assignment7-8_solution

Mark Rempel mark.rempel@utoronto.ca November 8 , 2022 ECO 349 – Assignment 7 - 8 Firm financing, banks and regulation Due Date: Friday, 11 am, Nov. 18 Submit a single excel file and pdf write-up. Complete in the same assignment groups of 2 - 3 . P roblem 1 : ( practical exercise ) inspecting banks balance - sheets 1 . Choose two of the big six Canadian banks and download their latest supplemental financial results and Q 3 Pillar 3 disclosure forms. Choose one which is a global systematically important bank (G-SIB) according to the Financial Stability Board (FSB) 2021 list and one which is not. • RBC: RBC financial disclosures RBC Pillar 3 • TD: TDQ 3 Pillar 3 disclosures link • BMO: BMO Pillar 3 disclosures link • National bank: Disclosure documents; Pillar 3 pdf • CIBC: Disclosures CIBC Pillar 3 • Scotia Bank: Financial disclosures; Scotia bank Pillar 3 2 . From their supplemental financial disclosures for both banks (putting side by side) in excel sheet 1 (renamed "SupplementalHighlights") copy from Financial Highlights their (i) income statement information (e.g. from Net interest income to Net income attributable to equity shareholders), (ii) reported profitability measures, (iii) Capital ratio measures, (iv) Market price to book value With this information, for both banks (a) Compute the fraction of revenues coming from interest bearing assets, and the net income from from non-interest assets. Compare the two’s exposure to interest bearing assets and non-core banking activity performance. Which is likely more exposed to interest rate changes? Based on the time-series dimension of this data (and ignoring all other effects besides the rise in interest rates over the past few months), what does the pattern of net interest income and non-interest net income suggest about these banks performance as interest rates rise further? (b) Compare the profitability measures of the two banks. Does the determination of which bank is more profitable depend on the measure used? Map one of the measures to the objects from the competition - stability model. (c) Examine the capitalization of the two banks. For a given bank, how does the Tier 1 capital ratio compare to their leverage ratio? Is it the same for both banks? Explain what drives the difference in these measures for bank capitalization. Which bank is better capitalized / safer based on these metrics? Based on these results, does there seem to be a tradeoff between profitability and capitalization? Does the size of the bank (for convenience proxied in terms of amount of risk-weighted assets) tie in intuitively to these patterns? 1

Mark Rempel mark.rempel@utoronto.ca November 8 , 2022 ECO 349 – Assignment 7 - 8 (d) Using the information downloaded give an appropriate measure of each bank’s charter value. Explain what charter value means and link to a parameter from the model. Which bank has higher charter value? How is it correlated with profitability, capitalization and net income? Which has been more volatile over the past 3 years? 3 . In excel sheet 3 (renamed "BalanceSheets"), copy the LI 1 : DIFFERENCES BETWEEN AC- COUNTING AND REGULATORY SCOPES OF CONSOLIDATION... (a) What share of deposits are personal for each bank? (b) Simplify the balance sheet by aggregating assets in terms of cash-like & illiquid / market-price dependent ones; and liabilities in terms of deposits, debt and equity (c) What fraction of assets do not need to be traded on the market in order to meet immediate deposit cash demands? From this, which bank appears better protected from a bank run? Does this ranking correspond to the ranking of charter value or performance? P roblem 2 : ( theory exercise ) capital structure decisions through the lens of holmstrome - tirole Consider the model of Holmstrome-Tirole from class on firm indirect / direct financing. First consider the case with only a single entrepreneur needing to invest I = 1 to start a project and with wealth w < 1 , hence requiring outside funds to start the project. The project generates y = 1.25 in profits if it successfully gets off the ground and zero otherwise. If the entrepreneur works hard, they will have p hard = .9 probability of success, while if they are lazy, the probability of success is p lazy = .1. If an entrepreneur is lazy they get a side benefit of B = .5 . There are a large number of outside investors with ample funds to invest but have an outside option to invest in government bonds that offers a yield of 6 % on the same horizon as the project. Investors are risk-neutral and only care about the termination payoff. Assume that investor contract is set up as equity where the entrepreneur promises to pay a dividend of d to the outside shareholders as a percent of the project profits, but has limited liability. 1 . Write the entrepreneur’s expected payoff given their promised dividend policy if they work hard. Give a condition which their dividend policy must satisfy so that sceptical investors will believe the entrepreneur’s assurance that they will work hard. Write the condition for general y , d , B , p hard , p lazy and then use the numerical values to give a precise constraint on d . Answer ( 5 points): The incentive compatibility condition for the entrepreneur to work hard is p hard y ( 1 - d ) ≥ p lazy y ( 1 - d ) + B where the left-hand side is the expected payoff to the entrepreneur from working hard given their dividend policy and the right-side is the payoff if they are lazy. 2

