Deck 4: The Time Value of Money

Question 1

British Airways Plc plans to set aside investment funds now for replacing 34 of the airline's aging long- haul fleet of Boeing 747s and 767s, which will be delivered 5 years from now. How much will the company need to have in its investment fund now if the cost of the fleet is $1000 million and the company earns a rate of return of 3% per year?

Answer 1

$862,600,000.00

Question 2

What is the effective interest rate per 6 months for a nominal interest rate of 15% per year compounded every 3 months?

Answer 2

0.0764 or 7.64%

Question 3

How much must be deposited each month for 8 months at an interest rate of 5% per month to allow for a single withdrawal of $44,500 at the same time as the last deposit?

Answer 3

$4659.15

Question 4

A U.S. auto maker plans to build two more plants in China as it aims to harness continued growth in Asia. The company estimates that it must make annual investments of $40 million over a 8- year period. How much would the company have to invest now at an interest rate of 3% per year to sufficiently provide for the annual payments, if the first payment will begin 4 years from now?

Question 5

What value of G makes the two series of cash flows described below equivalent at an interest rate of 3% per year, compounded every 3 months?
A: 22 annual deposits in the amount of $400
B: 11 annual deposits in the amount of $400 in the first year, and increasing by $G each year.

Question 6

Acme Corp. plans to expand its relationship with a soft drink manufacturer to make Acme ready- to- drink coffee beverages available in Asia. The company wants to set aside $50 million now in its investment fund for the possible expansion 6 years from now. How much will the company have in its investment account at the end of year 6, if the company earns a rate of return of 8% per year?

Question 7

What value of G makes the two series of cash flows described below equivalent at an interest rate of 18% per year?
A: 14 annual deposits in the amount of $150
B: 7 annual deposits in the amount of $150 in the first year, and increasing by $G each year.

Question 8

Susan made 4 uniform annual deposits of $1800 in a savings account that earned an interest rate of 2% per year. Her last deposit was made 7 years ago. What is the future value of her savings 13 years from now, if she leaves the account untouched?

Question 9

Acme Manufacturing Company is considering purchasing a maintenance contract for its new waste management systems. Acme plans to begin the contract in year 5 and continue through year 10. The cost of the contract is $11,300 per year, increasing by $300 each year. If the company wishes to pre- pay the contract with uniform payments in year 1 through year 5, what is the annual payment that Acme has to pay? Assume Acme's minimum attractive rate of return is 13% per year.

Question 10

Longhorn Fabricators Inc. plans to expand its metals- forming facility over the next 5 years. The company will add 20,000 square feet to its 100,000- square- foot plant as it adds robotic welding units, additional laser technology, and automated loading facilities. Construction at the plant is expected to start by the end of next year. The company expects to pay 5 equal payments of $250,000 every 12 months over the 5 year period. What is the future value of the total improvement cost, if the interest rate is 18% per year, compounded every 12 months?

Question 11

Arian is about to borrow $2350 from his uncle. He has an option to repay the loan at the end of year 5 with 10.75% simple interest per year or with 5% interest per year, compounded annually.
What is the difference of the total interest paid over 5 years between the two options?

Question 12

Orlando International Airport plans to extend passenger capacity of its existing terminal to accommodate its forecasted growth. A new terminal would be needed once the state's busiest airport reached 40 million passengers annually. Based on current growth rates, Orlando International should reach the 40 million mark 11 years from now. The expansion cost is expected to be $400 million. The airport service areas will also need attention. These include passenger security checkpoints, ticketing lines, entering/exiting weaves, terminal ramps, baggage claim, and baggage handling. Improvements in these areas will cost an additional $240 million. How much does the airport need to set aside now to pay for these costs, if the company can earn 10% per year, compounded every 4 months.

Question 13

Drugs, Inc. recently received approval from the Food and Drug Administration for its new supplemental drug application for a 300- milligram tablet of an antiplatelet treatment. The company invested $170 million in the research and development fund for this drug application 7 years ago. What is the present worth of the investment now, if the company achieves a rate of return of 2% per year?

