Reading 6 Flashcards
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, Waldrup’s joint venture partner will buy out Waldrup’s interest for C$10 million. Waldrup’s chief financial officer has estimated that the appropriate discount rate for this proposal is 12 percent. The expected cash flows are given below.
Year Cash Flow (C$) 0 −13,000,000 1 3,000,000 2 3,000,000 3 3,000,000 4 3,000,000 5 10,000,000 Calculate this proposal’s NPV.
Make a recommendation to the CFO (chief financial officer) concerning whether Waldrup should enter into this joint venture.
(Institute 205)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
We can calculate the present value of the cash inflows in several ways. We can discount each cash inflow separately at the required rate of return of 12 percent and then sum the present values. We can also find the present value of a four-year annuity of C$3 million, add to it the present value of the t = 5 cash flow of C$10 million, and subtract the t = 0 outflow of C$13 million. Or we can compute the present value of a five-year annuity of C$3 million, add to it the present value of a cash inflow of C$7 million = C$10 million − C$3 million dated t = 5, and subtract the t = 0 outflow of C$13 million. For this last approach, we illustrate the keystrokes for many financial calculators.
Notation Used on Most Calculators Numerical Value for This Problem N 5 %i 12 PV compute X PMT 3,000,000 FV 7,000,000 We find that the PV of the inflows is C$14,786,317.
Therefore, NPV = C$14,786,317 − C$13,000,000 = C$1,786,317.
Waldrup should undertake this project because it has a positive NPV.
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
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 1, C$1,500,000 at the end of Year 4, and C$7,000,000 at the end of Year 5.
Demonstrate that the internal rate of return of the investment is 13.51 percent.
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.
(Institute 205)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
The internal rate of return is the discount rate that makes the NPV equal zero:
NPV=CF0+CF1(1+IRR)1+CF2(1+IRR)2+…+CFN(1+IRR)N=0
To show that the investment project has an IRR of 13.51 percent we need to show that its NPV equals zero, ignoring rounding errors. Substituting the project’s cash flows and IRR = 0.1351 into the above equation,
NPV=−C$5,500,000+C$1,000,000(1.1351)1+C$1,500,000(1.1351)4+C$7,000,000(1.1351)5=−C$5,500,000+C$5,499,266=−C$734
Given that the cash flows were of the magnitude of millions, the amount C$734 differs negligibly from 0.
The internal rate of return is unaffected by any change in any external rate, including the increase in Waldrup’s opportunity cost of capital.
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
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.
Calculate the NPV for the planned advertising.
Calculate the internal rate of return.
Should the company go forward with the planned advertising? Explain.
(Institute 205)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
NPV is the sum of the present values of all the cash flows associated with the investment, where inflows are signed positive and outflows are signed negative. This problem has only one outflow, an initial expenditure of $10 million at t = 0. The projected cash inflows from this advertising project form a perpetuity. We calculate the present value of a perpetuity as CF⎯⎯⎯⎯⎯/r , where CF⎯⎯⎯⎯⎯ is the level annual cash flow and r is the discount rate. Using the opportunity cost of capital of 12.5 percent as the discount rate, we have
NPV=−$10,000,000+1,600,000 / 0.125=−$10,000,000+12,800,000=$2,800,000
In this case, the cash inflows are a perpetuity. Therefore, we can solve for the internal rate of return as follows:
Initialinvestment=(Annualcashinflow)/IRR10,000,000=1,600,000/IRRIRR=16percent
Yes, Bestfoods should spend $10 million on advertising. The NPV of $2.8 million is positive. The IRR of 16 percent is also in excess of the 12.5 percent opportunity cost of capital.
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
Trilever is planning to establish 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 4,000,000 2 4,000,000 3 4,000,000 4 4,000,000 5 4,000,000 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.
Calculate the internal rate of return of this project.
Make a recommendation to the CFO concerning whether to undertake this project.
(Institute 205)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
Using the IRR function in a spreadsheet or an IRR-enabled financial calculator, we enter the individual cash flows and apply the IRR function. We illustrate how we can solve for IRR in this particular problem using a financial calculator without a dedicated IRR function. The cash flows from t = 1 through t = 6 can be treated as a six-year, $4 million annuity with $7 million − $4 million = $3 million, entered as a future amount at t = 6.
Notation Used on Most Calculators Numerical Value for This Problem N 6 %i compute X PV −15,000,000 PMT 4,000,000 FV 3,000,000 The IRR of the project is 18.25 percent.
Because the project’s IRR is less than the hurdle rate of 19 percent, the company should not undertake the project.
