Reading 7: Discounted Cash Flow Applications

Question 1

NPV (Definition)

Answer 1

(1) The PV of cash inflows associated with the project; less
(2) PV of expected cash outflows,
(3) discounted at the appropriate cost of capital

Question 2

NPV (Procedure)

Answer 2

(1) Identify all costs (outflows) and benefits (inflows) associated with the investment
(2) Determine an appropriate discount rate (opportunity cost)
(3) Calculate the PV of each of the cash flows. NB: inflows are positive and will increase NPV and outflows are negative and will decrease NPV
(4) Sum the DCFs

Question 3

IRR (Definition)

Answer 3

The rate of return that equates the PV of an investment project’s benefits (cash inflows) with the PV of its costs (cash outflows) i.e. the discount rate for which the NPV is zero

TM Comment: Break even point

Question 4

IRR (Methodology)

Answer 4

Calculating the IRR requires that we only identify the relevant cash flows to the investment opportunity being evaluated. Market determined discount rates or external (market-data) is not necessary with the IRR procedure

Question 5

IRR (Relationship to NPV and Discount Rate)

Answer 5

In Capital Budgeting, the initial cash flow (CF0) relates to the initial cost of the investment, so will be a negative number.

As such, any discount rate less than the IRR will result in a positive NPV and a discount rate higher than the IRR will result in a negative NPV.

Therefore, when Discount Rate = IRR, NPV = 0.

Question 6

NPV Decision Rule

Answer 6

1. Accept projects with positive NPV. They will increase shareholder wealth
2. Reject projects with negative NPV. They will decrease shareholder wealth
3. Where projects are mutually exclusive (i.e. only one can be chosen), choose the project with the highest positive NPV

Question 7

IRR Decision Rule

Answer 7

Provides the analyst with a result in terms of rate of return. Summarized as:

1. Accept projects with an IRR greater than the firm/investor’s required rate of return
2. Reject projects with an IRR less than the firm/investor’s required rate of return

Question 8

NPV/IRR Conflicts

Answer 8

1. Mutually Exclusive Projects
2. Reinvestment Rate (NPV = market-based opp cost of capital, IRR = IRR)
3. Goal = maximization of shareholder wealth so when they conflict choose the project with the greatest NPV

Question 9

Holding Period

Answer 9

Can be any period of time

Question 10

Holding Period Return (Definition)

Answer 10

Percentage change in the value of an investment over the period it is held

Question 11

Total Return

Answer 11

Holding Period Return + Value of Interim Cash Flows during the Holding Period (dividends/interest payments)

Question 12

Holding Period Return (Formula)

Answer 12

HPR = Ending Value / Beginning Value - 1

Question 13

Total Return (Formula)

Answer 13

TR = (Ending Value + Cash Flow Received) / Beginning Value - 1

Question 14

Money Weighted Return of a Portfolio

Answer 14

The internal rate of return of a portfolio taking into account all cash inflows and outflows.

Rate where inflows = outflows

Note that the beginning value and all inflows are treated as inflows whereas all outflows and the ending value are treated as outflows

Question 15

Time Weighted Rate of Return (Definition)

Answer 15

1. Measures Compound Growth
2. Rate at which $1 compounds over a specified performance horizon
3. Process of averaging a set of values over time

Preferred method of performance measurement (in investment management), because it is not affected by the timing of cash inflows and outflows

Question 16

Time Weighted Rate of Return (Methodology)

Answer 16

1. Form Subperiods that correspond to the dates of deposits and withdrawals
2. Compute the HPR of the portfolio for each subperiod
3. Compute the product for each subperiod to obtain a total return for the entire measurement period.

NB: If greater than 1 period then you will need to calculate the geometric mean i.e. the square root of (HPR1 x HPR2) (if using two periods)

Question 17

Geometric Mean (Usage)

Answer 17

Used for Time Weighted Returns where there is more than 1 number

Question 18

Geometric Mean (Formula)

Answer 18

1. Multiple relevant %s together
2. Nth root of the outcome
   N = Count of numbers

Question 19

Time Weighted Return v Money Weighted Return

Answer 19

1. Time Weighted is preferred as removes distortions in cash flows
2. If manager has complete control over cash flows then money weighted will be preferred
3. Money weighted would be higher if cash inflow before period of higher portfolio performance and vice versa

Question 20

Bank Discount Yield (“BDY”) (Definition)

Answer 20

How T-Bills are quoted, which is based on the face value of the instrument, rather than its purchase price

TM: Essentially it is the return of a T-Bill

Question 21

Bank Discount Yield (“BDY”) (Formula)

Answer 21

RBD = D/F x 360/t
Where:
RBD = Annualized yield on a bank discount basis
D = Dollar discount. Difference between face value and purchase price
F = Face Value of the Instument
t = number of days until maturity
360 = bank convention for a year

Question 22

Bank Discount Yield (Key Distinctions)

Answer 22

1. Dollar discount is expressed as a fraction of the face value, not the market price of the instrument
2. Annualized by 360 as opposed to 365
3. Assumes no compounding

Question 23

Bank Discount Yield (Limitations)

Answer 23

1. Based on simple interest (Ignores the effect of compounding)
2. Based on Face Value, not purchase price (should be based on amount invested)
3. Annualized over 360yr as opposed to 365yr

Question 24

Holding Period Yield (Definition)

Answer 24

Annual Return between purchase date and maturity date

Question 25

Holding Period Yield (Formula)

Answer 25

(P1 - P0 + D1) / P0 =  
(P1 + D1) / P0 -1
Where:
P1 = Price of investment at maturity 
D1 = interest payment / distribution
P0 = Purchase Price

(Same as Total Holding Return calculation)

Question 26

Effective Annual Yield (“EAY”) (Definition)

Answer 26

Annualized HPY, based on a 365 year, that accounts for compounding interest

Question 27

Effective Annual Yield (“EAY”) (Formula)

Answer 27

EAY = (1+HPY)365/t - 1

Question 28

EAY to HPY

Answer 28

1. Use the EAY before you minus the 1
2. To the power of t/365
3. minus 1
   = HPY

“Using the reciprocal of the exponent”

Question 29

Money Market Yield (Definition)

Answer 29

Equal to the annualized holding period yield (HPY) assuming a 360-day year

Does not account on compounding (assumes simple interest)

Question 30

Money Market Yield (Formula)

Please explain both the HPY conversion and the Bank Discount Yield conversion

Answer 30

RMM = HPY x (360/t)
Where:
HPY = Holding Period Yield

Or:

RMM = 360 x rbd / 360 - (t*rbd)
Where:
RBD = Bond Discount Yield

Question 31

Bond Equivalent Yield (Definition)

Answer 31

2 x semiannual discount rate.

Coupon interest is paid in two semiannual payments

Question 32

Bond Equivalent Yield (Formula)

Answer 32

BEY = [((1+effective annual yield)^0.5)-1] x2