Finance Exam 1 Ch 6
Assume that you borrow $100,000 today for 30 years at 5% per year. How much will you have to pay every year to repay the loan?
$6,505.14 This is a PV of annuity problem, in which you have to find the PMT CLR TVM 100,000 PV, 30 N, 5 I/Y, CPT PMT PMT = -6,505.14
You invest the following cash flow into an account. Assuming a 6% annual interest rate, what is that cash flow worth at time 0? Time // CF 0 0 1 $3,000 2 $2,000 3 $3,500 4 $3,500
$10,321.18 This is a multiple uneven cash flow. You have to find its PV. CF CLR WORK CFo = 0 scroll down C01 = 3,000 ENTER scroll down F01 = 1 scroll down C02 = 2,000 ENTER scroll down F02 = 1 scroll down C03 = 3,500 ENTER scroll down F03 = 2 ENTER NPV I = 6 ENTER scroll down NPV = CPT NPV = 10,321.18
You invest the following cash flow into an account. Assuming a 10% annual interest rate, what is the future value of this cash flow at time 4? Time // CF 0 -$500 1 $1,000 2 $3,000 3 $4,500 4 $5,500
$14,678.95 This is a multiple uneven cash flow. You have to find its PV first and then its FV! Step 1: CF CLR WORK CFo = 500 +/- ENTER scroll down C01 = 1,000 ENTER scroll down F01 = 1 scroll down C02 = 3,000 ENTER scroll down F02 = 1 scroll down C03 = 4,500 ENTER scroll down F03 = 1 scroll down C04 = 5,500 ENTER scroll down F04 = 1 NPV I = 10 ENTER scroll down NPV = CPT NPV = 10,025.92 Step 2: CLR TVM 10,025.92 PV, 4 N, 10 I/Y, CPT FV FV = -14,678.95
Assuming that you can earn a 5% annual return. What amount of money do you have to deposit into an account so that you can withdraw 100,000 per year indefinitely? be able to solve for the missing third variable, given 2 variables in a . perpetuity
$2,000,000 Use the PV of perpetuity formula: PV of perpetuity = C/r = $100,000/.05 = $2,000,000
You invest $200 each month for 10 years. If the APR under monthly compounding is 9%, how much money will you end up with?
$38,702.86 This is a FV of annuity problem, in which you have to find the future value (FV). The frequency of the annuity is "monthly", so enter the time in months and the rate as a monthly effective rate. CLR TVM 200 PMT, 10 x 12 = 120 N, 9/12 = .75 I/Y, CPT FV FV = - 38,702.86
You borrow $100,000 for 30 years to buy your house. What are the monthly payments you have to make at the BEGINNING of each month to repay your loan fully if the APR under monthly compounding is 4.5%?
$504.79 This is a PV of annuity DUE problem, in which you have to find the payments (PMT). The frequency of the annuity is "monthly", so enter the time in months and the rate as a monthly effective rate. Since this is an annuity DUE, set your calculator into the BGN mode. 2nd PMT, 2nd ENTER, 2nd QUIT. CLR TVM 100,000 PV, 30 x 12 = 360 N, 4.5/12 = .375 I/Y, CPT PMT PMT = -504.79 Note: when you are done, make sure you set your calculator back into the regular END mode! 2nd PMT, 2nd ENTER, 2nd QUIT.
Paradise, Inc., has identified an investment project with the following cash flows. Year // Cash Flow 1 . $525 2 . 825 3 . 1,150 4 . 1,275 (a) If the discount rate is 8 percent, what is the future value of these cash flows in year 4? (b) What is the future value at a discount rate of 20 percent? (c) What is the future value at discount rate of 28 percent?
