Understanding Economic “Equivalence” Enrico Suarez just graduated with a B.S. in engineering and landed a new job with a starting annual salary of $48,000. There are a number of things that he would like to do with his newfound “wealth.” For starters, he needs to begin repaying his student loans (t

Question

Understanding Economic “Equivalence”

Enrico Suarez just graduated with a B.S. in engineering and landed a new job with a starting annual salary of [latex]\$ 48,000[/latex]. There are a number of things that he would like to do with his newfound "wealth." For starters, he needs to begin repaying his student loans (totaling [latex]\$ 20,000[/latex] ) and he d like to reduce some outstanding balances on credit cards (totaling [latex]\$ 5,000[/latex] ). Enrico also needs to purchase a car to get to work and would like to put money aside to purchase a condo in the future. Last, but not least, he wants to put some money aside for his eventual retirement.

Our recent graduate needs to do some financial planning for which he has selected a 10-year time frame. At the end of 10 years, he'd like to have paid off his current student loan and credit card debt, as well as have accumulated [latex]\$ 40,000[/latex] for a down payment on a condo. If possible, Enrico would like to put aside [latex]10 \%[/latex] of his take home salary for retirement. He has gathered the following information to assist him in his planning.*

Student loans are typically repaid in equal monthly installments over a period of 10 years. The interest rate on Enrico's loan is [latex]8 \%[/latex] compounded monthly.
Credit cards vary greatly in the interest rate charged. Typical APR rates are close to [latex]17 \%[/latex], and monthly minimum payments are usually computed using a 10-year repayment period. The interest rate on Enrico's credit card is [latex]18 \%[/latex] compounded monthly.
Car loans are usually repaid over three, four, or five years. The APR on a car loan can be as low as [latex]2.9 \%[/latex] (if the timing is right) or as high as [latex]12 \%[/latex]. As a first-time car buyer, Enrico can secure a [latex]\$ 15,000[/latex] car loan at [latex]9 \%[/latex] compounded monthly to be repaid over 60 months.
A 30-year, fixed rate mortgage is currently going for 5.75%-6.0% per year. If Enrico can save enough to make a [latex]20 \%[/latex] down payment on the purchase of his condo, he can avoid private mortgage insurance that can cost as much as [latex]\$ 60[/latex] per month.
Investment opportunities can provide variable returns. "Safe" investments can guarantee [latex]7 \%[/latex] per year, while "risky" investments could return [latex]30 \%[/latex] or more per year.
Enrico's parents and older siblings have reminded him that his monthly take home pay will be reduced by income taxes and benefit deductions. He should not count on being able to spend more than [latex]80 \%[/latex] of his gross salary.

[latex]{ }^{*}[/latex] The stated problem data are current as of 2014 .

As Enrico's friend (and the one who took Engineering Economy instead of Appreciating the Art of Television Commercials), you have been asked to review his financial plans. How reasonable are his goals?

Accepted Answer

Since all repayments are done on a monthly basis, it makes sense to adopt the month as Enrico's unit of time. There are five categories for his cash flows: debt repayment, transportation costs, housing costs, other living expenses, and savings. The following paragraphs summarize his estimates of monthly expenses in each of these categories.

Debt Repayment

Enrico's student loan debt is [latex]\$ 20,000[/latex] and is to be repaid over the next 120 months (10 years) at a nominal interest rate of [latex]8 \%[/latex] compounded monthly [latex]\left(i_{ ext {month }}=8 / 12 \%= ight.[/latex] [latex]2 / 3 \%)[/latex]. His monthly loan payment is then

[latex]A_{ ext {Student Loan }}=\$ 20,000(A / P, 2 / 3 \%, 120)=\$ 20,000(0.01213)=\$ 242.60[/latex] per month.

Enrico's credit card debt is [latex]\$ 5,000[/latex] and is to be completely repaid over the next 120 months at a nominal interest rate of [latex]18 \%[/latex] compounded monthly [latex]\left(i_{ ext {month }}=1.5 \% ight)[/latex]. His monthly credit card payment, assuming no additional usage, is then

[latex]A_{ ext {Credit Card }}=\$ 5,000(A / P, 1.5 \%, 120)=\$ 5,000(0.01802)=\$ 90.10[/latex] per month.

