April 24

Economics Review Questions

This economics review questions section should be used in conjunction with the Economics Study Guide and the compound interest tables that are on this website. A good idea is to print out those two documents  for easy reference.

Review Questions

1. You have $100,000 in a mutual fund which is drawing 9% a year annually. You are planning to purchase a house for $300,000. How long must you wait if you want to purchase the house with only the mutual fund?
A) 12 years
B) 13 years
C)  9 Years
D) 11 Years

2. You are evaluating two options for purchase of equipment. The first option is to purchase the item outright for $15,000. The second option is to put $5000 down and pay the reaming off over the next 5 years at 18% per year. How much extra would option two cost?
A) $2,000
B) $6,000
C) $5,250
D) $5,000

3. You purchased some farm equipment for $150,000 that has an expected life of 7 years. At the end of the first year how much can the equipment be depreciated using the MACRS method?
A) $12,450
B) $21,450
C) $15,000
D) $30,000

4. You work for a company that produces sprockets. You boss, Mr Spacely pays a yearly operating expense of $1,500,000. If each sproket cost $0.71 and sells for $3.14 how many sprockets do you need to sell to break even?
A) 817,658
B) 1,500,000
C) 716,824
D) 617,284

Review Answers

1. This is a Single Payment Present Worth question (it can also be a Single Payment Compound Interest). You are given the present amount, the interest and the future amount, but you are missing the period. Since the interest in annual you just need to look at the compound interest chart that is for 9%. Then look down the F/P line until you get to the first one that is over 3. Which is roughly going to be at the 13th period. So the answer would be 13 years

2. In this problem you are asked to find the amount you will pay over the next 5 years. You know that the amount that needs paying off is $10,000 and the time is 5 years or 60 months. Next you look for the charts that deal with 18% yearly interest or have an interest of 1.5%. Then you go to the capital recovery (A/P) and go down to the 60 interval mark and you have a multiplier of .0024. Now take the $10,000 and multiply it by 0.0025 and you end up with $250 per month.  To find out the total cost in present dollars you multiply $250 by 60 months and you get $15,000 for a total cost of $20,000 for option 2. This is $5,000 more than option 1.

3. Since the equipment has a useful life for 7 years, we look at that column and go to the row that is for 1 year. The depreciation is 14.3%. Now multiply 14.3% by the original amount of $150,000 to get $21,450 which is how much the farm equipment has depreciated in value.

4. This is a straight forward break even analysis. First you need to calculate the total cost per year. Once you have the total cost you divide that by the profit per sprocket.

Cost = $1,5000,000 + $0.71 * Number\ of\ sprockets

Revenue = ($3.14-$0.71) * Number\ of\ sprockets

Set the cost equal to the revenue and solve for number of sprockets

Number/ of/ sprockets = \frac{1,500,000}{3.14-0.71} = 617,284

April 18

Economics Study Guide

Economics is the Study of Money.

Economics is the study of how money behaves over time. You may come across situations where you need to analyze cash flow over a period of time, see how much an item will depreciate, or analyze multiple options to see which choice would be the most economically feasible. In this economics study guide you will learn how to analyze the problem and find the best solution out of the choices you are given.
Once you are finished going through this study guide. I have some review questions here

Time Value of Money

When looking at cash flow one needs to think in two terms. One is the current worth of the cash, and the second is the future value of the cash
If you place $1,000 in a bank drawing 5% interest you would have $1050 in one year. Now if you spent that money to buy equipment that cost $1,000, but made you $700 and had a resale of $400 at the end of the year. Which would be the obvious choice? You would choose the equipment purchase because it made the most cash at the end.
For the PE Exam you will most likely find at least 1 question for economics. These questions can be easily broken down to looking at two or more options, one a current amount, a second  future amount, and a third cash transactions in the middle. You will ultimately have to evaluate the options with present cash value or future cash value.

Economic Terms

A is the annual amount. This is an amount that is paid each time interest is earned
C is the initial cost which can be the present cost of the item.
F is the future worth of the item
G is the gradient amount. This is like the annual payment, but on each payment the amount is increased by the amount being paid. For instance, $50, $100, $150,
i is the interest rate. This can be given as a yearly rate (think compound interest, like your credit cards) or an annual rate
n is the number of compounding periods
P is the present worth of the item
r is the nominal rate, or rate per anum

Economic Equations

There are essentially 9 different types of equations you may be using. The next section briefly will explain each of them and show you the equation you need to use with each problem. Do not worry about having to know all these equations. The following equations are shown for reference, or if you want you can use them on the exam, but there is a free compound interest cheat sheet you can print out and bring with you.

