Chapter 6 Notes

Chapter 6 - Discounted Cash Flow Application

LOB

a. Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment, contrast the NPV rule to the IRR rule, and identify any problems associated with the IRR rule.
b. Define, calculate and interpret a holding period return (total return)
c. Calculate, interpret, and distinguish between the money-weighted and time-weighted rates of return of a portfolio and appraise the performance of portfolios based on these measures
d. calculate and interpret the bank discount yield, holding period yield, effective annual yield, and money marktet yield for a U.S. Treasury bill and interpret and convert among holding period yields, money market yields, effective annual yields and the bond equivalent yields.

Summary

Applied the concepts of present value, net present value and internal rate of return to the fundamental problems of valuing investments. we applied these concepts first to corporate investment, the well-known capital budgeting problem. we then examined the fundamental problem of calculating the return on a portfolio subject to cach inflows and outflows. Finally we discussed money market yields and basic bond market terminology.
1. The Net present value (NPV) of a project is the present value of its cach inflows minus the present value of its cach 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.
2. The NPV rule for decision making is to accept all projects with possitive 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.
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. Timeweighted rate of return is the standard in the investment management industry. Money-weighted rate of return can be appropriate if the invester excercises control over additions and widthdrawals to the portfolio.
4. The money-weighted rate of return is the internal reate of return on a protfolio, taking account of all cash flows
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.
6. The bank discount yield for U.S. Treasury bills (and other money-market instruments sold on a discount basis) is given by
rBD = (F - P0) / F x 360 / t = D/F X 360/t, where F is the face amount to be received at maturity, Po is the price of the Treasury bill, t is the number of days to maturity, and D is the dollar discount.
7. For a stated holding period or horizon, holding period yeild (HPY) = (Ending Price - Beginning Price + Cash distributions ) / (Beginning price). For a U.S. Treasury bill, HPY = D/Po.
8. The effective annual Yield (EAY) is ((1 + HPY) (power 365/t)) - 1.
9. The money market yield is given by rmm = HPY X 360/t, where t is the number of days to maturity.
10. For a Treasury bill, money market yield can be obtained from the bank discount yield using rmm = (360 x rBD) / (360 -t X rBD).
11. we can convert back and forth between holding period yields, money market yields, and equivalent annual yields by using the holding period yield. which is common to all the calculations.
12. The bond equivalent yield of a yield stated on a semiannual basis is that yield multiplied by 2.

Examples

6.1 Evaluating a Research and Development Program using the NPV rule.
As an analyst covering the RAD Corporation, you are evaluating its R&D program for the current year. Management has announced that it intends to invest $1million in R&D. Incremental net cash flows are forcasted to be $150,000 per year in perpetuity. RAD corp's opportunity cost of capital is 10%.
a. State whether RAD's R&D program will benefit shareholders, as judged by the NPV rule.
b. Evaluate whether your answer to Part 1 changes if RAD corporations opportunity cost of capital is 15 percent rather than 10%
6.2 Evaluating a R&D program using IRR Rule
In the previous RAD corp, example, the initial outlay is $1 million and the program's cash flows are $150,000 in perpetutiy. Now you are interested in determining the program's IRR. Address the following:
1. Write the equation for determining the IRR of this R&D program
2. Calculate the IRR.
6.3 The IRR and NPV rules side by side
The Japanese company Kageyama LTD, is considering whether or not to open a new factory to manufacture capacitors used in cell phones. The factory will require an investment of Yen 1000 million. The factory is expected to generate level cash flows of Yen 294.8 m per year in each of the next five years. According to info in its financial reports, Kegma's opportunity cost of capital for this type of project is 11 percent.
a. Determine whether the project will benefit k's shareholders using NPV rule.
b. Determine whether the project will benefit k's shareholders using the IRR rule.
6.4 Time-weighted Rate of return
Sturbeck Corp sponsors a pension plan for its employees. It manages part of the equity portfolio in-house and delegates mgt of the balance to super trust co. As CIO of Struback, you want to review the performance of the in-house and ST portfolios over the last four quarters. You have arranged for outflows and inflows to the portfolios to be made at the very begining of the quarter. Give table summarizes the inflows and outflows as well as the two portfolio's valuations. In the table, the ending value is the portfolio's value just prior to the cach inflow or outflow at the begining of the quarter. The amount invested is the amount each portfolio manager is responsible for investing.
Q1 Q2 Q3 Q4
In-House Account
Bgn. Value 4,000,000 6,000,000 5,775,000 6,720,000
Bgn. of period inflow (outflow) 1,000,000 (500,000) 225,000 600,000
Amount invested 5,000,000 5,500,000 6,000,000 6,120,000
Ending Value 6,000,000 5,775,000 6,720,000 5,508,000
Super Trust A/c
Bgn. Value 10,000,000 13,200,000 12,240,000 5,659,200
Bgn. Period Inflow (outflow) 2,000,000 1,200,000 7,000,000 400,000
Amount Invested 12,000,000 12,000,000 5,240,000 5,259,200
Ending Value 13,200,000 12,240,000 5,659,200 5,469,568
Based on the information given, address the following:
a. Calculate the time-weighted rate of return for the in-house account.
b. Calculate the time-weighted rae of return for the Super Trust A/c

