yilunzhao/KnowledgeMath huggingface dataset:
Topic: Asset Classes & Derivatives

Based on the data provided for the trio of shares listed in the chart, determine the return on the price-weighted index over a month's span.

|          | March 31,20X7                        | April 30,20X7                         |
|----------|-----------------|---------------------------------|---------------|---------------------------------|
|          | Share Price     | Number of Shares Outstanding(thousands) | Share Price   | Number of Shares Outstanding(thousands) |
| Stock X  | $15             | 100                             | $20           | 100                             |
| Stock Y  | $20             | 1,000                           | $30           | 1,000                           |
| Stock Z  | $30             | 2,000                           | $25           | 2,000                           |
Topic: Asset Classes & Derivatives

Based upon the presented series of spot rates, what is the price of Bond Y if all three bonds pay their interest yearly?

| Bond | Coupon Rate | Time-to-Maturity | Spot Rates |
|------|-------------|------------------|------------|
| X    | 8%          | 3 years          | 8%         |
| Y    | 7%          | 3 years          | 9%         |
| Z    | 6%          | 3 years          | 10%        |
Topic: Accounting

Summit Resale operates through internet for people on an agreed basis. Summit gets the items from the owners, puts them up for sale online, and earns a 25 percent commission for any items sold. Summit collects the entire amount from the buyer and pays the gross amount after commission to the owner. If items remain unsold, they are returned to the owner after 90 days. During 2019, Summit had these details: • Total sales price of items sold on agreed basis during 2019 was €2,000,000. • Total commissions that Summit retained during 2019 for these items totalled €500,000. How much revenue should Summit report on its 2019 income statement?
Topic: Portfolio Management & Strategy

Given the historical data presented, what is the standard deviation for the two-asset portfolio displayed in the chart?

|                   | Asset A, Asset B | A and B |
|-------------------|------------------|---------|
| Standard deviation| 4.7%, 7.7%       |         |
| Portfolio weight  | 0.4, 0.6         |         |
| Correlation       |                  | 0.3     |
Topic: Accounting

If a financial expert is examining the amortization of a product patent purchased by the Italian firm, MAKETTI S.p.A., what would be the 2009 fiscal year's amortization expense on the patent using the units-of-production approach, based on the patent information he has collected?

| Acquisition cost | £5,800,000 |
| --- | --- |
| Acquisition date | 1 January 2009 |
| Patent expiration date | 31 December 2015 |
| Total plant capacity of patented product | 40,000 units per year |
| Production of patented product in fiscal year ended 31 December 2009 | 20,000 units |
| Expected production of patented product during life of the patent | 175,000 units |
Topic: Accounting

What is the FIFO method's reported Cost of Goods Sold in 2018 by a firm adopting the LIFO method in £?

|                        | 2018 | 2017 |
|------------------------|------|------|
| Cost of goods sold (COGS) | 50,800 | 48,500 |
| Ending inventories | 10,550 | 10,000 |
| LIFO reserve | 4,320 | 2,600 |
Topic: Portfolio Management & Strategy

As a risk-neutral investor, John Smith will use utility theory to select his investment portfolio. Given several investments with their expected return and expected standard deviation on the table, which one would he most probably invest in?

| Investment | Expected Return(%) | Expected Standard Deviation(%) |
|------------|-------------------|--------------------------------|
| 1          | 19                | 3                              |
| 2          | 21                | 9                              |
| 3          | 24                | 20                             |
| 4          | 19                | 35                             |
Topic: Asset Classes & Derivatives

If an investor places an immediate-or-cancel limit purchase order for 700 shares at a price of $20.50 in a market, what would probably be the average price the investor would be required to pay, considering the existing limit orders on its book for a specific stock?

| Buyer | Bid Size (# of shares) | Limit Price ($) | Seller | Offer Size (# of shares) | Limit Price ($) |
|-------|------------------------|-----------------|--------|--------------------------|-----------------|
| 1     | 500                    | 18.50           | 1      | 200                      | 20.20           |
| 2     | 300                    | 18.90           | 2      | 300                      | 20.35           |
| 3     | 400                    | 19.20           | 3      | 400                      | 20.50           |
| 4     | 200                    | 20.10           | 4      | 100                      | 20.65           |
| 5     | 100                    | 20.15           | 5      | 200                      | 20.70           |
Topic: Accounting

