QM LM2 time value of money in finance

Question 1

What are the 3 rules of money?

Answer 1

1. Larger cash flows are worth more
2. Less risky cash flows are worth more (lower discount rate)
3. Cash flows sooner rather than later are worth more (time value of money)

Question 2

What is the equity premium?

Answer 2

When a company liquidates debt holders get first priority on the liquidated assets. Therefore no matter how risky the debt, equity is always riskier. Hence whent taking an equity position, there must be an additional return to compensate for this additional risk.

Question 3

What is the formula for present value for a single cash flow?

Answer 3

PV = FV x e ^ (- r x T)

FV = Future value
e = Euler’s constant
r = rate of return
T = no. of periods

Question 4

What is the formula for future value for a single cash flow?

Answer 4

FV = PV x e ^ (r x T)

FV = Future value
PV = Present value
e = Euler’s constant
r = rate of return
T = no. of periods

Question 5

What is a bullet bond?

Answer 5

You pay back the interest periodically but you make one big payment at the end of principal

Question 6

What is a fully amortising bond?

Answer 6

• Typically in the format of a mortgage or auto loan.
• The investor receives level payments of both interest and principal.
• Before the final payment principal outstanding is close to zero

Question 7

What is a semi?

Answer 7

A bond that has a semi-annual coupon payment

Question 8

What is a perpetuity?

Answer 8

An investment that pays out a yield forever, rather than over a fixed and finite term

Question 9

How do you calculate present value of a perpetuity?

Answer 9

PV = payment received / r

Question 10

What is a constant growth dividend?

Answer 10

A dividend which grows every year
This can be used to value the present value of commercial real estate, where the rent you can collect grows each year

Question 11

What is the formula for calculating present value of a constant growth dividend?

Answer 11

PV = Dsub0 (1 + g) / [r - g]

Where Dsub0 is the current dividend we get,
g is the growth rate of the dividend,
r is the prevailing rate

Question 12

Why should you not use Dsub1 as the starting point of a calculation?

Answer 12

Dsub0 you must grow by g to get Dsub1.
It’s common to get questions which give you Dsub1, and let you walk into the trap of adding the growth rate to Dsub1, when it already includes it

Question 13

How can we find the expected growth rate if we have the present value and dividend payout ratio of a company?

Answer 13

PV/E = (Dsub0 / E) (1 + g) / [r - g]

PV = present value
E = earnings
Dsub0 / E = the dividend payout ratio
g = the expected growth rate
r = the prevailing rate

We can rearrange to find g.
We could also solve for r if we know the expected growth rate.

Question 14

Under what conditions would we expect forward PE to increase?

Answer 14

• If the forward dividend is expected to increase
• If growth is expected to increase

Question 15

How do you calculate r if you have the forward PE ratio and dividend payout ratio?

Answer 15

Forward PE = DPR / [r - g]

For example, if
- forward PE = 25
- DPR = 30%
- g = 5%

25 = 30% / [r - 5%]
25r - 1.25 = 0.3
25r = 1.55
r = 6.2%

Question 16

Find the expected growth rate given:
Forward PE = 14
DPR = 55%
r = 7%

Answer 16

Forward PE = DPR / [r - g]

14 = 55% / [7% - g]
0.98 - 14g = 0.55
0.43 = 14g
3.07% = g

Question 17

How do we determine whether a stock is a buy or sell based on the following:
Real forward PE = 32
DPR = 40%
r = 12%
g = 9%

Answer 17

Forward PE = DPR / [r - g]

Find what forward PE it should be trading at:

Fundamental forward PE = 40% / [12% - 9%]

FFPE = 40% / 3%
FFPE = 13.33
13.33 < 32, the real forward PE
Therefore sell

Question 18

What is the principle of no arbitrage?

Answer 18

• 2 economically equivalent strategies should have the same price
• This is how we price derivatives: both cashflows should net out

Question 19

What is a forward rate?

Answer 19

You can lock in rates in the future now.

Question 20

Why do you not use government debt spot rates when pricing derivatives?

Answer 20

The government does not participate in the derivatives market. It’s the investment banks which are counterparty to almost every transaction. Therefore you have to use an interbank rate. The LIBOR used to be used, now SOFR is being phased in

Question 21

How does the principle of no arbitrage affect the forex market?

Answer 21

You should be able to get an equal return in one currency as if you convert your money to another currency into another currency and buy debt in that currency
Thus when the rate for one currency goes up the value of that currency goes up to compensate.

Question 22

If the interest rate is higher on the numerator of a forex trade than the denominator, how does it affect the forward rate?

Answer 22

The forward rate will trade at a discount to a spot

Question 23

If the interest rate is higher on the denominator of a forex trade than a numerator, how does it affect the forward rate?

Answer 23

The forward rate will trade at a premium to the spot

Question 24

What is a pip?

Answer 24

Move the decimal place by four zeros
a hundred pips is 1%
ten thousand pips is 100%

This is the term used in currencies
When you’re dealing with interest rates they’re called basis points

Question 25

When would you use a one period binomial call options model?

Answer 25

When you have two value outcomes a few months in the future that can be fairly predicted
- buying land and waiting for surveys to see if you will get planning permission to build. Costs much less than paying the full price of the land upfront
- company buys a novel from a writer and pays them a small amount for a few months. Again less costly in case they cannot make a movie from it