6.5 Time-weighed and Money-weighted Rates of Return Side by Side
Your task is to compute the investment performance of the walbright Fund during 2003, The facts are as follows:
> On 1 Jan 2003, the Walbright Fund had a market value of 100 million
> During the period 1 Jan 2003 to 30 Apr 2003, the stocks in the fund showd a capital gain of $10 million
> On 1 May 2003, the stocks in the fund paid a total dividend of 2 million, All dividends were reinvested in additionl shares.
> Because the fund's performance had been exceptional, institutions invested an additional 20 million in walbright on 1 May 2003, raising assets under management to $132 million(100+10+2+20).
> On 31 Dec 2003, Walbright received total dividends of 2.64 million.
> The fund mad no other intermi cash payments during 2003
Based on the information given, address the following.
a. Compute the Walbright Fund's time-weighted rate of return.
b. Compute the Walbright Fund's money-weighted rate of return
c. Intepret the differences between the time-weighted and money-weighted rate of return.
6.6 The Bank Discount Yield
Suppose a T-Bill with a face value (or par value) of 100,000 and 150 days until maturity is selling for $98,000. What is its bank discount yield?
6.7 Using the Appropriate Discount Rate
You need to find the present value of a cash flow $1000 that is to be received in 150 days, You decide to look at a T-Bill maturing in 150 days to determine the relevant interest rate for calculating the present value. You have found a variety of yields for the 150 day bill. Use the below info
Short-term Money market yields
Holding period yeild 2.0408%
Bank discount Yield 4.8%
Money Market Yield 4.898%
Effective annual yield 5.0388%
Wich yield or yields are appropriate for finding the present value of the $1000 to be received in 150 days?