(a) If the discount rate is 8 percent, what is the future value of these cash flows in year 4? 4,140.63 (b) What is the future value at a discount rate of 20 percent? 4,750.20 (c) What is the future value at discount rate of 28 percent? 5,199.68 Explanation (a)To solve this problem, we must find the FV of each cash flow and add them. To find the FV of a lump sum, we use:FV = PV(1 + r)t FV@8% = $525(1.08)3 + $825(1.08)2 + $1,150(1.08) + $1,275 = $4,140.63 OR use your financial calculator: Note, you must go through 2 steps: first, find the NPV or present value of this multiple uneven cash flow at time 0. Second, then find the future value of this NPV at time 4, using your TVM keys. This second calculation is a "simple cash flow" calculation. Step 1: CF CLR WORK CF0 = 0 ENTER ↓ (enter a zero since there is no time 0 cash flow given) C01 = enter the first different cash flow from the time 0 cash flow 525 and hit ENTER ↓ F01 = enter the frequency with which the first different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C02 = enter the second different cash flow from the time 0 cash flow 825 and hit ENTER ↓ F02 = enter the frequency with which the second different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C03 = enter the third different cash flow from the time 0 cash flow 1,150 and hit ENTER ↓ F03 = enter the frequency with which the third different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C04 = enter the fourth different cash flow from the time 0 cash flow 1,275 and hit ENTER ↓ F04 = enter the frequency with which the fourth different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ NPV I = enter the interest rate 8 and hit ENTER ↓ NPV = CPT Step 2: CLR TVM The answer you just found for the NPV is the PV 4 N the interest rate 8 I/Y CPT FV (b)FV = PV(1 + r)t FV@20% = $525(1.20)3 + $825(1.20)2 + $1,150(1.20) + $1,275 = $4,750.20 OR use your financial calculator: Note, you must go through 2 steps: first, find the NPV or present value of this multiple uneven cash flow at time 0. Second, then find the future value of this NPV at time 4, using your TVM keys. This second calculation is a "simple cash flow" calculation. Step 1: CF CLR WORK CF0 = 0 ENTER ↓ (enter a zero since there is no time 0 cash flow given) C01 = enter the first different cash flow from the time 0 cash flow 525 and hit ENTER ↓ F01 = enter the frequency with which the first different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C02 = enter the second different cash flow from the time 0 cash flow 825 and hit ENTER ↓ F02 = enter the frequency with which the second different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C03 = enter the third different cash flow from the time 0 cash flow 1,150 and hit ENTER ↓ F03 = enter the frequency with which the third different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C04 = enter the fourth different cash flow from the time 0 cash flow 1,275 and hit ENTER ↓ F04 = enter the frequency with which the fourth different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ NPV I = enter the interest rate 20 and hit ENTER ↓ NPV = CPT Step 2: CLR TVM The answer you just found for the NPV is the PV 4 N the interest rate 20 I/Y CPT FV (c)FV = PV(1 + r)t FV@28% = $525(1.28)3 + $825(1.28)2 + $1,150(1.28) + $1,275 = $5,199.68 OR use your financial calculator: Note, you must go through 2 steps: first, find the NPV or present value of this multiple uneven cash flow at time 0. Second, then find the future value of this NPV at time 4, using your TVM keys. This second calculation is a "simple cash flow" calculation. Step 1: CF CLR WORK CF0 = 0 ENTER ↓ (enter a zero since there is no time 0 cash flow given) C01 = enter the first different cash flow from the time 0 cash flow 525 and hit ENTER ↓ F01 = enter the frequency with which the first different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C02 = enter the second different cash flow from the time 0 cash flow 825 and hit ENTER ↓ F02 = enter the frequency with which the second different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C03 = enter the third different cash flow from the time 0 cash flow 1,150 and hit ENTER ↓ F03 = enter the frequency with which the third different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C04 = enter the fourth different cash flow from the time 0 cash flow 1,275 and hit ENTER ↓ F04 = enter the frequency with which the fourth different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ NPV I = enter the interest rate 28 and hit ENTER ↓ NPV = CPT Step 2: CLR TVM The answer you just found for the NPV is the PV 4 N the interest rate 28 I/Y CPT FV
Seaborn Co. has identified an investment project with the following cash flows. Year // Cash Flow 1 . $750 2 . 1,050 3 . 1,320 4 . 1,120 (a)If the discount rate is 12 percent, what is the present value of these cash flows? (b) What is the present value at 18 percent? (c)What is the present value at 27 percent?
