All Minicase Cases with Excel Solutions for Principles of Corporate Finance 14th Edition by Richard Brealey, Stewart Myers, Franklin Allen and Alex Edmans
REEBY SPORTS Minicase solution, Chapter 4 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen What is Reeby Sports worth per share? We will value the company using George Reeby's forecasts. The spreadsheet accompanying this solution sets out a forecast in the same general format as Table 4.5. Historical results from 2014 to 2019 are also shown. Earnings per share (EPS) equals return on equity (ROE) times starting book value per share (BVPS). EPS is divided between dividends and retained earnings, depending on the dividend payout ratio. BVPS grows as retained earnings are reinvested. The keys to Reeby Sports’ future value and growth are profitability (ROE) and the reinvestment of retained earnings. Retained earnings are determined by dividend payout. The spreadsheet sets ROE at 15% for the six years from 2021 to 2025. If Reeby Sports will lose its competitive edge by 2025, then it cannot continue earning more than its 10% cost of capital. Therefore ROE is reduced to 10% starting in 2026.1 The payout ratio is set at .30 from 2021 onwards. Notice that the long-term growth rate, which settles in after 2026, is ROE × ( 1 – dividend payout ratio) = .10 × (1 .30) = .07. The spreadsheet allows you to vary ROE and the dividend payout ratio separately for 2021-2025 and for 2026-2027.2 But let’s start with the initial input values. To calculate share value, we have to estimate a horizon value at H = 2025 and add its PV to the PV of dividends from 2020 to 2025. Using the constant-growth DCF formula, 1
A more sophisticated spreadsheet could distinguish ROE on existing assets from ROE on new capital investment. For example, ROE on new investment could drop all the way to 10% in 2023, but ROE for existing assets could decline gradually. 2 You can vary these inputs, but be careful not to enter ROEs and dividend payout ratios that generate longterm growth rates close to or above the cost of capital. As the growth rate approaches the cost of capital, the DCF formula explodes. If the growth rate exceeds the cost of capital, the DCF formula says stock price is negative, which is impossible. The spreadsheet reports “Formula not applicable” in this case. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.
0.71 PVH = = 23.72 .10 - .07 The PV of dividends from 2020 to 2025 is $3.43 at the start of 2020, so share value is:3 PV = 3.43 +
23.72 = $16.82 (1.1)6
The spreadsheet also calculates the PV of dividends through 2027 and the horizon value at 2027. Notice that the PV at the start of 2020 remains at $16.82. This makes sense, since the value of a firm should not depend on the investment horizon chosen to calculate PV. (If you calculate a value that does depend on the horizon, you have made a mistake.) We have reduced ROE to the 10% cost of capital after 2025, assuming that Reeby Sports will have exhausted valuable growth opportunities by that date. With PVGO = 0, PV = EPS/r. 4 So we could discard the constant-growth DCF formula and just divide EPS in 2026 by the cost of capital:
2.37 PVH = = $23.72 .10 This PV is identical to the PV from the constant-growth DCF formula. It doesn’t matter how fast a company grows after the horizon date H if it only earns its cost of capital. How much of Reeby Sports’ value is due to PVGO? You can check by setting ROE = .10 for 2021 and all later years. You should get PV = $13.82. Thus PVGO = 16.82 – 13.82 = $3.00 per share for investments made in 2020 onward. George Reeby has also identified a "comparable," Molly Sports. We could use its P/E ratio of 13.1 to calculate horizon value in 2025 and PV at the start of 2020. Using the original inputs for ROE, EPS in 2026 is 2.37.5
3
This DCF calculation assumes that the first dividend will be received after one year, at the end of 2020. Normally dividends are paid quarterly, so it would be more realistic to assume receipt at the middle of the year. This “mid-year convention” would move all cash flows 6 months closer and therefore increase PV by 1.1.5. (In finance, “mid-year convention” does not mean June in Las Vegas.) 4 See Section 4.5. 5 Notice that the P/E ratio applies to the next year’s forecasted earnings. Sometimes “trailing P/Es” are used instead. Trailing P/Es are based on earnings over the previous year. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.
