/52 - 1]= .0862, 8.62% EAR = .0700 = [1 + (APR/365)]365 - 1 APR = 365[(1.0700)1/365 - 1]= .0677, or 6.77%

Find the EAR in each of the following cases Stated Rate (APR) Number of Times 9.00 % Quarterly % 17.00 Monthly 15.00 Daily 11.00 semiannually

EAR = [1 + (APR/m)]m - 1 EAR = [1 + (.0900/4)]4 - 1 = .0931, or 9.31% EAR = [1 + (.1700/12)]12 - 1 = .1839, or 18.39% EAR = [1 + (.1500/365)]365 - 1 = .1618, or 16.18% EAR = [1 + (.1100/2)]2 - 1 = .1130, or 11.30%

Vandermark Credit Corp. wants to earn an effective annual return on its consumer loans of 17.75 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers?

EAR = [1 + (APR/m)]m - 1 APR = m[(1 + EAR)1/m - 1]APR = 365[(1.1775)1/365 - 1]APR = .1634, or 16.34%

Wells, Inc., has identified an investment project with the following cash flows. YearCash Flow 1 $1,050 2 1,280 3 1,500 4 2,240 a. If the discount rate is 7 percent, what is the future value of these cash flows in Year 4? b. What is the future value at an interest rate of 13 percent? c. What is the future value at an interest rate of 22 percent?

FV = PV(1 + r)t FV@7% = $1,050(1.07)3 + $1,280(1.07)2 + $1,500(1.07) + $2,240 = $6,596.77 FV@13% = $1,050(1.13)3 + $1,280(1.13)2 + $1,500(1.13) + $2,240 = $7,084.47 FV@22% = $1,050(1.22)3 + $1,280(1.22)2 + $1,500(1.22) + $2,240 = $7,881.79

Given the same APR, when the frequency of compounding interest increase, we will have lower EAR. True or False?

False

Given the same number of periods and the same value of payment per period, the higher the interest rate, the higher the present value of annuities? True or False

False

Given the same payment every period, the higher the interest rate, the higher the present value of perpetuities? True or False

False

You're prepared to make monthly payments of $245, beginning at the end of this month, into an account that pays 8 percent interest compounded monthly. How many payments will you have made when your account balance reaches $64,000?

I/Y= 8/12 PV= 0 FV= 64,000 PMT= 245 CPT N=151.78

You want to borrow $69,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,200, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 78-month APR loan?

N=78 PV=69000 PMT=1,200 FV=0 CPT I/Y=.818

What is the future value of $1,730 in 15 years assuming an interest rate of 7 percent compounded semiannually?

N=15x2=30 I/Y=7/2=3.5 PV=-1730 PMT=0 CPT FV= $4,855.75

Mary is going to receive a 37-year annuity of $10,200. Nancy is going to receive a perpetuity of $10,200. If the appropriate interest rate is 10 percent, how much more is Nancy's cash flow worth?

N=37 I/Y=10 FV=0 PMT=10,200 CPTPV=$99,000.35

You want to buy a new sports car from Muscle Motors for $43,800. The contract is in the form of a 60-month annuity due at an APR of 7.05 percent. What will your monthly payment be?

N=60 I/Y=7.05%/12 PV=-43,800 Fv=0 PMT=868.25

You have arranged for a loan on your new car that will require the first payment today. The loan is for $42,500, and the monthly payments are $730. If the loan will be paid off over the next 77 months, what is the APR of the loan?

N=77 PV=42500 PMT=730 FV=0 CPT I/Y=.78 APR = .78%(12) = 9.33%

Larry's Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $34,000 per year forever. A representative for the company tells you the policy costs $590,000. At what discount rate would this be a fair deal?

PV = C/r $590,000 = $34,000/r We can now solve for the interest rate as follows: r = $34,000/$590,000r = .0576, or 5.76%

YearCash Flow 1 $1,090 2 940 3 1,490 4 1,850 A. If the discount rate is 12 percent, what is the present value of these cash flows? b.What is the present value at 15 percent? c.What is the present value at 21 percent?

