Reading 7 - Discounted Cash Flow Applications

Question 1

NPV

Answer 1

The net present value (NPV) of a project is the present value of its cash inflows minus the present value of its cash outflows. The internal rate of return (IRR) is the discount rate that makes NPV equal to 0. We can interpret IRR as an expected compound return only when all interim cash flows can be reinvested at the internal rate of return and the investment is maintained to maturity.

Question 2

NPV rule and IRR rule for decision making

Answer 2

The NPV rule for decision making is to accept all projects with positive NPV or, if projects are mutually exclusive, to accept the project with the higher positive NPV. With mutually exclusive projects, we rely on the NPV rule. The IRR rule is to accept all projects with an internal rate of return exceeding the required rate of return. The IRR rule can be affected by problems of scale and timing of cash flows.

Question 3

Money-weighted return vs. time-weighted return

Answer 3

Money-weighted rate of return and time-weighted rate of return are two alternative methods for calculating portfolio returns in a multiperiod setting when the portfolio is subject to additions and withdrawals. Time-weighted rate of return is the standard in the investment management industry. Money-weighted rate of return can be appropriate if the investor exercises control over additions and withdrawals to the portfolio.

Question 4

Money-weighted return

Answer 4

The money-weighted rate of return is the internal rate of return on a portfolio, taking account of all cash flows.

Question 5

Time-weighted return

Answer 5

The time-weighted rate of return removes the effects of timing and amount of withdrawals and additions to the portfolio and reflects the compound rate of growth of one unit of currency invested over a stated measurement period.

Question 6

Bank discount yield

Answer 6

The bank discount yield for US Treasury bills (and other money-market instruments sold on a discount basis) is given by r_BD = (F − P₀)/F × 360/t = D/F × 360/t, where F is the face amount to be received at maturity, P₀ is the price of the Treasury bill, t is the number of days to maturity, and D is the dollar discount.

Question 7

Holding period yield

Answer 7

For a stated holding period or horizon, holding period yield (HPY) = (Ending price − Beginning price + Cash distributions)/(Beginning price). For a US Treasury bill, HPY = D/P₀.

Question 8

Effective annual yield

Answer 8

The effective annual yield (EAY) is (1 + HPY)^365/t − 1.

Question 9

Money market yield

Answer 9

The money market yield is given by r_MM = HPY × 360/t, where t is the number of days to maturity.

Question 10

Money market yield for a treasury bill

Answer 10

For a Treasury bill, money market yield can be obtained from the bank discount yield using r_MM = (360 × r_BD)/(360 − t × r_BD).

Question 11

Converting back and forth between yields

Answer 11

We can convert back and forth between holding period yields, money market yields, and effective annual yields by using the holding period yield, which is common to all the calculations.

Question 12

Bond equivalent yield

Answer 12

The bond equivalent yield of a yield stated on a semiannual basis is that yield multiplied by 2.

Question 13

What are the three commonly used yield measures:

Answer 13

Holding Period Yield

HPY = (P₁ – P₀ + D₁)/P₀

Effective Annual Yield

EAY = (1 + HPY)^365/t – 1

Money Market Yield (CD Equivalent Yield)

r_MM = (360R_BD)/(360 – (t)(r_BD))