Finance 502 - Module 2 - Chapters 4 and 5
Moving cash flows from one point in time to another requires us to use what two things?
1. Present value 2. future value equations
time line
A graphical representation showing the size and timing of cash flows through time
amortized loan
A loan in which the principal as well as the interest is payable in monthly or other periodic installments over the term of the loan.
annuity
A stream of level and frequent cash flows paid at the end of each time period--often referred to as an ordinary annuity
amortization schedule
A table showing precisely how a loan will be repaid. It gives the required payment on each payment date and a breakdown of the payment, showing how much is interest and how much is repayment of principal.
AIG
American International Group
effective annual rate (EAR)
An interest rate that reflects annualizing with compounding figured in
Drawing on your past classes in accounting, explain why time lines must show one negative cash flow and one positive cash flow.
Cash flow accounting labels money spent as a negative cash flow for the firm. This type of cash flow is put in the debit column. When the cash is received, it is added as a positive cash flow and registered as a credit. Investments, deposits, and loans all include one cash flow where money leaves your (or the firm's) hands and one cash flow where money goes into your hands.
How is discounting the reverse of compounding?
Compounding increases present values into the future while discounting does the opposite. Discounting reduces future values into the present. The TVM equations show the relationship between a present value and a future value. When moving cash flows forward in time, we call it compounding. When moving cash flows back in time, we call it discounting.
Show that you must earn a 25 percent return to offset a 20 percent loss.
Consider a $100 investment that loses 20 percent to $80. This $80 would have to earn $20 to reach $100 again. A $20 profit on an $80 investment is a $20 ÷ $80 = 0.25, or 25 percent return.
What is one of the best ways to manage cash flow timing?
Create a time line which shows the magnitude of cash flows at different points in time, such as monthly, quarterly, semiannually, or yearly.
ordinary annuity
If the first payment occurs at the end of the period
How are interest rates in the economy related to the way people value future cash payments?
If the interest rates are high, then future payments are valued much lower today than they would be if interest rates were low.
simple interest
Interest earned only on the original deposit Any amount of interest earned above the $5 in any given year comes from compounding. Over time, the new interest payments earned from compounding can become substantial. How to differentiate between simple interest and any compounding interest can be seen in this example. FV of a 30-year investment of $100 at 5% a year. $100 x (1.05)^30 = $432.19 This is a $332.19 profit over your initial $100. Of this profit, only $150 (= $5 x 30 years) came from simple interest earned on the original deposit. The rest $182.19 (=$332.19 - $150), is from the compounding effect of earning interest on previously earned interest. Remember that the difference between earning 5% and 6% in interest on the $100 was only $1 the first year. So what is the future value difference after 15 years? Is it $15? No, the difference in future value substantially increases over time. The difference is $31.76 in year 15 and $142.15 in year 30.
Countrywide Financial
Large mortgage co. Which made 96 billion in subprime loans avoided bankruptcy when it was bought by BoA Jan 2008
Caveat emptor
Latin term for "buyer beware" Considering TVM can also work against you, let's go back to the mattress firm example where you don't have to pay back the mattress' cost for two years but after the second year you forget to pay that back. The compounding interest will now work against you. The $1000 mattress with a 10% interest rate will now have an additional charge of: ($1000 x 1.1^2 - $1000) = $210. Instead of saving money you now owe an additional sum that is relatively close to what you would have saved if you paid on time.
Why is a dollar worth more today than a dollar received one year from now?
Money has a time value because it can be invested to make more money. Thus, a dollar received in the future has lesser value than a dollar received today. Conversely, a dollar received today is more valuable than a dollar received in the future because it can be invested to make more money.
How does compounding help build wealth (or increase debt) over time?
More frequent compounding means your money will grow more quickly if it is in a bank account. ... Since the balance changes as the deposit or debt compounds, the amount you owe 5% on increases with each compounding period, so you wind up paying somewhat more than if the loan only compounded once a year.
