Quant: DCF Applications

Question 1

Key Concept LOS 6a

Answer 1

The: NPV is the present value of a project’s future cash flows, discounted at the firm’s cost of capital, less the project’s cost. IRR is the discount rate that makes the NPV = 0 (equates the PV of the expected future cash flows to the project’s initial cost).
The NPV rule is to accept a project if NPV > 0; the IRR rule is to accept a project if IRR > required rate ofreturn. For an independent {single) project, these rules produce the exact same decision.

Question 2

Key Concept LOS 6b

Answer 2

For mutually exclusive projects, IRR rankings and NPV rankings may differ due to differences in project size or in the timing of the cash flows. Choose the project with the higher NPV as long as it is positive.
A project may have multiple IRRs or no IRR.

Question 3

Key Concept LOS 6c

Answer 3

The holding period return (or yield) is the total return for holding an investment over a certain period of time and can be calculated as:

Question 4

Key Concept LOS 6d

Answer 4

The money-weighted rate of return is the IRR calculated using periodic cash flows into and out of an account and is the discount rate that makes the PV of cash inflows equal to the PV of cash outflows.
The time-weighted rate of return measures compound growth. It is the rate at which $ 1 compounds over a specified performance horizon.
If funds are added to a portfolio just before a period of poor performance, the money­ weighted return will be lower than the time-weighted return. If funds are added just prior to a period of high returns, the money-weighted return will be higher than the time-weighted return.
The time-weighted return is the preferred measure of a manager’s ability to select investments. If the manager controls the money flows into and out of an account, the money-weighted return is the more appropriate performance measure.

Question 5

Key Concept LOS 6e

Answer 5

Question 6

Key Concept LOS 6f

Answer 6

Question 7

NPV =

Answer 7

Question 8

IRR =

Answer 8

IRR = rate of return that equates the PV of expected inflows (revenue) with PV of expected outflows (costs). When IRR = discount rate for NPV calculations, NPV = 0.

When IRR > discount rate, NPV > 0.

When IRR < discount rate, NPV < 0.

USE THE IRR FUNCTION ON CALCULATOR

Question 9

NPV Rule =

Answer 9

Accept projects with positive NPV (increases shareholder wealth), reject negative. Choose between projects by picking the greater NPV.

Question 10

IRR Rule =

Answer 10

Accept projects when IRR > firm’s/investor’s required rate of return. Reject when IRR < reqd rate.

Question 11

Problems with IRR/NPV rules (and solution) =

Answer 11

Rules may give conflicting results due to a) different initial costs b) different timing of cash flows

For mutually exclusive projects choose the NPV recommendation.

Question 12

Holding Period Return (total return if including income received) =

Answer 12

= (ending val - beginning val)/beginning val

= (ending/beginning) -1

OR

= ( [ending + cash flow] / beginning) -1

Question 13

Calculating IRR for a stream of cash in/out flows =

Answer 13

= set the PVinflows equal to the PVoutflows and solve for r

= use the IRR function on the calculator, having entered the CFs (NB inflows and outflows must have opposite signs)

THIS IS THE MONEY-WEIGHTED RATE OF RETURN

Question 14

Calculating Time-Weighted Rate of Return =

Answer 14

= Break the period into subperiods based on the cash flows.

Work out the holding period return for each subperiod.

Compounding the sub period’s HPRs will give a total return.

(1 + TWRR)^n = (HPR₁)…(HPR_n) – SOLVE FOR TWRR

TWRR = [(HPR1)…(HPRn)]^1/n -1

Question 15

T bill quotes and bank discount yield =

Answer 15

T-bills are quoted on a bank discount basis, based on face value (NOT purchase price). BDY is annualized on a 360 day basis and assumes NO compounding.

Question 16

Shortfalls of BDY =

Answer 16

It is important for candidates to realize that a yield quoted on a bank discount basis is not representative of the return earned by an investor for the following reasons:

• Bank discount yield annualizes using simple interest and ignores the effects of compound interest.
• Bank discount yield is based on the face value of the bond, not its purchase price -­ investment returns should be evaluated relative to the amount invested.
• Bank discount yield is annualized based on a 360-day year rather than a 365-day year.

Question 17

Holding Period Yield (HPY) =

Answer 17

= total return earned between purchase date and sale/maturity date

Question 18

EAY (effective annual yield) =

Answer 18

= (1+ HPY)^365/t-1, where t is the time to maturity/holding period

EAY to HPY : HPY = (EAY +1)^t/365 -1

Question 19

MMY (Money Market Yield, or CD equivalent yield) =

Answer 19

is equal to an annualized holding period yield, assuming a 360 day year.

r_mm = HPY x (360/t)

Question 20

Given BDY, calculate MMY =

Answer 20

= (360 x BDY) / 360 - (t x BDY)

or

Question 21

Extra Notes - HPY, EAY, MMY (r_mm) =

Answer 21

Once we have established HPY, EAY, or rMM, we can use one as a basis for calculating the other two.

• The HPY is the actual return an investor will receive if the money market instrument is held until maturity.
• The EAY is the annualized HPY on the basis of a 365-day year and incorporates the effects ofcompounding.
• The rMM is the annualized (HPY) yield that is based on price and a 360-day year and does not account for the effects of compounding - it assumes simple interest.

Question 22

Bond equivalent yield =

Answer 22

based on semi annual coupon payments. BEY = 2x semi-annual HPY.

Thus, given a quarterly rate you would have to compound to get an effective semi annual yield, and multiply by 2 to get the BEY.

Given an EAY you would have to convert to a semi annual HPY {(EAY+1)^0.5}and multiply by 2 to get the BEY.