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
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 £2 million. Company B’s price is £3 million. After analysis, Westcott–Smith estimates that Company A’s profitability is consistent with a perpetuity of £300,000 a year. Company B’s prospects are consistent with a perpetuity of £435,000 a year. Westcott–Smith has a budget that limits acquisitions to a maximum purchase cost of £4 million. Its opportunity cost of capital relative to undertaking either project is 12 percent.
Determine which company or companies (if any) Westcott–Smith should purchase according to the NPV rule.
Determine which company or companies (if any) Westcott–Smith should purchase according to the IRR rule.
State which company or companies (if any) Westcott–Smith should purchase. Justify your answer.
(Institute 205)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
Company A. Let CF⎯⎯⎯⎯⎯ = £300,000 be the amount of the perpetuity. Then with r = 0.12, the NPV in acquiring Company A would be
NPV=CF0+CF⎯⎯⎯⎯⎯/r=−£2,000,000+£300,000 / 0.12=£500,000
Company B. Let CF⎯⎯⎯⎯⎯ = £435,000 be the amount of the perpetuity. Then with r = 0.12, the NPV in acquiring Company B would be
NPV=CF0+CF⎯⎯⎯⎯⎯/r=−£3,000,000+£435,000 / 0.12=£625,000
Both Company A and Company B would be positive NPV acquisitions, but Westcott–Smith cannot purchase both because the total purchase price of £5 million exceeds its budgeted amount of £4 million. Because Company B’s NPV of £625,000 is higher than Company A’s NPV of £500,000, Westcott–Smith should purchase Company B according to the NPV rule.
Company A. Using the notation from Part A, IRR is defined by the expression NPV = −Investment + CF⎯⎯⎯⎯⎯/IRR = 0. Thus −£2,000,000 + £300,000/IRR = 0 and solving for IRR,
IRR = £300,000/£2,000,000 = 0.15 or 15 percent
Company B.
IRR = £435,000/£3,000,000 = 0.145 or 14.5 percent
Both Company A and Company B have IRRs that exceed Westcott–Smith’s opportunity cost of 12 percent, but Westcott–Smith cannot purchase both because of its budget constraint. According to the IRR rule, Westcott–Smith should purchase Company A because its IRR of 15 percent is higher than Company B’s IRR of 14.5 percent.
Westcott–Smith should purchase Company B. When the NPV and IRR rules conflict in ranking mutually exclusive investments, we should follow the NPV rule because it directly relates to shareholder wealth maximization.
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
John Wilson buys 150 shares of ABM on 1 January 2012 at a price of $156.30 per share. A dividend of $10 per share is paid on 1 January 2013. Assume that this dividend is not reinvested. Also on 1 January 2013, Wilson sells 100 shares at a price of $165 per share. On 1 January 2014, he collects a dividend of $15 per share (on 50 shares) and sells his remaining 50 shares at $170 per share.
Write the formula to calculate the money-weighted rate of return on Wilson’s portfolio.
Using any method, compute the money-weighted rate of return.
Calculate the time-weighted rate of return on Wilson’s portfolio.
Describe a set of circumstances for which the money-weighted rate of return is an appropriate return measure for Wilson’s portfolio.
Describe a set of circumstances for which the time-weighted rate of return is an appropriate return measure for Wilson’s portfolio.
(Institute 205)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
The money-weighted rate of return is the discount rate that equates the present value of inflows to the present value of outflows.
Outflows:
Att=0(1January2012): 150sharespurchased×$156.30pershare=$23,445
Inflows:
Att=1(1January2013): 150shares×$10dividendpershare=$1,500 100sharessold×$165pershare=$16,500Att=2(1January2014): 50sharespurchased×$15dividendpershare=$750 50sharessold×$170pershare=$8,500
PV(Outflows)=PV(Inflows) 23,445=1,500+16,5001+r+750+8,500(1+r)2 =18,0001+r+9,250(1+r)2
The last line is the equation for calculating the money-weighted rate of return on Wilson’s portfolio.
We can solve for the money-weighted return by entering −23,445, 18,000, and 9,250 in a spreadsheet or calculator with an IRR function. In this case, we can also solve for money-weighted rate of return as the real root of the quadratic equation 18,000x + 9,250x2 − 23,445 = 0, where x = 1/(1 + r). By any method, the solution is r = 0.120017 or approximately 12 percent.
The time-weighted rate of return is the solution to (1 + Time-weighted rate of return)2 = (1 + r1)(1 + r2), where r1 and r2 are the holding period returns in the first and second years, respectively. The value of the portfolio at t = 0 is $23,445. At t = 1, there are inflows of sale proceeds of $16,500 and $1,500 in dividends, or $18,000 in total. The balance of 50 shares is worth $8,250 = 50 shares × $165 per share. So at t = 1 the valuation is $26,250 = $18,000 + $8,250. Thus
r1 = ($26,250 – $23,445)/$23,445 = 0.119642 for the first year
The amount invested at t = 1 is $8,250 = (50 shares)($165 per share). At t = 2, $750 in dividends are received, as well as sale proceeds of $8,500 (50 shares sold × $170 per share). So at t = 2, the valuation is $9,250 = $750 + $8,500. Thus
r2 = ($9,250 – $8,250)/$8,250 = 0.121212 for the second year
Time-weighted rate of return = (1.119642)(1.121212)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√−1=0.1204 or approximately 12 percent.