How did the alterations in the firm's deferred tax accounts impact the net income of 2015 according to US GAAP?

| 2015 | | 2014 |
| --- | --- | --- |
| Deferred tax assets $1,000,000 | | $800,000 |
| Deferred tax liabilities $600,000 | | $700,000 |
| Valuation allowance $500,000 | | $400,000 |
Topic: Quantitative Analysis & Valuation

The table underneath displays the monthly stock returns for Oak Inc. Based on the provided table, can you compute the standard deviation for Oak Inc.'s returns, considering that there are 6 observations in the population?

| Jan | Feb | Mar | Apr | May | Jun |
|-----|-----|-----|-----|-----|-----|
| 20% | 4%  | -5% | 12% | 3%  | 12% |
Topic: Accounting

Smith is a tax consultant who offers tax consciousness guidance to individual patrons. One of Smith's patrons is Emma. Emma requests Smith to assess Mutual Fund B, which has an inherent gain of 10% of the concluding portfolio value. Emma requests Smith to determine a post-disposal yield over the latest three-year duration. Mutual Fund B showed after-tax yields of 9.0% in the first year, 5% in the second year, and 8% in the third year, and capital profits are taxed at a 25% pace. What is the yearly after-tax post-disposal yield measured by Smith?
Topic: Market Analysis & Economics

A company that makes machines is examining its cost structure, and here lays out the meticulous data as specified in the table: If the company fabricates 3 machines, what is the average fixed cost?

| Quantity (unit) | Total Fixed Cost ($) | Total Variable Cost ($) |
| --------------- | -------------------- | ---------------------- |
| 0               | 400                  | 0                       |
| 1               | 400                  | 100                    |
| 2               | 400                  | 190                    |
| 3               | 400                  | 275                    |
| 4               | 400                  | 360                    |
Topic: Asset Classes & Derivatives

Amelia, as a fund manager, trades off a $50,000 vega notional of a one-year variance swap on the S&P 500 at a strike of 20% (annual volatility mentioned). As half a year has gone by, the S&P 500 has seen a realized volatility of 16% (annualized). The same day, the fair strike of a new six-month variance swap on the S&P 500 stands at 19%. The present value of the variance swap that Amelia sold (taking into account the annual interest rate is 2.5%) is:
Topic: Asset Classes & Derivatives

Jessica has projected that corporation B will disburse dividends of $1.5 and $2.5 respectively at the close of the first and second year. After the second year, dividends are anticipated to increase at a rate of 5%. Other relevant details can be found in the table below. What is the inherent value of the corporation's stock?

| Risk-free rate | 3% |
| -- | -- |
| Market risk premium | 7% |
| Company A's beta | 1.1 |
Topic: Accounting

Using the straight-line method, what is the annual depreciation expense for a machine purchased in Jan. 2015, according to the applicable information?

|                                     |      |
|-------------------------------------|------|
| Cost of the equipment $5,000,000    |      |
| Estimated residual value $500,000   |      |
| Expected useful life 9 years        |      |
| Total productive capacity 950,000 units |      |
| Production in FY2015 150,000 units  |      |
| Expected production for the next 9 years 100,000 units each year |      |
Topic: Accounting

The Sunshine Primary School provides its staff members with a defined benefit retirement plan. The school is in accordance with IFRS. The chosen details related to the pension plan in 2018 are this: the benefit obligations at the onset of the year being $3,000,000, the plan assets' fair value at the start of the year being $3,100,000 and the plan assets' book value equalling $2,800,000 at the beginning of 2018. So, what is the funded status of the scheme at the start of 2018?
Topic: Asset Classes & Derivatives

The pamphlet ends with the backstory of another private equity fund known as Pocatello Fund. As per the cash flows and distributions shown in Exhibit 1 for the initial five years of this fund, what was the total value paid into the Pocatello Fund in 2009?