Question 14

Eight energy corporations made plans to increase their combined spending on efficiency programs to $50 million per year for the next 8 years as a response to global warming initiatives set by the government. What is the future worth of total investments at the end of 8 years at an interest rate of 8% per year?

Question 15

Find the equivalent of present worth (t = 0) of a uniform series of $4550 for 8 years, if the payment is made every 12 months, starting 6 years from now. Assume the interest rate is 12% per year, compound continuously.

Question 16

How much would a company have to invest now in order to sufficiently provide for annual payments of $313,000 over a 8- year period? Assume the interest rate is 12% per year.

Question 17

TransAtlantic Petroleum Corp. plans to seek two additional production licenses from the Romanian government in addition to the three production licenses awarded to the company last year. The company estimates the costs to drill, acquire the seismic data, and conduct technical studies for these new fields will be $8.8 billion, 3 years from now. How much will the company need to set aside now for these expenses if the company earns a rate of return of 9% per year?

Question 18

A major defense supplier expects to generate additional revenue from its recently won government contract. The company expects the revenue will be $110 million in the first year and the revenue increasing by $2.5 million each year for the next 4 years. What is the future worth of the total revenue at the end of year 5, if the company's rate of return is 18% per year?

Question 19

A major electronics manufacturer expects to generate additional revenue from its recently won government contract. The company forecasts that the revenue will be $190 million in the first year, but will decline by $2 million every year for the next 3 years. What is the present worth of total revenue at an interest rate of 18% per year?

Question 20

$52,000 was deposited in a savings account 7 years ago, and the account earned interest at the rate of 12% per year. What is the amount of equal annual withdrawals that can be made to completely deplete the fund 7 years from now if the first withdrawal will be made now?

Question 21

What is the amount of equal annual deposits needed in years 7 through 14 to provide for a series of annual withdrawals of $2400 beginning 9 years from now and increasing at the rate of 2% per year through year 19? Assume an interest rate of 5% per year.

Question 22

An Australian- based energy drink manufacturer plans to expand its international markets to the untapped East- Asian region. The company expects that the expansion will bring additional net income of $30 million in the first year of the operation and amounts increasing by $4.5 million for the next 8 years. What is the annual equivalent amount of the net income at an interest rate of 13% per year?

Question 23

Barney's Liquids and Aunt Bee's Lemonade plan to expand their international partnership for the marketing and distribution of ready- to- drink tea products by adding 11 countries to their current markets. If the agreement is reached, operations are expected to begin 2 years from now. The snack and beverage company forecasts that the agreement will bring additional revenue of $80 million in the first year of the operation of the total revenue if the interest rate of 17% per year?

Question 24

Costs for maintaining buildings at an industrial complex over a 13- year period are expected to be $5400 in year 1, increasing at the rate of 15% per year through year 13. At an interest rate of 15% per year, what present worth (at time 0) is equivalent to the series of maintenance costs?

Question 25

How many years will it take for an investment of $A to increase to $8A if the interest rate is 9% per year?

Question 26

A Japanese carmaker plans to expand its production in the United States. The company borrowed $170 million for this expansion at an interest rate of 8% per year. The loan will be repaid in equal payments at the end of each year over a 15- year period. What is the amount of the annual payment?

Question 27

What is the amount of interest earned on $900 for 8 years at 10.5% simple interest per year?

Question 28

Volunteer Pharmaceuticals (VP) wants to set aside money in the R&D fund to seek supplemental drug applications of its two newly developed drugs. Instead of putting away $780 million now, VP plans to set aside $A each year from year 1 through 40. What should the value of A be if VP expects to earn 7% per year for the first 5 years and 2% per year for the remaining years?

Question 29

Upon his employment at the age of 22, Robert began to make a series of equal year- end deposits of $1100 to his retirement fund. After working for 5 years, he is now able to increase his saving. He plans to increase his annual deposits to $2200, starting at the end of next year , and continue his equal deposits of $7400 each year until the age of 60. He expects to retire at the age of 65. How much would his retirement fund be worth at the time of his retirement if it earns a rate of return of 10% per year?

Question 30

Find the 7 uniform annual deposits that can provide a single withdrawal of $38,500, 2 years after the last deposit is made at an interest rate of 5% per year.