Problems
1. Waldrup Industries is considering a proposal for a joint venture that will require an investment of C$13 Million. At the end of the fifth year, Wldrup's joint venture partner will buy out Waldrup's interest for C$10 Million. Waldrup's Chief finanfial Officer has estimated that the appropriate discount rate for this proposal is 12 percent. The expected cash flows are given below.
Year Cash Flow
0 -C#13,000,000
1 to 4 yr C$3,000,000 per year
5 C$10,000,000
A. Calculate this proposal's NPV.
B. Make a recommendation to the CFO concerning wther waldrup should enter inot this joint venture
2. Waldrup Industries has committed to investing C$5,500,000 in a project with expected cash flows of C$1,000,000 at the end of Year, C$1,500,000 at the end of Year 4, and c$7,000,000 at the end of Year 5.
A. Demonstrate that the internal rate of return of the investment is 13.51 percent.
B. State how the internal rate of return of the investment would change if Waldrup's opportunity cost of capital were to increase by 5 percentage points.
3. Bestfoods, Inc. is planning to spend $10 million on advertising. The company expects this expenditure to result in annual incremental cash flows of $1.6 million in perpetuity. The corporate opportunity cost of capital for this type of project is 12.5 percent.
A. Calculate the NPV for the planned advertising.
B. Calculate the Internal Rate of Return
C. Should the company go forward with the planned advertising? Explain.
4. Trilever is planning to estabilish a new factory overseas. The project requires an initial investment of $15 million. Management intends to run this factory for six years and then sell it to a local entity. Trilever's finance department has estimated the following yearly cash flows:
Year Cash Flow
0 -$15,000,000
1 to 5 yr $4,000,000 for each year
6 $7,000,000
Trilever's CFO decides that the company's cost of capital of 19 percent is an appropriate hurdle rate for this project.
A. Calculate the internal rate of return of this project.
B. Make a recommendation to the CFo concerning whether to undertake this project.
5. Westcott-Smith is a privately held investment management company, Two other investment counseling companies, which want to be acquired, have contacted Westcott-Smith about purchasing their business. Company A's price is British pound 2 million. Company b's price is British pound 3 million. After analysis, Westcott-smith estimates that Company A's profitability is consistent with a perpetuity of BP300, 000 a year. Company B's prospects are consistent with a perpetuity of BP435,000 a year. Westcott-Smith has a budget that limits acquisitions to a maximum purchase cost of BP4 million. Its opportunity cost of capital relative to undertaking either project is 12 percent.
A. Determine which company or companies (if any) Westcott-Smith should purchase according to the NPV rule.
B. Determine which company or companies (if any) Westcott-Smith should purchase according to the IRR rule.
C. State which company or companies (if any) Westcott-Smith should purchase. Justify your answer.
6. John Wilson buys 150 shares of ABM on 1 January 2002 at a price of $156.30 per share. A divident of $10 per share is paid on January 2003. Assume that this divident is not reinvested. Also on 1 January 2003, wilson sells 100 shares at a price of $165 per share. On 1 January 2004, he collects a divident of $15 per share (on 50 shares) and sells his remaining 50 shares at $170 per share.
A. Write the formula to calculate the money-weighted rate of return on Wilson's portfolio.
B. Using any method, compute the money-weighted rate of return.
C. Calculate the time-weighted rate of return on Wilson's portfolio.
D. Describe a set of circumstances for which the money-weighted rate of return is an appropriate return measure for Wilson's Portfolio.
E. Describe a set of circumstances for which the time-weighted rate of return is appropriate return measure for Wilson's portfolio.
7. Mario Luongo and Bob Weaver both purchase the same stock for $100. One year later, the stock price is $110 and it pays a divident of $5 per share. Weaver decides to buy another share of $110 (he does not reinvest the $5 divident, however). Luongo also spends the $5 per share divident but does not transact in the stock. A the end of the second year, the stock pays a dividend of $5 per share but its price has fallen back to $100. Luongo and Weaver then decide to sell their entire holdings of this stock. The performance for Luongo and Weaver's investments are as follows:
Luongo:
Time-weighted return = 4.77 percent
Money-weighted return=5.00 percent
Weaver:
Money-weighted return = 1.63 percent
Briefly explain any similarities and differences between the performance of Luongo's and Weaver's investments.
8. A Treasury bill with a face value of $100,000 and 120 days until maturity is selling for $98,500
A. What is the T-bill's bank discount yield?
B. What is the T-bill's money market Yield?
C. What is the T-bill's effective annual yield?
9. Jane Cavell has just purchased a 90-day U.S. Treasury bill. She is familiar with yield quotes on German Treasury discount paper but confused about the bank discount quoting convention for the U.S. T-Bill she just purchased.
A. Discuss there reasons why bank discount yield is not a meaningful measure of return.
B. Discuss the advantage of money market yield compared with bank discount yield as a measure of return.
C. Explain how the bank discount yield can be converted to an estimate of the holding period return Cavell can expect if she holds the T-bill to maturity.