| Year | Paid-In Capital | Mgmt Fees | Operating Results | NAV before Distributions | Carried Interest | Distributions | NAV after Distributions |
|------|-----------------|-----------|-------------------|--------------------------|------------------|---------------|-------------------------|
| 2005 | 40             | 0.8       | -3                | 36.2                     |                  |               | 36.2                    |
| 2006 | 55             | 1.1       | 4                 | 54.1                     |                  |               | 54.1                    |
| 2007 | 80             | 1.6       | 11                | 88.5                     |                  |               | 88.5                    |
| 2008 | 100            | 2         | 27                | 133.5                    | 4.2              | 19            | 110.3                   |
| 2009 | 125            | 2         | 34                | 167.3                    | 6.6              | 38            | 122.7                   |
Topic: Accounting

A merchant is analyzing various methods for assessing inventory worth. The merchant has a single product that they trade for $50. What is the final inventory's value for the first quarter if the merchant employs a continuous LIFO inventory evaluation technique?

|  |  | Units Purchased and Sold (first quarter) |  |  |  |  |
|---|---|---|---|---|---|---|
|  |  | Date |  |  |  |  |
|  |  | Units Purchased | Purchase Price | Units Sold | Selling Price | Inventory Units on Hand |
|  | 2 Jan | 1,000 | $20.00 |  |  | 1,000 |
|  | 17 Jan |  |  | 500 |  | $50.00, 500 |
|  | 16 Feb | 1,000 | $18.00 |  |  | 1,500 |
|  | 3 Mar |  |  | 1,200 |  | $50.00, 300 |
|  | 13 Mar | 1,000 | $17.00 |  |  | 1,300 |
|  | 23 Mar |  |  | 500 |  | $50.00, 800 |
|  | End of quarter totals: | 3,000 | $55,000 | 2,200 |  | $110,000 |
| Identifying Header | Exhibit 2: | Comparison of Inventory Methods and Models |  |  |  |  |
|  | End of Quarter Valuations |  |  |  |  |  |
| 31 March |  | Perpetual LIFO,Periodic LIFO, Perpetual FIFO |  |  |  |  |
| Sales |  | $110,000 | $110,000 | $110,000 |  |  |
|  | Ending inventory |  | $16,000 | $13,600 |  |  |
|  | Cost of goods sold |  | $39,000 | $41,400 |  |  |
|  | Gross profit |  | $71,000 | $68,600 |  |  |
|  | Inventory turnover ratio | 279% |  |  |  |  |
|  | Note: LIFO is last in, first out and FIFO is first in, first out. |  |  |  |  |  |
Topic: Asset Classes & Derivatives

Using the multistage RI model for estimating the value of PBRI, John gathers extra data. He predicts a yearly growth rate for residual income of 15% over a prediction range of 5 years (Years 1 to 5) and decides to discount the final year’s residual income as perpetuity. Considering the information in Exhibit 3, what is John's approximation of the contribution that the terminal value of the income stream will make to the present value of equity after five years?

| Most recent year's net income | $8.0 million | Cost of equity capital | 12.40% |
|---|---|---|---|
| Interest expense | $1.2 million | WACC | 10.60% |
| Equity capital book value | $20.97 million | Tax rate | 40% |
Topic: Market Analysis & Economics

A financial expert is aiming to determine the worth of a 1-year European call option using the BSM model. He has gathered the following data: the present stock price is $90, the strike price is $75, the risk-free rate calculated through continuous compounding is 4%, and the yearly volatility rate is 20%. What would be the call option's value? N(-1.21) =0.1131; N(-1.01) =0.1562.
Topic: Risk Management

Given that a chart from a credit reporting agency indicates that the count of A-ranked entities that upgraded to AAA is 1, those which advanced to AA were 6, those who maintained at A were 41, those who were demoted to BBB were 2, and those that defaulted were 3. Assuming a fresh entity with an A grade credit score, what is the chance that it will experience a reduction in rating or end up defaulting after one year?
Topic: Market Analysis & Economics

What is the value of the Paasche index for the consumption basket of December displayed in Exhibit 1?

| Date | November 2010 Quantity | November 2010 Price | December 2010 Quantity | December 2010 Price |
|------|-----------------|-----------------|------------------|------------------|
| Sugar| 70kg           | £0.90/kg        | 120kg            | £1.00/kg         |
| Cotton| 60kg           | £0.60/kg        | 50kg             | £0.80/kg         |
Topic: Portfolio Management & Strategy

