Module 4 Time Value of Money Concepts and Calculations Flashcards
An investor wants to have $150,000 available at the end of 15 years. He plans to make equal year-end payments in an investment expected to yield a 10% annual rate of return. What is the approximate annual amount of each of these payments?
A)
$4,721
B)
$4,292
C)
$7,388
D)
$10,000
The answer is $4,721.
END Mode
1, DOWNSHIFT, P/YR
C ALL
150,000, FV
15, DOWNSHIFT, N (15 periods on display)
10, I/YR;
Solve for PMT = –4,721.0665, or $4,721 rounded.
LO 4.1.6
Abdullah needs an income stream equivalent to $50,000 in today’s dollars at the beginning of each year for the next 12 years to maintain his standard of living. He assumes inflation will average 4.5% over the long term and he can earn a 9% compound annual after-tax rate of return on investments. What lump sum does Abdullah need to invest today to fund his income need?
A)
$480,878.04
B)
$455,929.00
C)
$476,445.85
D)
$461,025.81
The answer is $480,878.04.
BEG Mode
1, DOWNSHIFT, P/YR
C ALL
50,000, PMT
[(1.09 ÷ 1.045) − 1] × 100 = 4.3062, I/YR
12, DOWNSHIFT, N (12 periods on display)
Solve for PV = -480,878.0383, or $480,878.04 rounded.
LO 4.2.4
A client wants to save $125,000 to achieve a future goal. He has $26,000 to invest and can invest another $2,500 at the end of each quarter toward his goal. If the investment vehicle selected earns 10% annually, how many years will it take to achieve his goal?
A)
5.87
B)
5.46
C)
6.06
D)
4.34
The answer is 5.87.
END Mode
4, DOWNSHIFT, P/YR
C ALL
10, I/YR
26,000, +/‒, PV
2,500, +/‒, PMT
125,000, FV
Solve for N = 23.4815 ÷ 4 quarters per year = 5.8704, or 5.87 years rounded
LO 4.2.4
Roberto purchased 80 acres of land four years ago to develop a winery. His purchase price was $1,425 an acre. At the end of each of the past four years, he incurred the following expenses or received the following cash payments to develop the vineyard:
Year 1—purchase of plants: $12,450
Year 2—
income from wine tours: $1,295
vineyard management for year: $3,270
Year 3—vineyard management for year: $3,860
Year 4—vineyard management and equipment: $6,300
At the end of the fourth year, Roberto had the property appraised and found that its value had increased to $2,000 per acre. What has been the internal rate of return for this investment over the four-year period?
A)
3.54%
B)
4.03%
C)
3.15%
D)
6.30%
The answer is 4.032%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
CF0: 114,000, +/-
CF1: 12,450, +/-
CF2: 1,975, +/-
CF3: 3,860, +/-
CF4: 153,700
DOWNSHIFT, IRR/YR = 4.032, or 4.03% rounded.
LO 4.3.1
Ellen is considering investing in a piece of equipment for her business. The purchase price is $100,000, and she expects to be able to sell the equipment for $40,000 at the end of five years. During the five-year period, she expects the equipment to increase her annual cash flows by $25,000, $30,000, $20,000, $15,000, and $10,000. What is the internal rate of return (IRR) of this investment?
A)
15.79%
B)
−11.39%
C)
11.39%
D)
8.78%
The answer is 11.39%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
100,000, +/-, CFj (for year 0)
25,000, CFj (year 1)
30,000, CFj (year 2)
20,000, CFj (year 3)
15,000, CFj (year 4)
50,000, CFj (year 5; final annual cash flow of $10,000 plus the anticipated sale price of $40,000); DOWNSHIFT, IRR/YR = 11.3874, or 11.39%..
LO 4.3.1
Today, Bob purchased an investment-grade gold coin for $50,000. He expects the coin to increase in value at a rate of 12% compounded annually for the next five years. How much will the coin be worth at the end of the fifth year if he achieves his expected return?
A)
$89,542.38
B)
$66,911.28
C)
$89,792.82
D)
$88,117.08
The answer is $88,117.08.
END Mode
1, DOWNSHIFT, P/YR
C ALL
50,000, +/‒, PV
12, I/YR
5, DOWNSHIFT, N (5 periods on display)
Solve for FV = 88,117.0842, or $88,117.08 rounded.
LO 4.1.2
Nick purchased 100 shares of a limited partnership for $150 per share. At the end of two years, he sold all the shares for $250 per share. At the end of each year, the investment paid a dividend of $1.50 per share. What was the investment’s internal rate of return (IRR) over the two-year period?
A)
21.82%
B)
19.07%
C)
29.99%
D)
12.45%
The answer is 29.99%.
END Mode
1, DOWNSHIFT, P/YR
C ALL
15,000, +/‒, CFj (year 0)
150, CFj (year 1)
25,150, CFj (year 2); DOWNSHIFT, IRR/YR = 29.9871, or 29.99%.
LO 4.3.1
Phan expects to receive $5,000 at the end of each of the next four years. His opportunity cost is 14% compounded annually. What is this sum worth to Phan today?