If Wilson is a private investor with full discretionary control over the timing and amount of withdrawals and additions to his portfolios, then the money-weighted rate of return is an appropriate measure of portfolio returns.
If Wilson is an investment manager whose clients exercise discretionary control over the timing and amount of withdrawals and additions to the portfolio, then the time-weighted rate of return is the appropriate measure of portfolio returns. Time-weighted rate of return is standard in the investment management industry.
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
Mario Luongo and Bob Weaver both purchase the same stock for €100. One year later, the stock price is €110 and it pays a dividend of €5 per share. Weaver decides to buy another share at €110 (he does not reinvest the €5 dividend, however). Luongo also spends the €5 per share dividend but does not transact in the stock. At 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.
(Institute 205)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
Similarities. The time-weighted returns for Luongo’s and Weaver’s investments will be equal, because the time-weighted return is not sensitive to additions or withdrawals of funds. Even though Weaver purchased another share at €110, the return earned by Luongo and Weaver each year for the time-weighted return calculation is the same.
Differences. The money-weighted returns for Luongo and Weaver will differ because they take into account the timing of additions and withdrawals. During the two-year period, Weaver owned more shares of the stock during the year that it did poorly (the stock return for Year 1 is (110 + 5 − 100)/100 = 15 percent and for Year 2 it is (100 + 5 − 110)/110 = −4.55 percent). As a consequence, the money-weighted return for Weaver (1.63 percent) is less than that of Luongo (5.00 percent). The money-weighted return reflects the timing of additions and withdrawals. Note, the cash flows for the money-weighted returns for Luongo and Weaver are (for t = 0, 1, and 2) Luongo: −100, +5, +105; Weaver: −100, −105, +210.
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
A Treasury bill with a face value of $100,000 and 120 days until maturity is selling for $98,500.
What is the T-bill’s bank discount yield?
What is the T-bill’s money market yield?
What is the T-bill’s effective annual yield?
(Institute 205)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
In this solution, F stands for face value, P stands for price, and D stands for the discount from face value (D = F − P).
Use the discount yield formula (Equation 3), rBD = D/F × 360/t:
rBD=($1,500/$100,000)×(360/120)=0.0150×3=0.045
The T-bill’s bank discount yield is 4.5 percent a year.
Use your answer from Part A and the money market yield formula (Equation 6), rMM = (360 × rBD)/(360 − t × rBD):
rMM=(360×0.045)/(360−120×0.045)=0.04568
The T-bill’s money market yield is 4.57 percent a year.
Calculate the holding period yield (using Equation 4), then compound it forward to one year. First, the holding period yield (HPY) is
HPY=P1−P+D1P0=(100,000−98,500)/98,500=0.015228
Next, compound the 120-day holding period yield, a periodic rate, forward to one year using Equation 5:
Effectiveannualyield=(1+HPY)365/ t− 1Effectiveannualyield=(1.015228)365/ 120− 1=0.047044
The T-bill’s effective annual yield is 4.7 percent a year.
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
Jane Cavell has just purchased a 90-day US Treasury bill. She is familiar with yield quotes on German Treasury discount paper but confused about the bank discount quoting convention for the US T-bill she just purchased.
Discuss three reasons why bank discount yield is not a meaningful measure of return.
Discuss the advantage of money market yield compared with bank discount yield as a measure of return.
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.
(Institute 205-206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
In the United States, T-bill yields are quoted on a bank discount basis. The bank discount yield is not a meaningful measure of the return for three reasons: First, the yield is based on the face value of the bond, not on its purchase price. Returns from investments should be evaluated relative to the amount that is invested. Second, the yield is annualized based on a 360-day year rather than a 365-day year. Third, the bank discount yield annualizes with simple interest, which ignores the opportunity to earn interest on interest (compound interest).
The money market yield is superior to the bank discount yield because the money market yield is computed relative to the purchase price (not the face value).
The T-bill yield can be restated on a money market basis by multiplying the bank discount yield by the ratio of the face value to the purchase price. Cavell could divide the annualized yield by 4 to compute the 90-day holding period yield. This is a more meaningful measure of the return that she will actually earn over 90 days (assuming that she holds the T-bill until it matures).
(Institute 206)
Institute, CFA. 2015 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. Wiley Global Finance, 2014-07-14. VitalBook file.