How are the present value and future value related?
Present value takes the future value and applies a discount rate or the interest rate that could be earned if invested. Future value tells you what an investment is worth in the future while the present value tells you how much you'd need in today's dollars to earn a specific amount in the future.
How are present values affected by changes in interest rates?
Present values are not affected by changes in interest rates. The lower the interest rate, the larger the present value will be.
Compound interest vs Simple interest
Simple interest is calculated on the principal, or original, amount of a loan. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as "interest on interest."
What are factors to consider when making time value of money decisions?
Size of the cash flows Time between the cash flows Rate of return we can earn
Regarding the concepts of increasing the income with the $350 million example, in what other areas of business can these time-value concepts be used?
TVM concepts can be used in many business areas. Moving cash flows, investment, debt, and growth are important in fields such as accounting, entrepreneurship, marketing, management, and manufacturing.
Say you double your money in three years. Explain why the rate of return is NOT 33.3 percent per year.
The 33.3 percent estimate misses the effect of compounding. Earning interest-on-interest allows money to double in three years at a 26 percent rate.
loan principal
The balance yet to be paid on a loan
Interest rate
The cost of borrowing money denoted as a percent Using this in addition with TVM you'll notice that $100 today, being put in a bank with a 5% interest rate would be worth $105 in a year.
Why does doubling the interest rate or time quickly cause more than a doubling of the future value?
The cumulative interest earned on that deposit and the cumulative interest-on-interest earned. By the 27th year, the money from the interest-on-interest exceeds the interest earned on the original deposit. By the 40th year, interest-on-interest contributes more than double the interest on the deposit. The longer money can earn interest, the greater the compounding effect. Would you double your gain by simply investing that same $100 at double the interest rate, 10 percent? No, because compounding changes the nature of the investment so that your money grows exponentially, not in a simple linear relationship. The future value of $100 in five years at 10 percent is $161.05. The $61.05 gain is more than double the gain of $27.63 earned at 5 percent. Tripling the interest rate to 15 percent shows a gain of $101.14 that is nearly quadruple the gain earned at 5 percent. The effect occurs when we increase the time. When the deposit earns 10 percent per year for five years, the gain is $61.05. When we double the amount of time to 10 years, page 120the gain more than doubles to $159.37. If we double the time again to 20 years, the gain increases not to just $318.74 (= $159.37 × 2) but to $572.75. At 10 percent for 30 years, the gain of $100 is a whopping $1,644.94. Interest rates and time are both important factors in compounding.
discount rate
The interest rate on the loans that the Fed makes to banks The interest rate, i. If you receive a $100 cash flow in five years, then its present value is $78.35, discounted at 5%. Higher interest rates discount future cash flows more quickly and dramatically.
annual percentage rate (APR)
The interest rate per period times the number of periods in a year
The Rule of 72
The number of years it takes for a certain amount to double in value is equal to 72 divided by its annual rate of interest. The approximate number of years to double an investment = 72/interest rate
Set up a time line, given a 6% interest rate, with a cash inflow of $200 today and a cash outflow of $212 in one year
The period of zero years with $200 dollars going on 6% over a year comes to -$212
What do you think of the following statement? "I am going to receive $100 two years from now and $200 three years from now, so I am getting a $300 future value." How could the two cash flows be compared or combined?
These are two separate cash flows over a three year period. The discount rate of the currency will affect them greatly. You have a future value of $300 but with inflation and depreciation, you would use the PV formula to determine how much less effective that money is in the future compared to now.
At what interest rate (and the number of years) does the Rule of 72 become too inaccurate to use?
This depends on what level of accuracy is needed. Interest rates that are too low or too high cause less accurate Rule of 72 estimates. The Rule of 72 is reasonably accurate for interest rates that fall in the range of 6% and 10%. When dealing with rates outside this range, the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate diverges from 8% threshold. For example, the rate of 11% annual compounding interest is 3 percentage points higher than 8%.