A)
$17,165.41
B)
$19,568.56
C)
$14,568.56
D)
$16,608.16
The answer is $14,568.56.
END Mode
1, DOWNSHIFT, P/YR
C ALL
5,000, PMT
14, I/YR
4, DOWNSHIFT, N (4 periods on display)
Solve for PV = -14,568.5615, or $14,568.56 rounded.
LO 4.1.3
Calculate the number of years it will take $2,500 to grow to $25,000, assuming an annual rate of return of 7% (rounded to two decimal places).
A)
34.03
B)
33.65
C)
34.43
D)
35.00
The answer is 34.03.
2,500, +/‒, PV
7, I/YR
25,000, FV
Solve for N = 34.0324 (34.03, rounded)
LO 4.1.5
Fritz has asked his financial adviser how much he would accumulate if he were to start adding $5,000 at the end of each year for the next 20 years to his investment account, which is currently worth $22,450. He anticipates earning an average annual return of 6.5% on his investments. What would Fritz’s investment account be worth in 20 years, assuming he earns this annual rate of return?
A)
$285,851
B)
$308,622
C)
$273,232
D)
$296,773
The answer is $273,232.
END Mode
1, DOWNSHIFT, P/YR
C ALL
22,450, +/-, PV
5,000, +/-, PMT
20, DOWNSHIFT, N (20 periods on display)
6.5, I/YR
Solve for FV = 273,232.3750, or $273,232 rounded.
LO 4.2.1
Pete would like to purchase a boat in 10 years for $40,000. Approximately how much should he invest at the beginning of each quarter to have enough money to purchase the boat if he can earn 6% annual interest, compounded quarterly, on his investment?
A)
$726
B)
$530
C)
$606
D)
$737
The answer is $726.
BEG Mode
4, DOWNSHIFT, P/YR
C ALL
40,000, FV
6, I/YR
10, DOWNSHIFT, N (40 periods on display)
Solve for PMT = −726.1912, or $726 rounded
LO 4.1.6
Juanita deposits $1,000 into an account earning an annual interest rate of 8% compounded monthly. Assuming she makes no withdrawals or additions to this account, approximately how many years will it take for Juanita to double her money?
A)
10.00
B)
8.00
C)
8.69
D)
8.25
The answer is 8.69.
END Mode
12, DOWNSHIFT, P/YR
C ALL
1,000, +/−, PV
2,000, FV
8, I/YR
Solve for N = 104.3183 ÷ 12 months = 8.6932, or 8.69 years rounded.
LO 4.1.5
Andrea wants to invest $2,000 annually at the end of each year into her Roth IRA. How much will she have in her account after 15 years if she can achieve a 9% annual earnings rate?
A)
$33,572
B)
$37,671
C)
$63,069
D)
$58,722
The answer is $58,722.
END Mode
1, DOWNSHIFT, P/YR
C ALL
- PV
2,000, +/−, PMT
9, I/YR
15, DOWNSHIFT, N
Solve for FV = 58,721.8324, or $58,722 rounded.
LO 4.1.2
Calculate the following inflation-adjusted return based on the following rates: 4.5% rate of return, 2% inflation rate.
A)
2.50%
B)
2.45%
C)
2.75%
D)
2.25%
The answer is 2.45%.
[(1.045 ÷ 1.02) ‒ 1] × 100 = 2.4510 (2.45, rounded)
Note: Alternate calculation for this problem would be 1.02, INPUT 1.045, DOWNSHIFT, % CHG
Solve for I/YR = 2.45%
LO 4.2.2
Calculate the following inflation-adjusted return based on the following rates: 7% rate of return, 2.5% inflation rate.
A)
1.04%
B)
2.80%
C)
4.39%
D)
0.36%
The answer is 4.39%. [(1.07 ÷ 1.025) ‒ 1] × 100 = 4.3902 (4.39, rounded)
Note: Alternate calculation for this problem would be 1.025, INPUT
1.07, DOWNSHIFT, % CHG
Solve for I/YR = 4.39%
LO 4.2.2
Liang secures a $350,000 mortgage with a 15-year repayment term and an annual interest rate of 4%. What is the monthly payment on Liang’s mortgage?
A)
$2,580.31
B)
$2,588.91
C)
$2,357.45
D)
$2,625.01
The answer is $2,588.91.
END Mode
12, DOWNSHIFT, P/YR
C ALL
350,000, PV;
15, DOWNSHIFT, N (180 periods on display)
4, I/YR
Solve for PMT = –2,588.9077, or $2,588.91 rounded.
LO 4.2.1
As Jamie Manor approaches retirement, she wants to establish a fund that will provide her with $6,000 per year after retirement to supplement her other income. Assuming that she can earn 5.5% and that she takes interest only from the fund, how much must Jamie have at retirement to provide this income?
