F305 TVM

When evaluating an investment, how does the tax rate affect the cash flow stream?

The tax rate reduces the cash flow by decreasing net income.

What are essential components to consider when calculating the internal rate of return (IRR)?

Timing of cash flows, Net cash flows over the investment period, Initial Investment

What is the core principle that prevents money received at different times from being directly added?

Money has a time unit, making it akin to different currencies. To aggregate it, you must first convert all amounts to a common time unit using an exchange rate for time (the discount factor).

What is the primary tool for visually representing when cash flows occur?

A timeline. It places cash flows (CF) with subscripts (e.g., CF0, CF1) at their corresponding time periods (0, 1, 2…), where period 0 typically represents "today."

What is the "exchange rate for time" called in finance?

The discount factor. It is calculated as 1 + R to the power of T, where R is the discount rate and T is the number of time periods.

What does R represent in the discount factor 1+R to the power of T ((1+R)^T)?

R is the rate of return offered by investment alternatives in the capital markets of equivalent risk. It is also called the discount rate, hurdle rate, or opportunity cost of capital.

What is the process called for moving a future cash flow to an earlier point in time?

Discounting. This involves dividing the future cash flow by (1+R)^t (where t is positive), giving it a present value.

What is the value of a future cash flow as of today (period 0) called?

Its Present Value (PV). It represents the discounted value of that cash flow.

What is the fundamental rule when dealing with cash flows from different time periods?

Never add or subtract cash flows from different time periods. They must first be converted to a common time unit via discounting or compounding.

What is the process called for moving a cash flow to a later point in time?

Compounding. This involves multiplying the cash flow by (1+R)^t (where t is positive), giving it a future value.

What is the value of a cash flow moved forward to a later time period called?

Its Future Value (FV).

What is an Annuity?

A finite stream of cash flows of identical magnitude, received at equal intervals of time.

What is the key assumption for the standard present value of an annuity formula?

The first cash flow arrives one period from today (at t=1).

What is a Perpetuity?

An infinite stream of cash flows of identical magnitude, received at equal intervals of time forever.

What is the formula for the present value of a perpetuity?

PV = CF/R , where CF is the constant cash flow and R is the discount rate.

What is a Growing Annuity?

A finite stream of cash flows that grow at a constant rate (g), received at equal intervals of time.

What is a Growing Perpetuity?

An infinite stream of cash flows that grow at a constant rate (g), received at equal intervals of time.

What is the formula for the present value of a growing perpetuity?

PV = CF1/(R - g), where CF1 is the cash flow one period from today, R is the discount rate, and g is the constant growth rate (with R > g).

PV = CF1

(R - g), where CF1 is the cash flow one period from today, R is the discount rate, and g is the constant growth rate (with R > g).

What is the formula for the after-tax discount rate? (Rt)

Rt = R * (1 - t), where R is the pre-tax discount rate and t is the tax rate.

How do taxes affect an investment's dollar return?

Taxes reduce the dollar return. The after-tax return is lower than the pre-tax return.

In the context of the time value of money, what does the "opportunity cost of capital" refer to?

The return foregone by investing in a particular project instead of in an alternative investment of equivalent risk in the capital markets.

What does the Discount Rate (R) fundamentally reflect about a cash flow stream?

It reflects the risk of the cash flow stream. Riskier cash flows are associated with a higher discount rate.

According to the course motivation, what is the broad purpose of corporate finance tools?

To quantify the costs and benefits of decisions to enable better financial decision-making, applicable to both corporate and personal finance.

Why is money received today worth more than the same amount received in the future?

Because of the opportunity cost of not being able to invest it today. Money today can be put to work to earn a return.

What is the relationship between risk and the opportunity cost/discount rate?

Higher risk implies a higher opportunity cost/discount rate. Low risk, low cost; high risk, high cost.

In the bank account example with taxes, why did the investor run out of money before the fourth withdrawal when using the pre-tax rate?

Because the pre-tax analysis ignored that interest earned in the account is taxed, reducing the actual funds available for withdrawal.