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MN1050- Corporate Finance For Managers > The Time Value of Money > Flashcards

The Time Value of Money Flashcards

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1
Q

What is opportunity cost?

A

The next best alternative foregone return in decision making

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2
Q

What is the saying about the time value of money?
Explain

A

A dollar today is worth more than a dollar tomorrow.
One reason for this is the opportunity costs of holding cash instead of investing in higher-return projects. Also, inflation.

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3
Q

What does the time value of money concern?

A

Both present value (PV) and future value (FV)

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4
Q

What is the measure of time value of money?

A

Interest rate (r):
- Expected rate of return
- Discount rate
- Opportunity cost of money

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5
Q

Is travelling from the future the expected rate of return?

A

No, that is the discount rate.
Travelling to the future is the expected rate of return.

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6
Q

What is the equation showing the FV of a single cash flow?

A

FV = C x (1 + r)^t

C= Cash flow
r = Periodic interest rate
t= No. of period interest is calculated

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7
Q

What happens when funds are invested for a long time in terms of interest?

A

The longer the funds are invested, the greater the advantage with compound interest

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8
Q

Define annuity

A

A stream of equal cash flows that occurs yearly over a given period

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9
Q

Example of future value of annuities:
Your education account – an annuity of £2,000 for 15 years. The FV of the account at the end of year 15 is the sum of the FV of the 15 individual CFs, given r = 3%:

A

FV1st CF = £2,000 x 1.0314 = £3,025.18
FV14th CF = £2,000 x 1.031 = £2,060.00

FV annuity = FV1st CF + FV2nd CF + … + FV15th CF = £37,197.83

> £30,000 so your educational cost is safely covered

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10
Q

What is the equation for the FV of an annuity?

A

FV annuity = C / r x [(1 + r+)^t - 1]

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11
Q

What is the equation for the PV of a future single cash flow?

A

PV = C / (1+r)^t = C x 1 / (1 + r)^t

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12
Q

What is 1 / (1 + r)^/t known as?

A

The discount factor

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13
Q

How can you calculate the discount factor?

A

PV / C

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14
Q

What is the equation for the present value of multiple cash flows happening at different periods (Discounted cash flow formula (DCF) ?

A

PV0 = [C1 / (1+r)^1] + [C2 / (1+r)^2 + …

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15
Q

In the discounted cash flow formula, if t is a finite or infinite number, what is it the PV of?

A

Annuity if t is a finite number.
A perpetuity if t is an infinite number.

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16
Q

In the discounted cash flow formula, if t is a finite or infinite number, what is it the PV of?

A

Annuity if t is a finite number.
A perpetuity if t is an infinite number.

17
Q

Your education will increase your annual salary (without the degree) by £1,800 for the next 30 years. Given a discount rate of 5%, the PV of salary increase is?

A

PV = (1800 / 0.05) X [1 - (1 / (1 + 0.05)^30 )] = £27,670.41

18
Q

What is the equation for the PV of annuities?

A

PVannuity= [C / r] x [1 - (1 / (1 + r)^t]

19
Q

What is the net present value (NPV) of a project or investment?

A

It is the difference between the present value of its benefits and the required investment

20
Q

What is the NPV formula?

A

NPVo= Co + PVo = Co + Sigma[Ct / (1 +r)^t]

Co = initial investment for the project. Cash outflow so has a negative sign
r = opportunity cost of capital

21
Q

What is the NPV rule?

A

Accept investments with positive NPVs

22
Q

What is meant by perpetuity?

A

Like annuity but the cash flow goes on forever

23
Q

What is the formula for the PV of perpetuities?

A

PV perpetuity= C / r

24
Q

What is the formula for the PV of growing annuities?

A

PV of growing annuities = [C1 / (r - g)] x [1 - [(1 + g) / (1 + r)]^t]

g= the annual growth rate of cash flow

25
Q

What is the equation of the PV of a growing perpetuity?

A

PV of a growing perpetuity = C1 / (r - g)

26
Q

What is the effective annual rate (EAR)?

A

The annual rate of return actually earned after adjustments have been made for different compounding periods

27
Q

What is the annual percentage rate (APR)?

A

Annualised interest rate without compounding (the quoted rate)

28
Q

How do you calculate EAR?

A

EAR = (1 + periodic rate)^m - 1

Periodic rate = stated annual rate /m
m = the number of compounding periods per year

29
Q

Compute EAR if the stated annual rate (this is the annual percentage rate, APR) is 12%, compounded semi-annually

A

Here m = 2 , so the periodic rate is 12/2= 6%.
Thus, EAR= (1 + 0.06)2 - 1 = 1.1236- 1 = 0.1236 = 12.36%

MN1050- Corporate Finance For Managers (10 decks)

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