# The future value of a constantly growing annuity

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### The future value of a constantly growing annuity

The basic set up for the exam can be found in the file: f380.fall18.exam1.data.xlsx. That file contains nine worksheets that you are to complete. Each worksheet is named (and the number in parentheses is the points allotted to the problem). The following information should help you complete the problems:

EARLY [15] Banks often try to find ways to induce customers to pay off loans early. Consider Premium Bank, which offers a +10 mortgage. Basically, the bank calculates a mortgage payment in the usual way, then increases the payment by 10%. For example, a conventional mortgage for $300,000 at 5% annual interest would require 30 years of monthly payments of $1,610.46. The bank increases the payment to $1,610.46+ $161.05 = $1,771.51. The result is that the mortgage is paid off much more quickly. Write a spreadsheet that calculates a traditional mortgage payment, increases it by 10 percent and provides a loan amortization schedule for the loan assuming the customer pays the increased payment monthly. The spreadsheet should also report the life of the loan (how long it takes the customer to pay off the loan) in months and use only those cells necessary. This spreadsheet should work for any loan from 1-30 years and requiring monthly payments.

FVGA [15] The future value of a constantly growing annuity is:

Where PMT1 is the first payment (next year), g is the growth rate in the annuity, r is the interest rate earned on investment, and n is the length of the growing annuity. This equation calculates the future value immediately after the last payment. Write a spreadsheet that allows the user to enter an initial payment (PMT1, the number of years, an interest rate, and a growth rate. The spreadsheet returns the Future Value of the Growing Annuity and an amortization schedule. Restrict n to being less than or equal to 20 years, and r>g.

RETIRE [15] Write a spreadsheet that allows the user to input his (or her) age today, salary today, growth rate in salary (assumed constant throughout his or her working life), initial investment in both the bond and stock fund (which may or may not be $0 and can vary across funds), proportion of salary invested, age at retirement and planned age at death. The spreadsheet allows the user to invest a portion of his or her salary in two retirement vehicles (or funds) – a bond fund whose return is 4% and a stock fund with a return of 10%. The proportion invested in bonds equals the decade of the individual’s age. For example, in their 20s (i.e. from 20 through 29), they will invest 20% in bonds and 80% in stock. In the 30s, 30% in bonds and 70% in stock and so on. Immediately after retirement, ALL FUNDS will be transferred into an account with a guaranteed constant return of 3% per year. The funds are to be withdrawn starting one year after retirement and ending with the last payment at the age at death (there should be a zero balance after the last withdrawal). The spreadsheet should return the annual retirement benefit and show that the terminal value is zero. The spreadsheet should work for all ages from 16 to 100 and use only those cells necessary.

BREWSKI [10] This tab contains data on beer for all fifty states plus the District of Columbia. The variables are :

BCPC: Beer consumption (in gallons), per capita.

INC: Per capita annual income

MB: total number of microbreweries in the state

TAX: Tax per gallon assessed on beer

FPCT: Proportion of the state’s population that is female

POP: State population in millions

TEMP: Mean state temperature

Calculate the number of microbreweries per million population. (Call it MBPC). Then, create an indicator (or dummy) variable that takes on a value of one if the mean temperature is above 60 degrees and zero otherwise (call it TDUM). Run a multiple regression predicting beer consumption per capita (BCPC) as a function of INC, MBPC, FPCT, and TDUM. Indicate the significant coefficients.

RAISE [10] This worksheet contains salary levels for twelve employees at Weather-Tite Windows. Each employee is slated to receive a raise that potentially has three components. First, is an across-the-board cost of living adjustment (COLA) (everybody gets an x% raise). Second, is an incentive bonus based on productivity. Each employee is expected to produce 10,000-12,000 windows per year, but can earn an additional one percent raise per 1,000 windows over 12,000 produced. (For example, if you produce 17,000 windows, you would get an additional 5% raise.) Based on past performance, the production manager has provided estimates of the maximum number of windows each worker could produce. Third, each female employee MUST receive an additional raise of $2,500 to correct past pay inequities. (Assume the gender equity raise is NOT affected by the cost of living adjustment). The raise pool for this year must not exceed $85,000. Use solver to determine the maximum cost of living adjustment (COLA) the firm can offer. (Note, the incentive raises are based on this coming year’s salaries, not last year’s.)

NPV [15] This worksheet contains cash flows after tax for two capital budgeting projects. For each project, calculate the NPV assuming a discount rate of 12% and the IRR. For each project, calculate NPVs for whole discount rates from 0% to 30%, and graph both NPV profiles on the same graph. You will notice that the two lines cross. Determine this crossover rate – the rate at which the two projects have the same NPV.

SIM [10] Consider the function . Generate 100 integer values of X between -10 and +10, and graph Y as a function of F. Your graph should be dynamic – each calculation (F9) should redraw the graph.

AOI [5] Before the Truth in Lending Act, auto dealers used to use a trick called add on interest. Suppose you bought a $30,000 car and financed it over 5 years at 6% interest. To calculate your payment, they’d take $30,000x5yearsx.06=$9,000. Your monthly payment would be ($30,000+$9,000)/12x5years = $650 per month. Write a spreadsheet that allows the user to enter the amount borrowed, the life of loan in years and the annual interest rate. The spreadsheet calculates the add-on interest payment, what the payment should be if calculated correctly, and the effective annual interest rate on the loan if the add-on interest payment is used.

WEEK [5] For any loan, loan length (up to 30 years) and interest rate, the spreadsheet calculates monthly payment in the ordinary fashion. Then, the borrower makes ½ a monthly payment every two weeks. (Assume bi-weekly compounding at a rate of r/26). Write a spreadsheet that determines how long it takes to pay off the loan in years.