Module 7: Finance- TVM and Multiple Cash Flows

A ____ _____ is an annuity whose payments grow at a constant rate for the life of the contract. The equation for a growing annuity is similar to that of an ordinary annuity with the addition of the variable _ as the rate of growth for the annuity. Note, that to qualify as a growing annuity, the growth rate, _, in each period has to be the ___ for every period, and cannot _____ the periodic rate.

A growing annuity is an annuity whose payments grow at a constant rate for the life of the contract. The equation for a growing annuity is similar to that of an ordinary annuity with the addition of the variable g as the rate of growth for the annuity. Note, that to qualify as a growing annuity, the growth rate, g, in each period has to be the same for every period, and cannot equal the periodic rate.

An adjustment needs to be made for this one extra period while calculating the ___ ____ of an annuity due - the present value of an annuity due is equal to the present value of an ordinary annuity times one plus the periodic rate. Similarly, the ____ _____ of an annuity due is equal to the future value of an ordinary annuity compounded for one additional period. Therefore the value of an annuity due must be one period of interest _____ than that of anordinary annuity, which makes sense because you get or pay the money one period ______.

An adjustment needs to be made for this one extra period while calculating the present value of an annuity due - the present value of an annuity due is equal to the present value of an ordinary annuity times one plus the periodic rate. Similarly, the future value of an annuity due is equal to the future value of an ordinary annuity compounded for one additional period. Therefore the value of an annuity due must be one period of interest greater than that of anordinary annuity, which makes sense because you get or pay the money one period sooner.

An amortized loan is a loan where the ______ of the loan is paid off over the life of the loan, rather than entirely at the end of the loan term. Each payment consists of interest and repayment of principal. This breakdown is often presented in a ___ ______ _____. The interest component is the ______ in the first period, and it declines over the life of the loan as the outstanding principal balance of the loan decreases. The repayment of the principal is the ____ in the first period, and it _______ thereafter.

An amortized loan is a loan where the principal of the loan is paid off over the life of the loan, rather than entirely at the end of the loan term. Each payment consists of interest and repayment of principal. This breakdown is often presented in a loan amortization schedule. The interest component is the largest in the first period, and it declines over the life of the loan as the outstanding principal balance of the loan decreases. The repayment of the principal is the smallest in the first period, and it increases thereafter.

An _____ is a series of equal payments made at fixed alternatives for a specified number of time periods. If the payments occur at the end of the period, as they typically do, the annuity is an _____ annuity.

An annuity is a series of equal payments made at fixed alternatives for a specified number of time periods. If the payments occur at the end of the period, as they typically do, the annuity is an ordinary annuity.

Conceptually, the IRR is simply the rate of return on an investments. That investment should be accepted if its IRR is _____ than the rate of return offered from the next best similar investment. Simply put, ____ the investment if its rate of return is higher than the opportunity cost.

Conceptually, the IRR is simply the rate of return on an investments. That investment should be accepted if its IRR is greater than the rate of return offered from the next best similar investment. Simply put, accept the investment if its rate of return is higher than the opportunity cost.

Financial managers are interested in knowing the present value of an asset's cash flow stream becausethe present value represents t h e v a l u e o f t h e a s s e t t o d a y , which can then be compared to the price of the asset todetermine if the investment adds value to the firm. This process is referred to as finding the ____ ____ ______.

Financial managers are interested in knowing the present value of an asset's cash flow stream becausethe present value represents t h e v a l u e o f t h e a s s e t t o d a y , which can then be compared to the price of the asset todetermine if the investment adds value to the firm. This process is referred to as finding the net present value (NPV).

If an annuity's payments occur at the _____ of each period, such as a rent or lease agreement, it is called an annuity due. The difference between an ordinary annuity and anannuity due is ___ _____ period of compound interest

If an annuity's payments occur at the beginning of each period, such as a rent or lease agreement, it is called an annuity due. The difference between an ordinary annuity and anannuity due is one extra period of compound interest

In other words, NPV is the difference between what you ___ for an asset and what the asset is _____.

In other words, NPV is the difference between what you pay for an asset and what the asset is worth.