(a) If the discount rate is 12 percent, what is the present value of these cash flows? 3,158.03 (b) What is the present value at 18 percent? 2,770.76 (c)What is the present value at 27 percent? 2,316.49 Explanation (a) To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use: PV = FV/(1 + r)t PV@12% = $750/1.12 + $1,050/1.122 + $1,320/1.123 + $1,120/1.124 = $3,158.03 or use the financial calculator: CF CLR WORK CF0 = 0 ENTER ↓ (enter a zero since there is no time 0 cash flow given) C01 = enter the first different cash flow from the time 0 cash flow 750 and hit ENTER ↓ F01 = enter the frequency with which the first different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C02 = enter the second different cash flow from the time 0 cash flow 1,050 and hit ENTER ↓ F02 = enter the frequency with which the second different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C03 = enter the third different cash flow from the time 0 cash flow 1,320 and hit ENTER ↓ F03 = enter the frequency with which the third different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C04 = enter the fourth different cash flow from the time 0 cash flow 1,120 and hit ENTER ↓ F04 = enter the frequency with which the fourth different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ NPV I = enter the interest rate 12 and hit ENTER ↓ NPV = CPT You will see the answer for the NPV! (b) PV = FV/(1 + r)t PV@18% = $750/1.18 + $1,050/1.182 + $1,320/1.183 + $1,120/1.184 = $2,770.76 or use the financial calculator: CF CLR WORK CF0 = 0 ENTER ↓ (enter a zero since there is no time 0 cash flow given) C01 = enter the first different cash flow from the time 0 cash flow 750 and hit ENTER ↓ F01 = enter the frequency with which the first different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C02 = enter the second different cash flow from the time 0 cash flow 1,050 and hit ENTER ↓ F02 = enter the frequency with which the second different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C03 = enter the third different cash flow from the time 0 cash flow 1,320 and hit ENTER ↓ F03 = enter the frequency with which the third different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C04 = enter the fourth different cash flow from the time 0 cash flow 1,120 and hit ENTER ↓ F04 = enter the frequency with which the fourth different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ NPV I = enter the interest rate 18 and hit ENTER ↓ NPV = CPT You will see the answer for the NPV! (c) PV = FV/(1 + r)t PV@27% = $750/1.27 + $1,050/1.272 + $1,320/1.273 + $1,120/1.274 = $2,316.49 or use the financial calculator: CF CLR WORK CF0 = 0 ENTER ↓ (enter a zero since there is no time 0 cash flow given) C01 = enter the first different cash flow from the time 0 cash flow 750 and hit ENTER ↓ F01 = enter the frequency with which the first different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C02 = enter the second different cash flow from the time 0 cash flow 1,050 and hit ENTER ↓ F02 = enter the frequency with which the second different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C03 = enter the third different cash flow from the time 0 cash flow 1,320 and hit ENTER ↓ F03 = enter the frequency with which the third different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ C04 = enter the fourth different cash flow from the time 0 cash flow 1,120 and hit ENTER ↓ F04 = enter the frequency with which the fourth different cash flow from the time 0 cash flow occurs, 1, and hit ENTER ↓ NPV I = enter the interest rate 27 and hit ENTER ↓ NPV = CPT You will see the answer for the NPV!
Calculate PV and FV of multiple cash flows
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remember that the PMT & PV (or PMT & FV) have the opposite sign in an annuity calculation
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the settings in your calculator should be P/Y = 1 and C/Y = 1
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watch out for the way the rates are given, never use a quoted rate, always use an effective rate
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You invest $1,000 each month for 48 months and end up with $54,000. At what monthly interest rate did you invest the money? given 3 variables, calculate the 4th missing variable in a FV of annuity problem
.4926% This is a FV of annuity problem, in which you have to find the interest rate (I/Y) CLR TVM 1,000 PMT, 48 N, 54,000 +/- FV, CPT I/Y I/Y = .4926 (in percent)
What is the effective monthly interest rate if the APR is 15% under monthly compounding?What is the effective monthly interest rate if the APR is 15% under monthly compounding?
1.25% Take the APR and divide it by m, where m is the number of compounding periods per year. Effective monthly rate = .15/12 = .0125
Convert an EAR of 8% into an APR with semi-annual compounding. The APR is EAR & APR (or quoted annual rate), convert one into the other
7.85% Since you are converting one "annual" into the other "annual" rate, you can use the ICONV function. 2nd, 2, NOM = , scroll down, EFF = 8 enter, scroll down, C/Y =2 enter, scroll down, NOM = CPT. NOM = 7.85 (in percent). This is the APR under semi-annual compounding. Or you can use the following formula: 1 + EAR = (1+APR/m)^m 1 .08 = [1+APR/2)^2 ] 1.08 ^ 1/2 = 1+ APR/2 1.03923 = 1+ APR/2 (subtract 1 from both sides) .03923 = APR/2 (multiply both sides times 2) .07846 or 7.85% = APR
What is the highest possible effective annual interest rate a bank can charge under continuous compounding if it quotes the rate as 9% APR?
9.42% Take the natural number e and raise it to the power of the APR, then subtract 1. EAR = (e ^ APR) - 1 = (e ^ .09) -1 = .0942 Note: on your calculator, type in .09, then 2nd, then the LN key, then "- 1" , and "=".
Interest Only Loan
A loan that only requires the payment of interest for a stated period of time with the principal due at the end of the term. a loan that calls for periodic interest payments and a lump sum principal payment?
Amortized Loan
Either equal or unequal principal payments over the life of the loan. Requires that each loan payment pays down at least some of the principal amount. a loan that is repaid in equal payments over its life an annuity for which the total principal amount borrowed is repaid during the life of the loan
perpetuity
a state of infinite or indefinitely long duration a constant cash flow at regular intervals that goes on forever Unending equal payments paid at equal time intervals.
Regular Annuity
an annuity in which the payments occur at the end of each period
annuity due
an annuity whose payments occur at the beginning of each period