A)
$140,099
B)
$109,091
C)
$71,702
D)
$103,600
The answer is $109,091. This is simply a calculation for capitalization of a number. On any calculator, divide the desired income, $6,000, by the decimal equivalent of the expected interest rate, .055. There is nothing in the question indicating a desire to maintain purchasing power. Additionally, when interest only is being taken from the fund, the principal is being retained so that the income will be provided indefinitely.
LO 4.1.1
Catherine expects to receive $95,000 in six years as part of a final settlement of a testamentary trust. How much would this be worth in today’s dollars assuming an 8% after-tax interest rate, compounded annually?
A)
$59,866
B)
$59,604
C)
$58,878
D)
$58,855
The answer is $59,866.
END Mode
1, DOWNSHIFT, P/YR
C ALL
95,000, FV
8, I/YR
6, DOWNSHIFT, N (6 periods on display)
Solve for PV = −59,866.1146, or $59,866 rounded.
LO 4.1.3
What is the inflation adjusted return for a portfolio that has earned 7.8% while the inflation rate has been 1.9%?
A)
5.79%
B)
6.01%
C)
5.90%
D)
5.84%
The answer is 5.79%.
1.019, INPUT
1.078, DOWNSHIFT, % CHG = 5.79%
For a reality check you should make sure the inflation adjusted rate is lower than the simple difference between the rate of return and the inflation rate. The difference between the 7.8% rate of return and 1.9% inflation rate in this example is 5.9%, and the inflation adjusted return of 5.79%, which is less.
LO 4.2.2
Joellen wants to save $500,000 (in today’s dollars) for her retirement, which is 25 years away, by depositing money in an investment at the end of every year using the serial payment method. She assumes she can earn 9% on her investment and that inflation will average 4% over the 25-year savings period. How much will Joellen need to deposit at the end of the second year to meet her goal?
A)
$11,634.87
B)
$10,757.09
C)
$10,326.81
D)
$11,187.37
The answer is $11,634.87.
END Mode
1, DOWNSHIFT, P/YR
C ALL
500,000, FV
[(1.09 ÷ 1.04) − 1 × 100] = 4.8077, I/YR
25, DOWNSHIFT, N (25 periods on display)
Solve for PMT = –10,757.0884
A payment of –10,757.0884 × 1.04 inflation rate = 11,187.3720 (end of 1st year, change sign)
A payment of 11,187.3720 × 1.04 = 11,634.8669, or $11,634.87 (rounded; end of 2nd year).
LO 4.2.3
Bernie and Betty purchased their home eight years ago for $239,500. They made a 20% down payment, and financed the balance using a 30-year mortgage with a 5.15% interest rate. Taxes and insurance increase the payment by $300 per month. What is their outstanding principal balance?
A)
$206,338
B)
$129,524
C)
$164,365
D)
$165,071
The answer is $165,071.
END Mode
12, DOWNSHIFT, P/YR
C ALL
191,600, PV ($239,500, the purchase price, less $47,900, the 20% down payment.)
30, DOWNSHIFT, N (360 periods on display)
5.15, I/YR
Solve for PMT = $1,046.1862
1, INPUT, 96, DOWNSHIFT, AMORT (1 – 96 on display)
Pressing the = key toggles you through amortization totals for months 1 – 96:
Enter = and the principal paid thus far in eight years will display: -26,529.4379
Enter = again and interest paid to date displays:-73,904.4373
Enter = one final time and the remaining principal balance will be displayed: $165,070.5621, rounded to $165,071
LO 4.2.1
Kieran is interested in investing $50,000 in the stock of a new company. The stock will pay no dividends, but Kieran anticipates he will be able to sell the investment for $75,000 in two years. If his required rate of return is 9%, what is the net present value (NPV) of this investment?
A)
$13,126
B)
$113,126
C)
−$13,126
D)
$18,807
The answer is $13,126.
END Mode
1, DOWNSHIFT, P/YR
C ALL
50,000, +/–, CFj (for year 0)
0, CFj (for year 1)
75,000, CFj (for year 2)
9, I/YR; DOWNSHIFT, NPV = 13,125.9995, or $13,126 rounded.
LO 4.3.2
Sam purchased a certificate of deposit yielding 3% annually for $6,000. Today, it matured for $12,004.25. Approximately how many years did Sam own the certificate of deposit (rounded to the nearest 0.00)?
A)
25.55
B)
23.40
C)
24.03
D)
23.46
The answer is 23.46.
END Mode
1, DOWNSHIFT, P/YR
C ALL
3, I/YR
-6,000, PV
12,004.25, FV
Solve for N = 23.4618, or 23.46 rounded.
LO 4.1.5
What is the present value of an investment that would provide the following inflows, assuming that the client’s required compound rate of return is 9%?
End of year Amount
1 $15,000
2 $20,000
3 $22,000
4 $25,000
A)
$65,646.99
B)
$65,433.45
C)
$65,543.90
D)
$65,293.73
The answer is $65,293.73.
END Mode
1, DOWNSHIFT, P/YR
C ALL
0, CFj
15,000, CFj
20,000, CFj
22,000, CFj
25,000, CFj
9, I/YR
DOWNSHIFT, NPV = $65,293.73.
LO 4.3.2