PV=FV/(1+r)^t a. 1090/1.12+940/1.12^2+1490/1.12^3+1850/1.12^4= 3,958.84 b. 3,696.04 c. 3,246.96

Given the same discount rate, the higher the payment every period, the higher the present value of perpetuity? True or False

True

Given the same number of periods, and the same value of payment per period, the higher the interest rate, the higher the future value of annuities? True or False

True

What is the present value of $3,325 per year, at a discount rate of 8 percent, if the first payment is received 7 years from now and the last payment is received 22 years from now?

Value at t = 6 N=16 I/Y=8 PMT=3325 fV=0 CPT PV=$29,430.80 value today N=6 I/Y=8 PMT=0 FV=$29,430.80 CPT PV=$18,546.40

You have just purchased a new warehouse. To finance the purchase, you've arranged for a 36-year mortgage loan for 80 percent of the $3,360,000 purchase price. The monthly payment on this loan will be $16,900. a. What is the APR on this loan? b.What is the EAR on this loan?

a. N= 36X12 PV= .8(3,360,000) PMT=16,900 FV=0 CPT I/Y=.576 APR = .576%(12) = 6.91% b. And the EAR is: EAR = [1 + (APR/m)]m - 1EAR = (1 + .00576)12 - 1EAR = .0714, or 7.14%

Suppose you just bought an annuity with 11 annual payments of $15,600 at the current interest rate of 11.5 percent per year. a. What is the value of the investment at the current interest rate of 11.5 percent? b. What happens to the value of your investment if interest rates suddenly drop to 6.5 percent? c. What happens to the value of your investment if interest rates suddenly rise to 16.5 percent?

a. N=11 I/Y=11.5 PMT=15,600 FV=0 CPT PV=$94,688.09 b. N=11 I/Y= PMT=15,600 FV=0 CPT PV=$119,949.06 c. N=11 I/Y= PMT=15,600 FV=0 CPT PV=$76,923.44

You've just joined the investment banking firm of Dewey, Cheatum, and Howe. They've offered you two different salary arrangements. You can have $7,000 per month for the next two years, or you can have $5,700 per month for the next two years, along with a $31,000 signing bonus today. Assume the interest rate is 6 percent compounded monthly. a. If you take the first option, $7,000 per month for two years, what is the present value? b.What is the present value of the second option?

a. N=24 I/Y=6/12 PMT=-7000 FV=0 PV=157,940.06 b. N=24 I/Y=6/12 PMT=-5700 FV=0 PV=157,940.06 157,940.06+31,000=159,608.34

Assume you deposit $5,900 at the end of each year into an account paying 11.75 percent interest. a. How much money will you have in the account in 21 years? b. How much will you have if you make deposits for 42 years?

a. PV=0 I/Y=11.75 N=21 PMT=-5900 FV=467,409.74 B. PV=0 I/Y=11.75 N=42 PMT=-5900 FV=5,285,721.62

Consider the following cash flows: YearCash Flow 2 $21,100 3 39,100 5 57,100 Assume an interest rate of 7.9 percent per year. a. If today is Year 0, what is the future value of the cash flows five years from now? b.If today is Year 0, what is the future value of the cash flows ten years from now?

a. FV = PV(1 + r)t FV = $21,100(1.079)3 + $39,100(1.079)2 + $57,100FV = $129,127.98 b. N=5 I/Y=7.9 PV=$129,127.98 PMT=0 CPT FV= $188,854.61

What happens to the future value of an annuity if you increase the rate, r? What happens to the present value?

assuming positive cash flows, the present value will fall and the future value will rise.

As you increase the length of time involved, what happens to the present value of an annuity? What happens to the future value?

present values shrink and future value rises (assuming its positive)

A 9-year annuity of 18 $8,800 semiannual payments will begin 10.5 years from now, with the first payment coming 11 years from now. a. If the discount rate is 12 percent compounded semiannually, what is the value of this annuity nine years and seven years from now? b.What is the value of the annuity today?

t=10.5 N=18 I/Y=12/2 FV=0 PMT=8,800 CPT PV=$95,282.91 a. t=9 N=1.5x2 I/Y=12/2 FV=±$95,282.91 PMT=0 CPT PV=$80,001.37 t=7 N=3.5x2 I/Y=12/2 FV=±$95,282.91 PMT=0 CPT PV=$63,368.58 b. value today N=10.5x2 I/Y=12/2 FV=±$95,282.91 PMT=0 CPT PV=$28,027.98