Investment cash flows are often more complicated than just a single inflow at a point in time anda single outflow at another point in time. Cash flows from an investment are often _____ and ________. An _______ cash flow stream is a series of cash flows in which the amount varies from one point to the next.

Investment cash flows are often more complicated than just a single inflow at a point in time anda single outflow at another point in time. Cash flows from an investment are often multiple and uneven. An uneven cash flow stream is a series of cash flows in which the amount varies from one point to the next.

Once the ____ _____ of an investment is known, we can find the future value of an uneven cash flow stream by treating the present value as a ___ ___ ______ and compounding it to the future period.

Once the present value of an investment is known, we can find the future value of an uneven cash flow stream by treating the present value as a lump sum amount and compounding it to the future period.

Perpetuities are financial assets that pay an _____ number of _____ occurring cash flows. In general, the word "perpetuity" is associated with a steam of payments that are all _____. These kinds of assets are sometimes called ___ or _____ perpetuities. A _____ perpetuity is an asset with an infinite number of payments, but the issuer increases the payments at a constant growth rate each period. For growing perpetuities every cash flow is a _____ amount, but all the payments are _____ through the asset's fixed growth rate.

Perpetuities are financial assets that pay an infinite number of regularly occurring cash flows. In general, the word "perpetuity" is associated with a steam of payments that are all identical. These kinds of assets are sometimes called level or constant perpetuities. A growing perpetuity is an asset with an infinite number of payments, but the issuer increases the payments at a constant growth rate each period. For growing perpetuities every cash flow is a different amount, but all the payments are related through the asset's fixed growth rate.

The _____ value of an ordinary annuity is the total amount you would have at the end of the annuity period if each payment were invested at a given interest rate and held to the end of maturity. The ____ value of an ordinary annuity is the single payment today that would be equivalent to the annuity payments spread over the annuity period

The future value of an ordinary annuity is the total amount you would have at the end of the annuity period if each payment were invested at a given interest rate and held to the end of maturity. The present value of an ordinary annuity is the single payment today that would be equivalent to the annuity payments spread over the annuity period

The ___ _____ of an uneven cash flow stream is the sum of the PVs of the individual cash flows of the stream. Similarly, the ____ _____ of an uneven cash flow stream is thesum of the FVs of the individual cash flows of the stream

The present value of an uneven cash flow stream is the sum of the PVs of the individual cash flows of the stream. Similarly, the future value of an uneven cash flow stream is thesum of the FVs of the individual cash flows of the stream

growing annuity

a annuity whose payments grow at a constant rate per period for the length of the contract

loan amortization schedule

a breakdown of the interest and principal payments on an amortized loan

amortized loan

a loan with scheduled periodic payments of both principal and interest. Payments are applied first towards reducing the interest balance, and any remaining sum towards the principal balance

growing perpetuity

a type of perpetuity where the regularly occurring cash flows grow at fixed rate per period forever. Every cash flow in the stream is different from every other, but they are related throughout the constant growth rate.

annuity due

an annuity whose payments are made at the beginning of each period. An AD is less common than an OA

ordinary annuity

an annuity whose payments are made at the end of each period. Most annuities come int he form of an OA

perpetuity

an infinite stream of cash flows that are paid or received with a regular frequency. In general, the word perpetuity is used to refer to a stream where all the cash flows are the same. This kind of stream is also called a level or constant perpetuity

The ___ ___ of ____ is the rate of return you get from aninvestment if the price you pay for an asset is exactly the same as what the asset is worth: NPV = 0. IRR is found through ___ and ___: plug various discount rates into the NPV equation until it is zero. Note, when the NPV is ____ the present value of the inflows exactly equals the present value of the outflows

he internal rate of return (IRR) is the rate of return you get from aninvestment if the price you pay for an asset is exactly the same as what the asset is worth: NPV = 0. IRR is found through trial and error: plug various discount rates into the NPV equation until it is zero. Note, when the NPV is zero the present value of the inflows exactly equals the present value of the outflows

trial and error

refers to solving for the IRR. Various discount rates are plugged into the equation to find the correct discount rate that sets the NPV to zero