Reading 6 LOS's

Question 1

LOS 6a: Calculate and interpret the net present value and the internal rate of return for an investment

LOS 6b: Contrast the NPV rule to the IRR rule, and identify problems associated with the IRR rule

Answer 1

The net present value (NPV) of an investment equals the present value of all expected inflows from the investment minus the present value of all expected outflows. The rate used to discount the cash flows is the appropriate cost of capital, which reflects the opportunity cost of undertaking the particular investment

NPV = Σ ( Cash Flows / (1+ r)^t )

Calculating a projects NPV requires the following steps:

1. Identify all cash inflows and outflows associated with the investment
2. Determine the appropriate discount rate
3. Compute the PV of all cash flows
4. Aggregate all the present values, with inflows as positive and outflows as negative

After the NPV has been calculated, the NPV rule is applied to determine whether the project should be undertaken

• Positive NPV means that project should be undertaken
• Negative NPV means it shouldn’t
• For mutually exclusive projects (where only one can be taken) the one with the highest NPV should be taken

Internal Rate of Return (IRR)
The IRR of a project is the discount rate that equate the project’s NPV to zero. Effectively it is the discount rate that equates the present vcalue of all inflows from a project to the present value or all project-related outflows. An important thing to remember regarding IRR is that it assumes that all cash flows from the project will be reinvested at the IRR

The IRR rules dictates

• Projects for which IRR exceeds the required rate of return should be accepted
• Projects for which IRR is lower than the required rate of return should be rejected

Problems Associated with IRR

For mutually exclusive projects, NPV and IRR may offer conflicting conclusions. This can happen in two scenarios:

1. When the projects initial cash outlays are different
2. When there is a difference in the timing of cash flows across the projects

NPV assumes that interim cash flows from the project will be reinvested at the required rate of return, whereas IRR assumes they will be reinvested at the IRR. When choosing between mutually exclusive projects, use the NPV rule if there is conflict

There are 2 additional problems with IRR

1. Multiple IRR problem projects with nonconventional cash flow pattern may have more than one IRR
2. No IRR Problem it is also possible to have a positive NPV project with no IRR, meaning there is no discount rate that results in a zero NPV

Question 2

LOS 6c: Calculate and interpret a holding period return (total return)

Answer 2

Holding period yield or return (HPY) is quite simply the return earned on an investment over the entire investment horizon.

HPY = P₁ - P₀ + D₁ / P₀

Question 3

LOS 6d: Calculate and compare the money-weighted and time-weighted rates of return of a portfolio and evaluate the performance of portfolios based on these measures

Answer 3

The money-weighted rate of return is simply the internal rate of return of an investment. It accounts for the timing and amount of all dollar flows into and out of the portfolio. To calculate follow these steps:

1. Determine the timing and nature of the cash flow.
2. Equate the PV of cash outflows to the PV of cash inflows
3. Calculate the value of r to find the money-weighted return. We can calculate r by using the IRR function on the calculator

The time-weighted rate of return measures the compounded rate of growth of an investment over a stated measurement period. In contrast to money-weighted return, the time-weighted return:

1. Is not affected by cash withdrawals or contributions to the portfolio
2. Averages the holding period returns over time

Important Takeaways

• The time-weighted rate of return is preferred because it is not affected by the timing and amount of cash inflows and outflows
• Decisions regarding contributions and withdrawals from a portfolio are usually made by clients. Since these decisions are not typically in investment managers hands, it would be inappropriate to evaluate their performance based on money-weighted returns
• If funds are deposited into the investment portfolio prior to a period of superior performance, money-weighted return will be higher than time-weighted return

Question 4

LOS 6e: Calculate and interprety the bank discount yield, holding period yield, effective annual yield, and money market yield for U.S. Treasury bills and other money market instruments

LOS 6f: Convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields.

Answer 4

Market Yields

Bank Discount Yield- This quoting convention is used primarily for quoting Treasury Bills. The bank discount yield (BDY) annualizes the discount on the instrument as a percentage of par or face value over a 360-day period. It is computed as:

• r= (D/F) x (360/t)
• where D = dollar discount (face value - purchase price)
• F = face value of bill

Yields presented on a bank discount basis do not hold much meaning to investors for the following reasons:

1. Investors want to evaluate returns based on the amount invested when purchasing the instrument. BDY calculates returns based on par
2. Returns are based on a 360-day year rather than a 365-day year
3. BDY assumes simple interest. In doing so it ignores interest earned on interest

Holding Period Yield the HPY equals the return realized on an investment over the entire horizon that it is held. It is an unannualized return that is calculated as follows:

• HPY = (P₁-P₀ + D₁) / P₀ = [(P₁+D₁) / P₀] - 1

Effective Annual Yield (EAY) this is an annualized return measure that accounts for compounding over 365-day period and is calculated as:

• EAY = (1 + HPY) ^t/365 - 1

we can also convert an EAY to HPY using the following formula

• HPY = (1 + EAY)^t/365 - 1

Money Market Yield or CD Equivalent Yield is the holding period yield annualized on a 360-day basis. Further it does not consider the effects of compounding. It is different from a bank discount yield as it is based on the purchase price, not par value. For treasuries, the money-market yield can be obtained from the bank discount yield using the following formula:

• R_MM = [(360 x r_BD) / (360 -(t x r_BD)] , or more conveniently
• R_MM= HPY x (360/t)

An easy way to get through these problems is to first calculate the HPY and then convert the HPY into the required return measure

• The HPY is the actual unannualized return an investor realizes over a holding period
• The EAY is the HPY annualized on a 365-day year with compounding
• the R_MM is the HPY annualized on a 360 day year without compounding

Bond Equivalent Yield

The BEY is simply the semiannual discount rate multipled by two. This convention comes from the US where bonds are quoted at twice the semiannual rate because coupon payments are made semiannually