Chapter 5: The Time Value of Money

Question 1

Formula for interest?

Answer 1

Interest = interest rate x initial investment

Question 2

Formula for Future Value (FV) of investment?

Answer 2

FV = investment x (1 + interest rate)^t

Question 3

The definition of FV?

Answer 3

Amount to which an investment will grow after earning interest (money received today is generally worth more than tomorrow).

Question 4

The definition of compound interest?

Answer 4

Interest earned on interest.

Question 5

The definition of simple interest?

Answer 5

Interest earned only on the original investment; no interest is earned on interest.

Question 6

Formula for Present Value (PV) of investment?

Answer 6

PV = FV / (1 + r)^t

Where:
FV=Future Value
r=Rate of return
t=Number of periods

Question 7

The definition of PV?

Answer 7

Value today of a future cash flow.

Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations.

KEY TAKEAWAYS
Present value is the concept that states an amount of money today is worth more than that same amount in the future. In other words, money received in the future is not worth as much as an equal amount received today.
Money not spent today could be expected to lose value in the future by some implied annual rate, which could be inflation or the rate of return if the money was invested.
Calculating present value involves making an assumption that a rate of return could be earned on the funds over the time period.

Question 8

The definition of discounted cash flow (DCF)?

Answer 8

Method of calculating present value by discounting future cash flows.

Discounted cash flow (DCF) is a valuation method used to estimate the value of an investment based on its future cash flows. DCF analysis attempts to figure out the value of an investment today, based on projections of how much money it will generate in the future. This applies to both financial investments for investors and for business owners looking to make changes to their businesses, such as purchasing new equipment.

KEY TAKEAWAYS
Discounted cash flow (DCF) helps determine the value of an investment based on its future cash flows.
The present value of expected future cash flows is arrived at by using a discount rate to calculate the discounted cash flow (DCF).
If the discounted cash flow (DCF) is above the current cost of the investment, the opportunity could result in positive returns.
Companies typically use the weighted average cost of capital for the discount rate, as it takes into consideration the rate of return expected by shareholders.
The DCF has limitations, primarily that it relies on estimations on future cash flows, which could prove to be inaccurate.

Question 9

The definition of discount rate?

Answer 9

Interest rate used to compute present values of future cash flows.

In this context of DCF analysis, the discount rate refers to the interest rate used to determine the present value. For example, $100 invested today in a savings scheme that offers a 10% interest rate will grow to $110. In other words, $110 (future value) when discounted by the rate of 10% is worth $100 (present value) as of today. If one knows - or can reasonably predict - all such future cash flows (like future value of $110), then, using a particular discount rate, the present value of such an investment can be obtained.

What is the appropriate discount rate to use for an investment or a business project? While investing in standard assets, like treasury bonds, the risk-free rate of return is often used as the discount rate. On the other hand, if a business is assessing the viability of a potential project, they may use the weighted average cost of capital (WACC) as a discount rate, which is the average cost the company pays for capital from borrowing or selling equity. In either case, the net present value of all cash flows should be positive to proceed with the investment or the project.

Question 10

The definition of discount factor?

Answer 10

The PV of a $1 future payment, aka 1 / (1+r)^t

Question 11

Why is “r” called the Opportunity Cost of Capital?

Answer 11

It is the return foregone by not investing in securities (projects) that involve the same expected risk (also referred to as the discount rate, the hurdle rate, the benchmark rate).

Question 12

What is the simple Annual Percentage Rate (APR)?

Answer 12

The periodic rate (e.g. weekly) multiplied by the number of periods per annum

Question 13

What is the real interest rate formula?

Answer 13

1+ R= (1+r)/(1+inflation rate)

Question 14

What is the Effective Annual Percentage Rate (EAR)?

Answer 14

EAR=1.01^52 - 1

Question 15

What is the rule of 72?

Answer 15

For any number of years ‘n’, if you divide 72/n you get the approximate interest rate needed to double your money.

Question 16

What is the formula for discount factor (DF)?

Answer 16

DF = 1 / (1+r)^n

Question 17

What is the formula for growing perpetuities?

Answer 17

PV of a growing perpetuity = next period’s cash flow / Cost of capital - growth rate (of C.F.’s)

Question 18

If you invest money at a given interest rate, what will be the FV of your investment?

Answer 18

An investment of $1 earning an interest rate of r will increase in value each period by the factor (1+r). After t periods, its value will grow to (1+r)^t. This is the FV of the $1 investment with compound interest.

Question 19

What is the PV of a cash flow to be received in future?

Answer 19

The PV of a future cash payment is the amt that you would need to invest today to produce the future payment.

Question 20

How can we calculate PV and FV of streams of cash payments?

Answer 20

A level stream of cash payments that continues indefinitely is known as a perpetuity; one that continues for a limited number of years is called an annuity. The PV of a stream of C.F.s is simply the sum of the PV of ech ind C.F. Similarly, the FV of an annuity is the sum of the FV of ech ind C.F. Shortcut formulas make the calculations for perpetuities and annuities easy.

Question 21

How should we compare interest rates quoted over different time intervals, for example, monthly versus annual?

Answer 21

Interest rates for short time periods are often quotes as annual rates by multiplying the per-period rate by the number of periods in a year; these are known as annual percentage rates (APRs). They do not recognised the effect of compound interest, and assume simple interest. The effective annual rate (EAR) annualises uses compound interest. It equals the rate of interest per period compounded for the number of periods in a year.

Question 22

What is the difference between real and nominal C.F.s and between real and nominal interest rates?

Answer 22

A dollar is a dollar, but the amount of goods that a dollar can buy is eroded by inflation. If prices double, the real value of a dollar halves. Financial managers and economists often find it helpful to reexpress the future cash flows in terms of real dollars.