Single Payment Compound Amount

Single payment compound amount is when you put one large sum of money in. Then over a period of time you accrue interest. This is basically like your bank.

F = P(1+i)^{n}

Single Payment Present Worth

Single payment present worth is when you take the future value you expect and see how much you need to invest at a certain percent interest to come up with that money.

P = F(1+i)^{-n}

Uniform Series Sinking Fund

Uniform series sinking fund is not as bad as it sounds. Basically you know the future amount and you want to know how much you need to pay each increment to hit that amount. Think of a mortgage, you pay x amount each month until you have paid off the house.

A = \frac{F*i}{(1+i)^{n}-1}

Capital Recovery

Capital recovery is where you give someone a sum of money and over time they pay it back. Kind of like giving someone a loan and they pay in increments until it is paid off

A = \frac{P*i(1+i)^{n}}{(1+i)^n-1}

Uniform Series Compound Amount

Uniform series compound amount is where you find out how much you need to pay over time to end up with a set amount at the end. Think of this as a 401k. You make payments through your life and hope to have a ton of cash there at the end.

F =\frac{A*(1+i)^n-1}{i}

Uniform Series Present Worth

Uniform series present worth is where you find out how much you need to pay at the present to get a certain amount back over time.

P=\frac{A*(1+i)^n-1}{i(1+i)^n}

Next come the gradient series. These are where an increasing amount is paid

Uniform Gradient Present Worth

P=G(\frac{(1+i)^n-1}{i^2(1+i)^n}-\frac{n}{i(1+i)^n})

Uniform Gradient Future Worth

F=G(\frac {(1+i)^n-1}{i^2}-\frac{n}{i})

Uniform Gradient Uniform Series

A=G(\frac {1}{i} - \frac {n}{(1+i)^n-1} )

Depreciation

The value of everything does not always go up. Some things will lose value like a car, equipment or mobile home. When this happens the item is considered to depreciate in value. Generally the item will be set to depreciate over a set amount of years until the worth is 0.
Originally depreciation could be found by using the Straight Line Depreciation Method

Depreciation=\frac{Initial\ Cost - Amount\ per\ Year}{Number\ of\ Years}

But in 1982 the US government sent out a mandate that uses either the Accelerated Cost Recovery System (ACRS) or Modified Accelerated Cost Recovery System (MACRS)

Modified Accelerated Cost Recovery System (MACRS)

The MACRS or ACRS uses two values when determining an items cost. One is the amount of years until the item is worth nothing. The second value is how long you have owned the item.

Years Recovery Period (Years)
3 5 7 10
1  33.3 20 14.3  10
2 44.5 32 24.5 18
3 14.8 19.2 17.5 14.4
4 7.7 11.5 12.5 11.5
5 11.5 8.9 9.2
6 5.8 8.9 7.4
7 8.9 6.6
8 4.5 6.6
9 6.5
10 6.5
11 3.3

 

Comparison of Alternatives

Now that you are familiar with how the value of an item or money can increase or decrease with time, it is time to look at ways of comparing the choices. In this economics study guide we will look at five different ways to make the comparison. These analyses are: present worth, annual cost, rate of return, cost benefit, and break even

Present Worth Analysis

Present worth analysis is when you take all the values that are given and you bring them to present terms. The equations you will likely be using are the Single Payment Present Worth and the Uniform Series Present Worth equations

Annual Cost Analysis

The annual cost analysis is looking at the cost of items that have a different length of life.   This analysis assumes that each item will be replaced by an identical one. This will allow you to evaluate the options over a set period of time.

Rate of Return Analysis

In the rate of return analysis a company picks a minimum attractive rate of return (MARR). Then the rate of return for the item is calculated. If the item returns more than the MARR, then the item is a viable option.

Cost-Benefit Analysis

A cost-benefit analysis is when you take all the cost and convert them to the present worth.. Then take all the benefits and convert them into present worth. Then divide the benefits by the cost. If the value is greater than one then the project would be acceptable.

Break Even Analysis

Last is the break even analysis. This is where you wish to find out how long until an item has been paid off.

Cost-Payback\ Period * Profit=0

 

April 17

HVAC Question 10

Calculating EER Rating

Problem

A 20 ton air conditioning unit has an average electrical load of 30 Kw. What is the EER rating?

Solution

The Energy Efficiency Ratio (EER) is a standard measure of air conditioning efficiency during a “normal” annual cooling hour

EER = BTU  of Cooling / Watt Hours of Electric Energy Input

1 Ton = 12,000 BTUH

EER=20\ ton*12,000\frac {btuh}{ton}\div 30,000\ watts

EER Rating = 8