Financial Management: Problems and Solution

Suppose Manij needs $ 138,000 to buy a new kitchen at the end of 2017. Assume that
Manij uses an account earning 2.45% yearly. What does Manij have to deposit at the beginning of 2012, assuming monthly compounding?
a. 119,152.42
b. 119,162.42
c. 119,172.42
d. 119,182.42
e. None of the above
Solution: The answer is A. FV=-138,000; I/Y=2.45; N=72; C/Y=P/Y=12; CPT PV
2. First Bank of Midesto Medeque pays a 9.45% nominal rate of interest compounded weekly. What is the effective rate of interest?
a. 9.60%
b. 9.70%
c. 9.80%
d. 9.90%
e. None of the above
Solution: The answer is D. ICONV: NOM=9.45; C/Y=52; CPT EFF3. QKL Co. plans a new project that will generate $ 265,000 of cash flow at the end of each year for 7 years and additionally $167,000 at the end of the project. If the continuously compounded rate of interest is 8%, estimate the present value of the cash flows.
a. 1,097,567.12
b. 1,271,062.87
c. 1,515,761.89
d. 1,459,704.54
e. None of the above
Solution: The answer is D.
!"#,!!! !!!
!!∗!.!"
!
!.!"!!
+167,000 ∗ �
!!∗!.!" = 1,459,704.54
4. Sandra decides to set up a retirement fund by depositing $ 525 at the end of each week for 22 years. How much will he have after 22 years, if the interest rate is 2.85%, compounded quarterly?
a. 312,000
b. 833,919.14
c. 834,019.14
d. 834,119.14
e. None of the above
Solution: The answer is C. N=1,144; I/Y=2.85; P/Y=52; C/Y=4; PMT=-525; CPT FV
5. Suppose you deposit $ 50,800 today and your account will accumulate to $ 74,000 in 7 years. What is the nominal annual rate of interest, given monthly compounding?
a. 5.09%
b. 5.19%
c. 5.29%
d. 5.39%
e. None of the above
Solution: The answer is D. PV=-50,800; FV=74,000; N=7; P/Y=1; C/Y=12; CPT I/Y6. Sara decides to set up a retirement fund by depositing $ 18 at the end of each day for 18 years. How much will she have then, if the interest rate is 6.45% compounded weekly and her account starts with $12,000 already deposited?
a. 125,081.90
b. 125,181.90
c. 125,281.90
d. 125,381.90
e. None of the above
Solution: The answer is E. N=6,570; I/Y=6.45; P/Y=365; C/Y=52; PMT=-18; PV=-12,000; CPT
FV=261,567.39
7. Calle Ocho Inc. expectsto pay a dividend of $324,000 at the end of the year and projects a growth in dividends of 6.35 percent per year. If k is 15.75 percent and it expects to grow for another six years, what is the present value of the dividends?
a. 1,541,343.41
b. 1,541,443.41
c. 1,541,543.41
d. 1,541,643.41
e. None of the above
Solution: The answer is D.
!"#,!!!
!.!"#"!!.!"#$
∗ 1−
!!!.!"#$
!!!.!"#"
!
= 1,541,643.41
8. What is present value of $ 135,800 deposited in 21 years if the rates of interest are 8 percent for the first six years, 9 percent for next 6 years and 11 percent for the remaining period? a. 19,937.64
b. 19,947.64
c. 19,957.64
d. 19,967.64
e. None of the above
Solution: The answer is B.
!"#,!""
!.!"!∗!.!"!∗!.!!!
= 19,947.649. You have the choice between two accounts: account A pays 8 % compounded continuously and account B pays 8.16% compounded semiannually. Rounded up to two decimal places, which account offers a better deal? (You must round the approximation after all the computations are done not at an intermediate stage )
a. A
b. B
c. Both are same
d. Cannot be answered because the amount of deposit is not given
e. Cannot be answered because neither the amount of deposit nor the life of the account is given.
Solution: The answer is C. �
!.!"
−1 = 1+
!.!"#$
!
!
−1 = 8.33%
10.ROFLCorporation expects to earn $256,000 at the end of the second year and projects a growth in earnings of 7 percent per year. If k is 8.45 percent, what is the present value of the earnings if the company will be liquidated after twenty yearsfrom now?
a. 4,744,297.28
b. 4,744,397.28
c. 4,744,497.28
d. 4,744,597.28
e. None of the above
Solution: The answer is E.
!"#,!!!
!.!"#$!!.!"
∗ 1−
!!!.!"
!!!.!"#$
!"
∗ 1.0845!!
= 3,673,686.56
11. What is the present value of $120,000 deposited today if the rate of interest is 5% compounded semiannually and you intend to keep that account for five years?
a. 153,610.15
b. 153,710.15
c. 153,810.15
d. 153,910.15
e. None of the above
Solution: The answer is E. The PV is 120,000.12. LOL Inc. expects to earn $768,000 this year and projects a growth rate in earnings of
5.5%/year thereafter (k=4.5%). What is the PV of the earnings if it expects to grow for another 8 years and to have then level earningsforever?
a. 24,497,871.63
b. 24,497,971.63
c. 24,498,071.63
d. 24,498,171.63
e. None of the above
Solution: The answer is B.