Johnson requests his research team to generate risk and anticipated return predictions for Funds X, Y, and Z as well as the benchmark, shown in Exhibit 1. Johnson opts to introduce a fourth fund to his group, Fund W, that will utilize the same benchmark embedded in Exhibit 1. Given the information from Exhibit 1, what would be the Sharpe ratio if Fund W, which Johnson estimates to have an information ratio of 0.35, is merged with a fund that mimics the benchmark?

|                   | Fund X | Fund Y | Fund Z | Benchmark |
|-------------------|--------|--------|--------|-----------|
| Sharpe ratio (SR) | 0.45   | 0.50   | 0.49   | 0.44      |
Note: Data are based on a risk-free rate of 2.3%.
Topic: Accounting

A researcher collected the following data from a corporation's 2010 financial reports (in $ millions): In 2010, the corporation declared and dispersed cash dividends of $10 million, and logged a depreciation expense of $25 million. The corporation classifies dividends paid as a financing activity. What was the corporation’s 2010 operational cash flow (in $ millions)?

| Balances as of Year Ended 31 December | 2009 | 2010 |
| ------------------------------------- | ---- | ---- |
| Retained earnings                     | 120  | 145  |
| Accounts receivable                   | 38   | 43   |
| Inventory                             | 45   | 48   |
| Accounts payable                      | 36   | 29   |
Topic: Accounting

Suppose that the price of a bond over the next two periods is detailed below. The starting value of the bond is $100. The likelihood of a rise in any given period is 40% and the chance of a fall in any given period is 60%. If we apply the binomial model, what is the likelihood that the bond's price will reach $101.20 after two periods?

| - |  Time=0 | Time=1 | Time=2 |
|---|:---:|:---:|:---:|
| - | S0=100 | Su=110 | Suu=121 |
| - |-| Sd=92 | Sud,du=101.20 |
| - |-| - | Sdd=84.64 |
Topic: Asset Classes & Derivatives

XYZ is a wealth management firm based in France. They have made an investment of $10 million in E Corporation's senior unsecured bond with a term of 10 years. Due to concerns of a potential default by E Corp, XYZ purchased a credit default swap (CDS) on E corp valued at $10 million with a designated coupon rate of 5%. After three months, E Corp goes bankrupt, resulting in a variety of activated CDS contracts. Consequently, XYZ examines the credit quality of the corporate bond they invested and the CDS's value on that bond. Here's some information on the current market status of E Corporation's bonds: Bond 1 is a 5-year senior unsecured bond trading at 40% of par, Bond 2 is a 10-year senior unsecured bond trading at 50% of par. Bond 3 is a 6-year subordinated unsecured bond trading at 30% of par. Based on these details, what is the cheapest
Topic: Asset Classes & Derivatives

In February 2007, you are investigating a theoretical company called Davis Global that experiences seasonal demand for its offerings. On 2 February 2007, Davis shares ended at $57.98. You believe that the period from 2003 through 2006 provides a fair representation of average earnings. When determining normalized EPS, we can consider the approach of historical average EPS or the average ROE method, so what is the difference in PE calculated using these two methods?

| Measure     | 2007   | 2006   | 2005  | 2004  | 2003  |
|-------------|--------|--------|-------|-------|-------|
| EPS         | $3.03  | $1.45  | $0.23 | $2.13 | $2.55 |
| BV per share| $19.20 | $16.21 | $14.52| $13.17| $11.84|
| ROE         | 16.0%  | 8.9%   | 1.6%  | 16.3% | 21.8% |
Topic: Portfolio Management & Strategy

What is the highest Sharpe ratio achievable by a fund manager when merging the S&P 500 benchmark portfolio and the Indigo Fund?

|                    | S&P 500 | Indigo Fund |
|--------------------|---------|-------------|
| Expected annual return | 9.0%    | 10.5%      |
| Return standard deviation | 18.0%  | 25.0%      |
| Sharpe ratio | 0.333   | 0.30       |
| Active return |         | 1.2%       |
| Active risk |           | 8.0%       |
| Information ratio |     | 0.15       |
Topic: Accounting