PVH 13.1 2.37 $31.05 PV 3.43
31.05 $20.96 (1.10)6
We could also use Molly’s P/E ratio to calculate Reeby Sports’ PV at the start of 2020 directly from 2020 EPS: PV = 13.1 2.03 = $26.59 Both values based on Molly’s P/E are higher than our DCF calculations. Is Molly significantly more profitable than Reeby Sports, or does our spreadsheet understate Reeby Sports’ prospects? What if Reeby Sports could continue to earn ROE = .15 for two extra years, until 2027? You can check by changing ROE for 2026-2027 from .10 to .15. (The ROE for 2028 and 2029 is hard-wired at .10.) You should get NPV of $18.04, somewhat higher than our original DCF calculations, but not enough for Reeby Sports to match Molly’s P/E. You may wish to experiment to find inputs that generate P/E = 13 for Reeby Sports at the start of 2020. Do you think these inputs are reasonable?
March 1, 2019 VEGETRON’S CFO CALLS AGAIN Minicase solution, Chapter 5 Principles of Corporate Finance, 14th Ed. R. A. Brealey, S. C. Myers and F. Allen
The high-temperature process produces $110,000 per year for 5 years. The lowtemperature process produces $85,000 per year for 7 years. Each costs $400,000. The NPVs (at 9%) and IRRs are:
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NPV
IRR
High-temperature
+$28,000
11.7%
Low-temperature
+$28,000
11%
The NPVs are identical. The high-temperature process has a slightly higher IRR because of its quicker payback. The CFO returns 30 minutes later: CFO: What did you find out? You: It’s a dead heat. The two projects are equally valuable. NPV is +$28,000 for each. The high-temperature process has a slightly higher DCF rate of return, but that’s typical of quick-payback projects. It doesn’t mean that the high-temperature process generates more value for the firm and its stockholders. CFO: And the book rates of returns are irrelevant? You: Yes. There’s not a single year when the book rate of return matches the true, DCF rate of return. Average book returns – for example the ratio of average income to average book investment – don’t measure the true rate of return. Book rates of return don’t help at all in making good capital investment decisions. CFO: Let’s stick with the low-temperature process. I’m not 100% confident that the high-temperature process will work.
NEW ECONOMY TRANSPORT (A) Minicase solution, Chapter 6 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen This is straightforward capital investment decision, with a few real-life complications. For example, some cash flows are stated in real terms, some in nominal terms. We will use a real discount rate for the real cash flows, a nominal rate for the nominal flows. The alternative is to convert all cash flows to real terms (discounting at a real rate) or all to nominal (discounting at a nominal rate).
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Assumptions The spreadsheet for this minicase uses the following assumptions (others could be equally valid): 1. NETCO must decide immediately (t = 0). 2. Marginal tax rate is 21%. 3. Forecasted revenues and operating costs are constant in real dollars. 4. Sale price for the Vital Spark and parts is $200,000. Sale will trigger tax on the difference between sale price and book value, that is .21(200,000 – 140,000) = $12,600. After-tax proceeds are $200,000 – 12,600 = $187,400. 5. Investments can be depreciated immediately, i.e. at t = 0. 6. Full operations would resume at t = 1, and cash flows are discounted from midyear, that is, t = 1.5, 2.5, … . 7. The nominal opportunity cost of capital for NETCO is 11%. Using the assumed long-term inflation rate of 2.5%, the real opportunity cost of capital for NETCO is: 1.11 1 .0829, about 8.3% 1.025
The spreadsheet for New Economy Transport (A) calculates PVs for each investment and cash flow category and adds everything up to NPV. NPV is +$774,000 for the basic overhaul (REHAB) and even better with the new engine and control system (+$1,207,000 for REHAB PLUS). The REHAB PLUS option is clearly attractive. NEW ECONOMY TRANSPORT (B) Minicase solution, Chapter 6 Principles of Corporate Finance, 14th Edition R. A. Brealey, S. C. Myers and F. Allen
We start with the assumptions and PV calculations in New Economy Transport (A). We could calculate the NPV of the new vessel in the same format. But the new vessel lasts for 20 years, 8 years longer than the rehabilitated Vital Spark. Thus we calculate equivalent annual cash flows. That is, we calculate the equivalent annual costs of the net investments required for the Vital Spark (with and without the new engine and control system) and for the new vessel. The equivalent annual costs are subtracted from net operating revenue. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.