List and describe the purpose of each part of a timeline with an initial cash inflow and future cash outflow. Which cash flows should be negative and which positive? Why?
Timelines are set up to organize cash flow timing. Using a timeline shows the amount of money at a given time or period. A period could be quarterly, semi-annual or annual. The period is normally shown horizontally on the top of the timeline along with the interest rate denoted for the period. Cash flow is shown horizontally below the timeline. Money received (or inflow) is denoted with a positive and money that is contributed (or outflow) is shown with a negative. Showing a negative or positive amount on the timeline shows where money has been contributed or lost (negative) and where money has been earned (positive). By using the negative and positive values for cash flow, the timeline is aligned with accounting practices of debits and credits
Say that you are the sales manager of a company that produces software for human resource departments. You are planning your staffing needs, which depend on the volume of sales over time. Your company currently sells $350 million of merchandise per year and has grown 7 percent per year in the past. How long will it take to double sales?
To double the sales at a 7 percent growth rate takes 10.24 years (using a TVM calculator with PV of −350, FV of 700, and PMT of 0.).
Would you prefer to have an investment earning of 5% for 40 years or an investment earning 10% for 20 years? Explain
Using the future value equation, you will find that the longer option of 40 years at 5% is worth more than the 20 years at 10%. Compound interest requires time to get started much like a freight train, once it gets going then there isn't much that can stop it.
Singe-period future value
Value in 1 year = Today's cash flow + Interest earned $105 = $100 + $5 ($100 x 5%). The equation to denote the percentage is usually represented as $100 + ($100 x 0.05) = $105 Which is the same as saying $100 x (1 + 0.05) = $105 Value in 1 year = Today's value x (1 + Interest rate) FV subscript 1 = PV x (1 + i) That subscript only means one year The 1 in the parenthesis is for the original deposit. The 0.05 is for the interest earned. We can generalize this computation to any amount of today's cash flow. We call cash today present value PV. We computer the future value one year from now, called FV1, using the interest rate i
In Example 4-4, could Timber, Inc., have performed its analysis by moving the $175,000 to year 2 and comparing? Would the firm then have made the same decision? This comparison is the 175,000 moving to year 2 with its own analysis or having the 195,000 court battle then moving the payment to year 2.
Yes, the $175,000 could be moved from year 1 to year 2 using the 7 percent interest rate and compared with the $195,000 year 2 payment. The two procedures are equivalent mathematically and will lead to the same decision. Also, they should get a new attorney.
add-on interest
a calculation of the amount of interest determined at the beginning of the loan and then added to the principal
Housing bubble
a rapid increase in the value of houses followed by a sharp decline in their value
annuity due
an annuity for which the cash flows occur at the beginning of the period
perpetuity
an annuity with cash flows that continue forever
Rule of 72
an approximation for the number of years needed for an investment to double in value
mortgage-backed securities
bonds backed by mortgage payments
outflow
cash payment, often a cost or the price of an investment or deposit Often represented as a negative number
inflow
cash received, often from income or sale of an investment It is usually denoted as a positive number
consols
investment assets structured as perpetuities
subprime lending
lending to home buyers who don't meet the usual criteria for being able to afford their payments
present value (PV)
the amount a future cash flow is worth today
time value of money (TVM)
the increase of an amount of money due to earned interest or dividends The money you have now will be worth more than an identical sum in the future. The difference in buying power for a dollar over time
Compounding
the process of adding interest earned every period on both the original investment and the reinvested earnings Interest on the interest that was earned in the initial deposit and on the earlier interest payments
discounting
the process of finding present value by reducing future values using the discount, or interest, rate The present value of the next period's cash flow = next period's value/one period of discounting it is the opposite of compounding
future value (FV)
the value of an investment after one or more periods If the interest rates were higher than the current rates then the future value of your investment would also be higher.
