chapter 1 spreadsheet basics - leeds school of …leeds-faculty.colorado.edu/donchez/fnce...

CHAPTER 7: THE TIME VALUE OF MONEY

Instructor’s Manual Problem Set

1. Using the Retirement Worksheet example (Exhibit 7-8) from Chapter 7 in the text, calculate the following:

a. Assume that your employer will raise your annual wage every year by at least the rate of inflation so that your retirement savings can also increase proportionally. Use the formula of the future value of a graduated annuity to determine the first year of required annual investment.

Worksheet:

Formulas:

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CHAPTER 7: THE TIME VALUE OF MONEYIM Problem Set & Solutions

b. To illustrate the importance of the return on your investment, set us a scenario analysis that shows your investment required today, the annual investment required, and the first annual investment required considering savings as graduate annuities. Assume four scenarios where your rate of return before retirement is 5%, 7%, 10%, and 17%. What these results suggest you about the importance of financial literacy?

Possible Answer: The higher the average rate of return, the lower your savings and the greater the probability that you will be able of keep your standard of living at retirement. Of course, only knowledgeable investors can achieve high rates of return according to the investment horizon and their particular financial goals.

c. To illustrate the impact of time, repeat the same scenario analysis as in part b but assuming that the number of years until retirement is 20, 30 and 40 with the corresponding years in retirement of 30, 20 and 15 respectively. What these results suggest you about your probable age for retirement?

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Possible Answer: The results clearly suggest that the longer you invest, the more you can save for retirement.

d. To illustrate the impact of the economy in the whole process, repeat the same scenario analysis as in part b but assuming that the rate of inflation gets out of control, so you will consider four scenarios with 7%, 5%, 3%, and 2% rate of inflation. What these results suggest you the impact of the monetary policy in your retirement plans?

Possible Answer: The results clearly show the significant impact of the monetary policy at personal level. Whether or not you will retire comfortably will depend primarily on you, but also in the right or wrong monetary policy decisions of the Federal Reserve.

2. You are planning to buy a new house. You currently have $15K and your bank told you that you would need a 15% down payment plus an additional 4% in closing costs. If the house that you want to buy costs about $150K and you can make a 7% annual return on your investment, determine the following:

a. When you will have enough money for the down payment and closing costs assuming that the $15K is the only investment that you make?

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Worksheet:

Formulas:

b. You decided that you want to buy that house in 3 years. How much do you need to save every month to achieve your goal?

Worksheet:

Formulas:

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c. Assume that five years later the house still has the same price and that you can get a 15-year mortgage from your bank at a fixed rate of 4.5%, what will be the monthly payments of the loan? How much you have to pay the bank every year? What is the total interest over the term of the loan? How much do you pay on interest and principal the first monthly payment? How much in the 50th month? (Hint: use the IPMT and PPMT functions)

Worksheet:

Formulas:

d. If the inflation rate during the 3-year period that you plan to save is 3%, how this would affect your monthly savings?

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Worksheet:

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e. How the assumptions on part d will affect the results on part c?

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Worksheet:

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3. You want to buy a house, but you still need to pay your car loan of $15,000 over the next 3 years. Your annual income is $50,000 and the bank estimates that your monthly mortgage payments should not represent more than 28% of your monthly income. You have decided to use that percentage of your current income to repay your car loan and to save for the down payment in the house. In this way you will adjust your current monthly expenses to be ready to make the same monthly payments for 30 years. You estimate that you can get a fixed interest rate of 6.5% on a 15-year mortgage. Closing mortgage costs are estimated to be 3% of the loan value and you can invest at an average rate of 5%. If the interest on the automobile loan is 8%, determine the following:

a. If you decide to repay your car loan and invest the rest for the down payment at the same time, how much money will the bank loan you in five years? How much can you offer for the house?

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Worksheet:

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b. Is there any change in your answers for part “a” if you decide to pay off the car before you begin to investment for the down payment?

Worksheet:

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c. Assume that your annual income will increase by at least an average rate of inflation of 3%, but that you keep constant the dollar amount representing the 28% of your initial annual income as your target for car payments and savings. How much money will the bank loan you in four years using your new annual income at that time? How much can you offer for the house?

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d. Is there any difference in your answers for part “c” if you decide to pay off the car before you begin to investment for the down payment?

Worksheet:

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Formulas:

4. Zebra micro-devices, Inc. is considering an investment in new equipment that will cost $120,000 and is estimated to provide the following annual savings over its 10-year life:

Year

Savings estimate1 $50,000

2 $40,0003 $30,0004 $20,0005 $10,000

a. Should the company acquire the new equipment if it can make a rate of return of 12% on all its investments?

Worksheet:

Formulas:

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Possible answer: Since the $116,268.65 present value of the savings are lower than the $120,000 cost of the new equipment, the firm should not invest in the new equipment.

b. Should the company acquire the new equipment if it can make a rate of return of 9% on all its investments?