Enrico's monthly debt repayment totals [latex]\$ 242.60+\$ 90.10=\$ 332.70[/latex].

Transportation Costs

The certified pre-owned vehicle Enrico would like to buy costs [latex]\$ 15,000[/latex]. The best rate he can find as a first-time car buyer with no assets or credit history is [latex]9 \%[/latex] compounded monthly with a 60 -month repayment period. Based on these figures, his monthly car payment will be

[latex]A_{ ext {Car }}=\$ 15,000(A / P, 0.75 \%, 60)=\$ 15,000(0.02076)=\$ 311.40 ext { per month } .[/latex]

Even though the car will be completely repaid after five years, Enrico knows that he will eventually need to replace the car. To accumulate funds for the replacement of the car, he wants to continue to set aside this amount each month for the second five years.

Insurance for this vehicle will cost [latex]\$ 1,200[/latex] per year, and Enrico has budgeted [latex]\$ 100[/latex] per month to cover fuel and maintenance. Thus, his monthly transportation costs total [latex]\$ 311.40+\$ 1,200 / 12+\$ 100=\$ 511.40[/latex].

Housing Costs

A nice two-bedroom apartment near Enrico's place of work has a monthly rent of [latex]\$ 800[/latex]. The rental office provided him with a monthly utility cost estimate of [latex]\$ 150[/latex] to cover water and electricity. Based on this information, [latex]\$ 800+\$ 150=\$ 950[/latex] per month has been budgeted for his housing costs.

Other Living Expenses

This expense category has troubled Enrico the most. While all the previous categories are pretty straightforward, he knows that his day-to-day spending will have the most variability and that it will be tempting to overspend. Nonetheless, he has developed the following estimates of monthly living expenses not already covered in the other categories:

Food	$200
Phone	$70
Entertainment	$100
Miscellaneous
(clothing, household items)	$150
Subtotal	$520

Savings

Enrico wants to accumulate [latex]\$ 40,000[/latex] over the next 10 years to be used as a down payment on a condo. He feels that if he chooses relatively "safe" investments (CDs and bonds), he should be able to earn [latex]6 \%[/latex] compounded monthly on his savings. He must then set aside

[latex]A_{ ext {Condo }}=\$ 40,000(A / F, 0.5 \%, 120)=\$ 40,000(0.00610)=\$ 244.00[/latex] per month to reach his goal.

Enrico's gross monthly starting salary is [latex]\$ 48,000 / 12=\$ 4,000[/latex]. Based on the information gathered from his family, he estimates his monthly net (take home) pay to be [latex]\$ 4,000(0.80)=\$ 3,200[/latex]. His monthly retirement savings will then be [latex]\$ 3,200(0.10)=\$ 320[/latex]. Thus, the total amount to be set aside each month for the future is [latex]\$ 244+\$ 320=\$ 564[/latex].

Monthly Financial Plan

Based on the preceding calculations, the following table summarizes Enrico's monthly financial plan.

	Net Income	Expense
Salary	$3,200
Debt repayment		$332.70
Transportation costs		511.40
Housing costs		950.00
Living expenses		520.00
Savings		564.00
Total	$3,200	$2,878.10

Enrico is aware that he has not explicitly accounted for price increases over the next 10 years; however, neither has he increased his annual salary. He is hopeful that, if he works hard, his annual salary increases will at least cover the increase in the cost of living.

You congratulate your friend on his efforts. You feel that he has covered the major areas of expenses, as well as savings for the future. You note that he has [latex]\$ 3,200-\$ 2,878.10=\$ 321.90[/latex] of "extra" money each month to cover unanticipated costs. With this much leeway, you feel that he should have no problem meeting his financial goals.

Question 4.C-S.17: Understanding Economic “Equivalence” Enrico Suarez just grad...

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