Mark Rempel mark.rempel@utoronto.ca November 8 , 2022 ECO 349 – Assignment 7 - 8 to receive funding from the investor, first for some general (feasible) d > 0 . Give a numerical value of wealth w ∈ [ 0, 1 ) which is the least required to fund the project. Answer ( 5 points): Since the NPV of lazy is negative, the investor will only finance if the entrepreneur works hard and receives d such that p hard yd - ( 1 + r )( I - w ) ≥ 0. The upper bound on d is solved for in an earlier sub-part d = 0.5 , so p hard dy = .9 · .5 · 1.25 = .5625, which plugging that in yields p hard y d - ( 1.06 )( 1 - w ) ≥ 0 which solving yields w = 1 - .5625 1.06 = .53 so that w ≥ w is needed for financing. 6 . Draw the net return of the investor over wealth w ∈ ( 0, 1 ) for a (feasible) level of d within the contract, as well as over the return for their outside investment option. Label any x / y intercepts, the region where the investor gets a positive net payoff, the slope, the lower / upper bounds on w as well as the highest / lowest feasible returns under an equity contract between an investor and the entrepreneur. Answer ( 10 points): Based on above, the (gross) return of the investor financing is p hard yd 1 - w , which is increasing in w , with slope p hard yd ( 1 - w ) 2 . The upper bound on d is solved for in an earlier sub-part d = 0.5 , so p hard dy = .9 · .5 · 1.25 = .5625 , so d must be less than or equal to this, and above 0 . Using the cutoff w , we know that this intersects the horizontal line with y-intercept ( 1 +r) = 1 . 06 which is the investor return on their outside option. The area to the right of w , above 1 + r and below p hard yd 1 - w is the net profits for the investor financing the firm above their outside option. Part II (harder) Now add a bank to the above, which can with their own effort E = .2 impose a cost of Z = .2 on the entrepreneur for being lazy, and assume the entrepreneur has the ability to dictate the terms to the outside investors of the contract. Suppose entrepreneurs are designing a debt contract to the bank promising c as a share of successful project output y . Assume banks have limited aggregate funds, K , as a share of total investment needed by entrepreneurs ( K < 1 ) and demand 1 + r bank per dollar invested. 1 . Write out the entrepreneurs expected payoff under hardwork receiving financing from both 4

Mark Rempel mark.rempel@utoronto.ca November 8 , 2022 ECO 349 – Assignment 7 - 8 a bank and investors. What is the new condition in terms of entrepreneur compensation share s = 1 - ( c + d ) which ensures hardwork? Answer ( 5 points): p hard y ( 1 - ( c + d )) - w ≥ p lazy y ( 1 - ( c + d )) + B - w the left-hand side is the expected payoff for financing as an entrepreneur by working hard plugging in s = 1 - ( c + d ) and solving we get s ≥ 1 - B y Δ p p hard y ( 1 - ( c + d )) - w ≥ p lazy y ( 1 - ( c + d )) + B - w 2 . What is the minimal share of the profits the bank must be paid to ensure they monitor? How does this minimal share depend on entrepreneurs wealth or the amount of capital injected by the bank? Is there any other condition needed for bank financing? What is the amount banks will finance if the bare minimum for monitoring is being asked for by the firm? Answer ( 10 points): Bank requires compensation share c so that p h cy - E ≥ p lazy cy or c ≥ c bank = E y Δ p = .2 1.25 ( .8 ) = .2 Thus bank requires 20 % stake in the firm to monitor, and is independent of (a) the entrepreneur’s wealth and (b) the amount of capital injected by the bank. In addition for it to be in the best interests of the bank to invest their funds into this entrepreneur it must be that for the amount of investment I bank p hard yc - ( 1 + r bank ) I bank ≥ 0. That is, the return to the bank must be p hard yc I bank ≥ 1 + r bank . Hence putting it all together, the minimal investment amount required for bank moni- toring is: I bank = p hard yc bank 1 + r bank . 5