Worksheet:

Formulas:The same as in part a)Possible answer: Since the $123,372.08 present value of the savings are higher than the $120,000 cost of the new equipment, the firm should invest in the new equipment.

c. Use the principal of value additivity to calculate the present value of the savings.

Worksheet:

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Formulas:

d. What is the implied annual rate of return is associated with the new equipment? Worksheet:

Formulas:

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5. You want to buy a car on credit for $15,000 at a rate of 7% for 3 years. a. Create an amortization table of the car loan that shows the portion of interest and principal on each payment. What will be the total dollar on interests that you would have paid at the end of the loan?

Worksheet:

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Formulas:

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b. Create a Stacked Column char that shows both interest and principal on each column.

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1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536$0

$100

$200

$300

$400

$500

Interest & Principal on Each Monthly Payment

PrincipalInterest

c. Repeat the same calculations on “a” and “b” assuming that your old vehicle was received by $5,000 as your down payment.

Worksheet:

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1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536$0

$50$100$150$200$250$300$350

Interest & Principal on Each Monthly Payment

PrincipalInterest

Formulas:

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The same as in part “a”

d. Suppose that you have the options of buying the car with a 3-year car loan or leasing the car during the same period of time. The 3-year lease option will require a $3,000 down payment and monthly payments of $350. If the salvage value of the new vehicle after two years is $5,000 and you can invest at a rate of return of 4%, what is your best option? (Ignore your old vehicle.)

Worksheet:

Formulas:

Test Bank

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1. You have decided to invest $4,000 at a rate of 10% compounded quarterly during 30 years. After that, you will be more careful with you money and expect to earn 5% compounded semiannually. Which is the correct formula for cell B8 that will allow you to determine how much money will you have after 45 years from now, assuming this is the only dollar amount you will invest during that time?

Remember that the basic syntax of the FV function is:

FV(rate,nper,pmt,pv,type)

a. =FV(B4/B6,30*B6,0,-B2,0)b. =FV(B5/B7,(B3-30)*B7,0,-B2,0)c. =FV(B4/B6,(B3-30)*B7,0,-FV(B5/B7,30*B6,0,-B2,0),0)d. =FV(B5/B7,(B3-30)*B7,0,-FV(B4/B6,30*B6,0,-B2,1),1)e. =FV(B5/B7,(B3-30)*B7,0,-FV(B4/B6,30*B6,0,-B2,0),0)Solution: e.

2. Twenty years ago, you invested $5,000 at a rate of 7% compounded annually. Fifteen years ago you added an additional $3,000 to that investment because the rate had increased to 10% compounded quarterly. What is the result of cell B9? Remember that the basic syntax of the FV function is: FV(rate,nper,pmt,pv,type)

a. $35,986.34

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b. $44,054.03c. $47,543.86d. $52,986.54e. $54,975.87Solution: e.

3. You invested $20,000 at 7% compounded quarterly for 5 years. Which is the correct formula for cell B8 that will allow you to determine how much additional money could you earn if you had invested that money at 9% compounded semiannually?

Remember that the basic syntax of the FV function is:

FV(rate,nper,pmt,pv,type)

a. =FV(B5,B2,0,B1,0)-FV(B3,B2,0,B1,0)b. =FV((B5/B6,B2*B6,0,B1,0)-(B3/B4,B2*B4,0,B1,0))c. =FV(B5/B6,B2*B6,0,-B1,0)+FV(B3/B4,B2*B4,0,-B1,0)d. =FV(B5/B6,B2*B6,0,-B1,0)-FV(B3/B4,B2*B4,0,-B1,0)e. =FV(B5/B6,B2*B6,0,B1,0)-FV(B3/B4,B2*B4,0,B1,0)Solution: d.

4. The student population of Moon University at the end of the last five years is provided on cells B2-B6. Which is the correct formula for cell B7 that will allow you to determine the student population growth rate from the end of year 1 to the end of year 5?

Remember that the basic syntax of

the NPER function is:RATE(nper,pmt,pv,fv,type,guess)

a. =RATE(A6,0,B2,B6,0)b. =RATE(A6,0,-B2,B6,0)c. =RATE(A6-A2,0,-B2,B6,0)d. =RATE(A6-A2,0,B2,B6,0)e. =RATE(A6-A2,0,-B2,B6,1)

Solution: c.

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5. Which is the correct formula for cell B6 that will allow you to determine how many years will it take to quadruple your savings at 11 percent compounded quarterly?

Remember that the basic syntax of the

NPER function is:NPER(rate,pmt,pv,fv,type)

a. =NPER(B4/B5,0,-B2,4*B3,0)/4b. =NPER(B4/B5,0,-B2,B2,0)c. =NPER(B4/B5,0,-B2,B2,0)/4d. =NPER(B4/B5,0,-B2,4*B2,0)e. =NPER(B4/B5,0,-B2,4*B2,0)/4

Solution: e.