768,000
1−
1.055
1.045
!
0.045−0.055 +768,000 ∗
1.055!
0.045 ∗ 1.045!
= 24,497,971.63
13. What is the future value of $73,258 deposited today at the end of 11 years, assuming the rate of interest is 0.8 percent, using simple rate of interest?
a. 79,704.70
b. 79,714.70
c. 79,724.70
d. 79,734.70
e. None of the above
Solution: The answer is A. 73,258 ∗ [1+(0.008)(11)] = 79,704.70
14. You own an oil pipeline that generates $12.6 million cash flow over the next year. The pipeline’s operating costs are negligible and it is expected to last for a very long time.
The interest rate is 5.45% but the volume of oil is expected to decline by 1.85% per year.
What is the PV of the cash flow if it is assumed to last forever?
a. 172.60 million
b. 182.45 million
c. 192.63 million
d. 202.19 million
e. None of the above
Solution: The answer is A.
!".!
!.!"#"! !!.!"#$
= 172.60 �������15. In how many years will $2,750 become $11,000 if k=3.5% simple interest per year?
a. 84 years
b. 86 years
c. 88 years
d. 90 years
e. None of the above
Solution: The answer is B.
!!.!!!
!.!"# !!
!.!"#
= 86
16. Mr. Philip Gonzalez deposits $ 14,051,709.86 today in an account earning 5.85% per year and will withdraw half of the accumulated amount every year for seven years. How much is left after the eighth year?
a. 170,000
b. 171,000
c. 172,000
d. 173,000
e. None of the above
Solution: The answer is D. 14,051,709.86 ∗
!!!.!"#" !
!
!!!
= 173,000
17. Suppose 25 years ago Zophia Wergarra deposited $ 84,600 in an account earning 6.85% yearly. After 7 years she withdrew $34,000. Obtain today’s value, assuming semiannual compounding. a. 341,378.93
b. 341,478.93
c. 341,578.93
d. 341,678.93
e. None of the above
Solution: The answer is A. PV=-84,600; N=7; P/Y=1; C/Y=2; I/Y=6.85; CPT FV; then -34,000 and input as –PV; N=18; CPT FV18. What is the present value of $35,000 deposited at the end of each year for four years, if the simple rate of interest is 5.35%?
a. 123,529.30
b. 123,629.30
c. 123,729.30
d. 123,829.30
e. None of the above
Solution: The answer is D.
!",!!!
!!!.!"#"
+
!",!!!
!!!∗!.!"#"
+
!",!!!
!!!∗!.!"#"
+
!",!!!
!!!∗!.!"#"
= 123,829.30
19. Djenkarlos Kanela will receive $148,000 at end of year 2018. What is its present value at the beginning of 2014 if the rate of interest is 3.45 percent?
a. 124,613.46
b. 124,713.46
c. 124,813.46
d. 124,913.46
e. None of the above
Solution: The answer is D.
!"#,!!!
!!!.!"#$ !
= 124,913.46
20. XKL Co. plans a new project that will generate $ 265,000 of continuous cash flow each year for 7 years and additionally $167,000 at the end of the project. If the continuously compounded rate of interest is 8%, estimate the present value of the cash flows.
a. 1,097,567.12
b. 1,271,062.87
c. 1,515,761.89
d. 1,459,704.54
e. None of the above
Solution: The answer is C.
!"#,!!! !!!
!!∗!.!"
!.!"
+167,000 ∗ �
!!∗!.!" = 1,515,761.8921. You inherited $65,000 from Auntie Paris. What is the maximum amount you can withdraw each year forever if the interest rate is 6.45%?
a. 4,182.5
b. 4,192.5
c. 4,202.5
d. 4,212.5
e. None of the above
Solution: The answer is B. 65,000 ∗ 0.0645 = 4,192.5
22. What is the future value of an annuity of 22 deposits of $ 12,600 at the end of each year with a nominal rate of interest of 12%, compounded continuously, in 25 years?
a. 1,843,222.50
b. 1,843,322.50
c. 1,843,422.50
d. 1,843,522.50
e. None of the above
Solution: The answer is B. !",!"" !
!!∗!.!"
!!
!
!.!"!!
∗ �
!.!"∗!
= 1,843,322.50
23. How many years does it take for an annual payment of $ 1,750 to grow to $ 37,000, assuming k = 3.85%, compounded weekly?
a. 15.50
b. 15.60
c. 15.70
d. 15.80
e. None of the above
Solution: The answer is C. PMT=-1,750; FV=37,000; I/Y=3.85; P/Y=1; C/Y=52; CPT N24. � =
!!
!!!
+
!!(!!!)
(!!!)
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+
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(!!!)
!
+ ⋯+
!!(!!!)
!!!
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a.
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b. !!
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c.
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d.
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e. none of the above
Solution: The answer is E. � =
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, r =
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25. Mr. Strange deposits $66 today and will deposit $6 each day. What is the future value after six days, assuming 6.6% rate of interest compounded daily?
a. 101.89
b. 101.99
c. 102.09
d. 102.19
e. None of the above
Solution: The answer is C. PV=-66; PMT=-6; I/Y=6.6; P/Y=365; C/Y=365; N=6; CPT=FV