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CFGB 6102: CORPORATE FINANCE
Exercise Questions (K)
Time Value of Money
You have a credit card with a balance of $18,000. The annual interest rate on the card is 18% compounded monthly, and the minimum payment is $400 per month. If you pay only the minimum payment each month and do not make any new charges on the card, how many years will it take for you to pay off the $18,000 balance?
You are considering purchasing common stock in AMZ Corporation. You anticipate that the company will pay dividends of $5.00 per share next year and $7.50 per share in the following year. You also believe that you can sell the common stock two years from now for $30.00 per share. If you require a 14% rate of return on this investment, what is the maximum price that you would be willing to pay for a share of AMZ common stock?
You have decided to invest $500 in a mutual fund today and make $500 end-of-the-year investments in the fund each year until you retire for 40 years. Assuming an opportunity cost of 12%, what do you estimate that you will have in this account at retirement?
You are planning to deposit $10,000 today into a bank account. Five years from today you expect to withdraw $7,500. If the account pays 5% interest per year, how much will remain in the account eight years from today?
You have borrowed $70,000 to buy a speed boat. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate, compounded monthly. Create an amortization schedule for the first two months of the loan.
Suppose you are 40 years old and plan to retire in exactly 20 years. 21 years from now you will need to withdraw $5,000 per year from a retirement fund to supplement your social security payments. You expect to live to the age of 85. How much money should you place in the retirement fund each year for the next 20 years to reach your retirement goal if you can earn 12% interest per year from the fund?
You have just purchased a car from Friendly Sam. The selling price of the car is $6,500. If you pay $500 down, then your monthly payments are $317.22. The annual interest rate is 24%. How many payments must you make?
An investment will pay $500 in three years, $700 in five years, and $1,000 in nine years. If the opportunity rate is 6%, what is the present value of this investment?
If Sparco, Inc. deposits $150 at the end of each year for the next eight years in an account that pays 5% interest, how much money will Sparco have at the end of eight years?
What is the value (price) of a bond that pays $400 semiannually for 10 years and returns $10,000 at the end of 10 years? The market discount rate is 10% paid semiannually.
Frank Zanca is considering three different investments that his broker has offered to him. The different cash flows are as follows:
End of YearABC13004002300330043003006005300630073008300600
Because Frank has enough savings for only one investment, his broker has proposed the third alternative to be, according to his expertise, the best in town. However, Frank questions his broker and wants to eliminate the present value of each investment. Assuming a 15% discount rate, what is Frank's best alternative?
What is the present value of the following perpetuities?
a. $600 discounted at 7%
b. $450 discounted at 12%
c. $1,000 discounted at 6%
d. $880 discounted at 9%
Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One bond is being offered from Hersheys and will mature in 10 years and pays 12% per year, compounded quarterly. The other alternative is a Mars bond that will mature in 20 years and that pays 12% per year, compounded quarterly. What would be the present value of each bond if the discount rate is 10%?
In order to send your oldest child to law school when the time comes, you want to accumulate $40,000 at the end of 18 years. Assuming that your savings account will pay 6% compounded annually, how much would you have to deposit if:
a. you want to deposit an amount annually at the end of each year?
b. you want to deposit one large lump sum today?
You have a credit card with a balance of $18,000. The annual interest rate on the card is 18% compounded monthly, and the minimum payment is $400 per month. If you pay only the minimum payment each month and do not make any new charges on the card, how many years will it take for you to pay off the $18,000 balance?
Calculator steps:
18,000 PV
-400 PMT
12 I/yr or I
N = Approximately 75 months = 6.25 years
You are considering purchasing common stock in AMZ Corporation. You anticipate that the company will pay dividends of $5.00 per share next year and $7.50 per share in the following year. You also believe that you can sell the common stock two years from now for $30.00 per share. If you require a 14% rate of return on this investment, what is the maximum price that you would be willing to pay for a share of AMZ common stock?
PV = $5.00 PVIF[14%, 1 yr] + ($7.50 + $30.00) PVIF[14%, 2 yr]
= $5.00 (.877) + ($37.50)(.769)
= $33.22
You have decided to invest $500 in a mutual fund today and make $500 end-of-the-year investments in the fund each year until you retire for 40 years. Assuming an opportunity cost of 12%, what do you estimate that you will have in this account at retirement?
Calculator steps:
-500 PV
-500 PMT
40 N
12 I/yr or I
FV = $430,071
You are planning to deposit $10,000 today into a bank account. Five years from today you expect to withdraw $7,500. If the account pays 5% interest per year, how much will remain in the account eight years from today?