6. You are planning for an early retirement, so you decide to invest $5,000 per year, starting at age 23. You plan to retire when you can accumulate $1M. If the average rate of return on your investments is %12. What should be the formula on cell B4 that will allow you to determine how old will you be when you retire?

Remember that the basic syntax of the NPER function is:

NPER(rate,pmt,pv,fv,type)

a. =NPER(B3,-B2,0,B1,0)b. =NPER(B3/12,-B2,0,B1,0)+23*12c. =NPER(B3,-B2,0,-B1,0)-23d. =NPER(B3,-B2,0,B1,0)+23e. =NPER(B2,-B3,0,B1,0)Solution: d.

7. You have a credit card balance of $5,000 that you want to pay in full before buying something else. If the interest rate of the credit card is 17%, what should be the formula on cell B5 that will allow you to determine how much longer in years will it take you to pay off this balance if you make monthly payments of $50, instead of $100?

Remember that the basic syntax of the NPER function is:

NPER(rate,pmt,pv,fv,type)

a. =(NPER(B2/12,B3,-B1,0)-NPER(B2/12,B4,-B1,0))/12b. =NPER(B2/12,B3,-B1,0)-NPER(B2/12,B4,-B1,0)/12c. =NPER(B2,B3,-B1,0)-NPER(B2,B4,-B1,0)d. =(NPER(B2/12,B3,B1,0,0)+NPER(B2/12,B4,B1,0,0))/12e. =(NPER(B3/12,B2,-B1,0)-NPER(B3/12,B2,-B1,0))/12Solution: a.

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8. What should be the outcome of cell B8? Remember that the basic syntax of the NPV function is: NPV(rate,value1,value2, ...)

a. “Accept”b. “Reject”c. “Indifferent”d. “HEEELP!!!”e. “I have no clue!”

Solution: a.

9. What should be the outcome of cell B? Remember that the basic syntax of the IRR function is: IRR(values,guess)

a. “Accept”b. “Reject”c. “Indifferent”d. “HEEELP!!!”e. “I have no clue!”

Solution: b.

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10. What should be the outcome of cell B7?

Remember that the basic syntax of the NPV and IRR function are:

NPV(rate,value1,value2, ...)IRR(values,guess)

a. 2,316.35b. 27.27%c. -2,316.35d. -14.36%e. 0

Solution: e.

11. Which is the correct formula in cell B4 to calculate the future value of $1,000 invested at 15% annual rate after 2 years using continuous compounding?a. =B3*EXP(B1*B2)b. =B2*EXP(B1*B3)c. =B1*EXP(B2*B3)d. =B1/EXP(B2*B3)e. =B1*EXP(B2+B3)Solution: c.

12. Which is the correct formula in cell B4 to calculate the present value of $1,000 to be received in three years discounted at 10% using continuous compounding?a. =B1/EXP(-B2*B3)b. =B1*EXP(-B2*B3)c. =B1*EXP(B2*B3)d. =B1*EXP(B2-B3)e. =B1*EXP(B2+B3)Solution: b.

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13. Your company is considering the purchase of new equipment. The quote consists of a quarterly payment of $5,000 for 7 years at 7 percent interest. What should be the formula on cell B4 that will allow you to determine the purchase price of the equipment?a. =PV(B3/4,B2/4,-B1,0)b. =PV(B3*4,B2*4,-B1,0)c. =PV(B3*4,B2/4,-B1,0)d. =PV(B3,B2,-B1,0)e. =PV(B3/4,B2*4,-B1,0)Solution: e.

14. You have been approved a credit to buy a TV with maximum payment of $100 a month for 4 years. The interest rate is 9 percent. What should be the formula on cell B4 to find the maximum price of a TV you can afford to purchase using the credit approved?a. =PV(B3/12,B1*12,-B2,0)b. =PV(B3*12,B1*12,-B2,0)c. =PV(B3/12,B1/12,-B2,0)d. =PV(B3*12,B1/12,-B2,0)e. =PV(B3,B1,-B2,0)Solution: a.

15. You borrowed 75 percent of a new car priced at $20,000 with an interest rate of 7 percent interest for 6 years. What is the amount of your monthly payment? What should be the formula on cell B4 to find the amount of your monthly payment?a. =PMT(B2*12,B3/12,-0.75*B1,0)b. =PMT(B2,B3,-B1,0)c. =PMT(B2/12,B3*12,-0.75*B1,0)d. =PMT(B2/12,B3*12,-B1,0)e. =PMT(B2/12,B3/12,-0.75*B1,0)Solution: c.

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chapter 1 spreadsheet basics - leeds school of …leeds-faculty.colorado.edu/donchez/fnce...

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