Discounted Cash Flow Applications (Reading 6)

Learning Outcome Statements (LOS)

a

Calculate and interpret the net present value(NPV) and the internal rate of return(IRR) of an investment:

     The NPV is the present value of a project’s future cash flow, discounted at firm’s cost of capital, less the project’s cost. IRR is the discount rate that makes the NPV=0.

     The NPV rule is to accept a project if NPV>0; the IRR rule is to accept a project if IRR>required rate of return. For an independent project, these rules produce the exact same decision.

     净现值是按照公司的资本成本，把将来现金流进行折现，减去初始的现金流支出得到的净值。内部回报率是使这个投资的现金流净现值为0的折现率。

     如果一个项目的NPV大于0，就应该投资这个项目；如果一个项目的IRR大于公司的要求回报率，就应该投资这个项目。对于独立的项目来说，NPV和IRR得到一样的结果。

b

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

     For mutually exclusive projects, IRR rankings and NPV rankings may differ due to differences in project size or in the timing of the cash flow. Choose the project with the higher NPV as long as it is positive.

     A project may have multiple IRRs or no IRR.

     对于两个互不相容的项目，由于项目规模或是现金流时间点不同，NPV和IRR可能会得到不用的结论。如果NPV大于0，选择NPV最大的项目。

     一个项目可能有多个IRR或是没有IRR。

c     

Calculate and interpret a holding period return(total return):

     The holding period return is the total return for holding an investment over a certain period of time.

     持有期收益率是在一定时间内进行一项投资所能获得的总收益。

d    

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:

     The money-weighted rate of return is the IRR calculated using periodic cash flow 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.

     价值加权回报率是在考虑所有现金流入或现金流出的情况下，一个投资组合的内部回报率。

     时间加权回报率用来衡量复合增长。

e  

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

     .

f

Convert among holding period yields, money market yield, effective annual yields, and bond equivalent yields:

Formulas:

Holding period yield

Money market yield

Effective annual yield

Holding period yield

Bond equivalent yield

Exercise Problems:

1.      A project offers the following incremental after-tax cash flow. The discount rate of the project is 10%:

The NPV and IRR of the project is closest to:

              NPV              IRR

A.            31.2              12.0%

B.             240               10.0%

C.             31.2              10.0%

 Ans: A;

Use calculator:

NPV=31.2

IRR=12.0%

2.      When considering two mutually exclusive capital budgeting projects with conflicting rankings, the most appropriate conclusion is to choose the project with the:   

A.    Shorter payback.

B.     Higher NPV.

C.     Higher IRR.

Ans: B; since the NPV of an investment represents the expected addition to shareholder wealth from an investment, and we take the maximization of shareholder wealth to be a basic financial objective of a company.

A is incorrect; Payback period refers to the period of time for the return on an investment to “repay” the sum of the original investment. The shortcoming is ignoring the cash flow after the payback period.

C is incorrect; IRR rules may be meaningless when the scale of projects or timing of cash flows is different. Also IRR calculation furthermore assumes reinvestment at the IRR, which always cannot be achieved.

3.      Nan Chen purchases 100 shares of Bao Capital’s stock at a price of $40 on March 1^st, 2012, and then sells them on $43 on August 1^st, 2012. During the year of 2012, Bao Capital paid dividends of $0.5 per share on January 1^st and July 1^st. the holding period return on the investment is closest to:

A.    7.50%

B.     8.75%

C.     10.00%

Ans: B; Holding period return determines the return that an investor will earn by holding the instrument to maturity; as used here, this measure refers to an unannualized rate of return. The formula to calculate holding period return is as below:

In this problem P₀=40, P₁=43, and D₁= 0.5, so HPY=8.75%

A is incorrect; since it ignores the dividend.

C is incorrect; though Bao Capital paid dividend twice in 2012, but there was only once during Nan held the shares, so dividend is $0.5, not $1.

4.      Junyun Lu purchases one share of stock for $50. Exactly one year later, the company pays a dividend of $1 per share. This is followed by one more annual dividends of $1.25. And then she sells the share for $60. The money-weighted rate of return on this investment is closest to:

A.  24.50% 

B.  20.00%

C.  11.68%

Ans: C ; The money-weighted rate of return is the IRR calculated using periodic cash flow 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. In this problem:

5.      An analyst gathers the following information about the performance of a portfolio:

The portfolio’s annual time-weighted rate of return is closest to:

A.    8%

B.     27%

C.     32%

Ans: C :  The time-weighted rate of return measures compound growth. It is the rate at which $1 compounds over a specified performance horizon. In this problem:

6.      On 1 January 2012, Yang Liu purchases 100 shares of stock for $10 a share. On 1 March 2012, she purchases 100 more shares of the sane stock for $12.5 a share. On 1 June 2012, she sells all 200 shares of the stock for $15 a share. The internal rate of return for this investment is best described as an example of a:

A.    Geometric mean return

B.     Time-weighted rate of return

C.     Money-weighted rate of return

Ans: C; since The money-weighted rate of return is the IRR calculated using periodic cash flow 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.

A is incorrect; given a time series of holding period returns R_t, the geometric mean return over the time period spanned by the returns R₁ to R_T is

B is incorrect; The time-weighted rate of return measures compound growth. It is the rate at which $1 compounds over a specified performance horizon.

7.      The dollar discount on a U.S. Treasury bill with 182 days until maturity is $20. The face value of the bill is $1,000. The holding period yield and the bank discount yield of the bill is closest to:

       HPY               r_BD

A.         2.04%            4.01%

B.          2.04%            3.96%

C.          4.10%            4.01%      

Ans: B; Holding period return determines the return that an investor will earn by holding the instrument to maturity; as used here, this measure refers to an unannualized rate of return. In this problem, no dividend paid during the holding period, so:

Bank discount basis is a quoting convention that annualizes, based on a 360-day year, the discount as a percentage of face value.

8.      A 91-day U.S. Treasury bill has a face value of $1,000 and currently sells for $975. Which of the following yields is most likely the highest?

A.    Bank discount yield

B.     Money market yield

C.     Effective annual yield

Ans: C; effective annual yield is calculated as below:

In this problem,

A is incorrect;

B is incorrect; money market yield (also known as the CD equivalent yield) makes the quoted yield on a T-bill comparable to yield quotations on interest-bearing money-market instruments that pay interest on a 360-day basis.

9.      The bond-equivalent yield for a semi-annual pay bonds is most likely:

A.    Equal to the effective annual yield

B.     More than the effective annual yield

C.     Equal to double the semi-annual yield to maturity

Ans: C; bond-equivalent yield calculated ignoring compounding, annualizing a semiannual yield by doubling is putting the yield on a bond-equivalent basis.

10.  Victor Chow, CFA, held a 10% coupon bond for six months while the following results:

     Initial price: 100% of par

     End of holding period price: 97% of par

The holding period yield and Effective annual yield of the bond is closest to:

         HPY             EAY

A.      7.00%          10.00%

B.       7.00%          14.49%

C.       14.00%        14.49%

 Ans: B; Holding period return determines the return that an investor will earn by holding the instrument to maturity; as used here, this measure refers to an unannualized rate of return. The formula to calculate holding period return is as below:

In this problem, assume par value is 100, P₀=100, P₁=97, and D₁= 10, so HPY=7%

effective annual yield is calculated as below:

In this problem,