FV = $10,000 FVIF[5%, 5 yr]
= $10,000(1.276) = $12,760
Amount to invest in remaining three years = $12,760 - $7,500 = $5,260
FV = $5,260 FVIF[5%, 3 yr]
= $5,260(1.158) = $6,091.08
You have borrowed $70,000 to buy a speed boat. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate, compounded monthly. Create an amortization schedule for the first two months of the loan.
MO Beg PMT Int. Princ. End
1 $70,000 $709.99 $525 $184.99 $69,815.01
2 $69,815.01 $709.99 $523.61 $186.38 $69,628.63
Suppose you are 40 years old and plan to retire in exactly 20 years. 21 years from now you will need to withdraw $5,000 per year from a retirement fund to supplement your social security payments. You expect to live to the age of 85. How much money should you place in the retirement fund each year for the next 20 years to reach your retirement goal if you can earn 12% interest per year from the fund?
Amount in fund at age 60 = $5,000 PVIFA[12%, 25 yr]
= $5,000(7.843) = $39,215
$39,215 = (annual contribution) FVIFA[12%, 20 yr]
$39,215 = (annual contribution)(72.052)
Annual contribution = $39,215/72.052 = $544.26
You have just purchased a car from Friendly Sam. The selling price of the car is $6,500. If you pay $500 down, then your monthly payments are $317.22. The annual interest rate is 24%. How many payments must you make?
$ 6,000 = $317.22 PVIFA[2%, ? periods]
18.914 = PVIFA[2%, ? periods] n = 24 months
An investment will pay $500 in three years, $700 in five years, and $1,000 in nine years. If the opportunity rate is 6%, what is the present value of this investment?
PV = $500(1/(1.06)3) + $700(1/1.06)5) + $1000(1/(1.06)9)
PV = $500(.840) + $700(.747) + $1000(.592)
= $420.00 + $522.90 + $592.00
= $1,534.90
If Sparco, Inc. deposits $150 at the end of each year for the next eight years in an account that pays 5% interest, how much money will Sparco have at the end of eight years?
FV = $150 FVIFA [5%, 8 yr]
FV = $150 (9.549)
= $1,432.35
What is the value (price) of a bond that pays $400 semiannually for 10 years and returns $10,000 at the end of 10 years? The market discount rate is 10% paid semiannually.
Bond value =
= $400 [12.462] + $10,000 [.377]
= $4984.80 + $3,770 = $8,754.80
Frank Zanca is considering three different investments that his broker has offered to him. The different cash flows are as follows:
End of YearABC13004002300330043003006005300630073008300600
Because Frank has enough savings for only one investment, his broker has proposed the third alternative to be, according to his expertise, the best in town. However, Frank questions his broker and wants to eliminate the present value of each investment. Assuming a 15% discount rate, what is Frank's best alternative?
Investment A
PV = $300 PVIFA [15%, 4 yr]
PV = $856.49
Investment B
PV = $300 pymt beginning at the end of the fourth year, 5 years, 15%
= $300 PVIFA [15%, 8 yr] - $300 PVIFA [15%, 3 yr]
= $300 [4.487] - $300 [2.204]
PV = $1,346.2 - $684.97
PV = $661.23
Investment C
PV = ($400, 1 year, 15%) + ($600, 4 years 15%) + ($600, 8 years, 15%)
PV = $348 + $343.05 + $196.14
PV = $887.19
Thus, investment C is the best as it has the highest NPV.
What is the present value of the following perpetuities?
a. $600 discounted at 7%
b. $450 discounted at 12%
c. $1,000 discounted at 6%
d. $880 discounted at 9%
a. PV = $600/.07
PV = $8,571.43
b. PV = $450/.12
PV = $3,750
c. PV = $1,000/.06
PV = $16,666.67
d. PV = $880/.09
PV = $9,777.78
Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One bond is being offered from Hersheys and will mature in 10 years and pays 12% per year, compounded quarterly. The other alternative is a Mars bond that will mature in 20 years and that pays 12% per year, compounded quarterly. What would be the present value of each bond if the discount rate is 10%?
Bond A
PV = $1,000, 10 years, 12% interest compounded quarterly, 10% discount rate
PV = $1,125.51
Bond B
PV = $1,000, 20 years, 12% interest compounded quarterly, 10% discount rate
PV = $1,172.26
In order to send your oldest child to law school when the time comes, you want to accumulate $40,000 at the end of 18 years. Assuming that your savings account will pay 6% compounded annually, how much would you have to deposit if:
a. you want to deposit an amount annually at the end of each year?
b. you want to deposit one large lump sum today?
a. Pymt = $1,294.26
b. Pymt = $14,013.75
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