In China, there's an education business known as PZ Corporation which adheres to IFRS. As of 2018, the corporation had a 15% non-controlling equity stake in T-web Corporation. The executives at PZ decided to boost the company’s stake in T-web to 50% through a straight cash buy on 1st January 2019, with no transactions between the companies. The table provided includes the financial statement details of both PZ and T-web corporations. Could you please compute the consolidated sales for 2019 for PZ corporation, after gaining control over T-web company:

|                         | 2018 | 2019 |
|-------------------------|------|------|
| Revenue                 | 5,000| 7,000|
| Cost                    | 2,000| 2,300|
| Operating income        | 3,000| 4,700|
| Net profit              | 1,650| 2,300|
| Total assets            | 4,000| 6,000|
| Total liabilities       | 1,200| 900  |
| Equity                  | 2,800| 5,100|

|                        | 2018  | 2019  |
| ---------------------- |:-----:| -----:|
| Revenue                | 2,000 | 2,500 |
| Cost                   | 1,200 | 1,300 |
| Operating income       | 800   | 1,200 |
| Net profit             | 460   | 820   |
| Dividends paid         | 230   | 410   |
| Total assets           | 1,000 | 1,100 |
| Total liabilities      | 600   | 650   |
| Equity                 | 400   | 450   |
Topic: Accounting

A corporation decided to trade a truck that it had bought three years prior for a piece of land owned by a different corporation. The following chart includes details about both items: The financial statement for the corporation that is getting rid of the truck is most likely going to report a loss of:

| | Truck* | Land** |
| --- | --- | --- | 
| Original cost | $57,000 | $18,000 |
| Estimated  life | 8 years | |
| Estimated salvage value at purchase | $15,000 | |
| Depreciation method | Declining balance, 20% per year | |
| Current fair value of item | $27,000 | $21,000 |

\* The last sale of a similar truck by the company occurred more than six months ago.

\*\* The land is one of four identical parcels of land recently sold by the company.
Topic: Portfolio Management & Strategy

Assuming an investment manager constructs this portfolio, and the covariance of returns for the two securities involved is -0.0240, what is the projected standard deviation of the portfolio?

| Security | Security Weight(%) | Expected Standard Deviation(%) |
| ---      | ---                | ---                           |
| 1        | 30                 | 20                            |
| 2        | 70                 | 12                            |
Topic: Asset Classes & Derivatives

Three months ago, a supervisor agreed to a receive-fixed and pay-equity swap. The yearly fixed rate was set at 3% and the equity index was 100 at the time the swap was made. The swap will mature in one year and has a quarterly reset, and nominal amount of $100 million. The value of the swap is up for evaluation, assuming the equity index is now 101 and the current spot rates are provided:

| Years to maturity | Present Value Factor |
|------------------|---------------------|
| 0.25                 | 0.997506               |
| 0.5                  | 0.992556               |
| 0.75                | 0.985222               |
| 1                     | 0.975610               |
Topic: Market Analysis & Economics

If, in a basic economy without a foreign sector, the ensuing formulas are valid: Consumption formula: C = 2,500 + 0.80 × (Y – T), Investment formula: I = 500 + 0.30 × Y – 25 × r, State expenditure: G = 1,000, Tax formula: T = –250 + 0.30 × Y, where Y signifies total income and r symbolizes real interest rate as a percentage, how much will the total income grow if the actual interest rate is 3% and state expenditure rises to 2,000?
Topic: Asset Classes & Derivatives

The details provided are related to a hedge fund named Trident Consultancy, which has:     AUM valued at $300 million as per the end of last year     A management fee set at 2% (calculated based on the AUM at year-end)     An incentive fee of 20% factored in: after deducting the management fee, considering a 5% soft hurdle rate, and utilizing a high-water mark (the high-water mark is $357 million)     The gross return for the current year for the fund stands at 20%. Could you calculate the total fee that Trident has earned this year?
Topic: Asset Classes & Derivatives

The Aquarius Pool of Funds puts GBP150 million into each of Beta Hedge Fund and XYZ Hedge Fund. Aquarius Pool of Funds operates a "1 and 10" fee system. Both management and incentive fees are evaluated separately at the end of each calendar year. After one year, factoring in their individual management and incentive fees, the value of Aquarius's investment in Beta stands at GBP 80 million and it's worth GBP240 million in XYZ. What is the yearly return for a investor in the Aquarius Pool of Funds, after taking into account the fees charged at the fund-of-funds level?
Topic: Accounting

Considering the available selected fixed asset details for a firm, what is the firm's fixed asset turnover ratio?

|                                | 2016 ($US millions) |
|--------------------------------|---------------------|
| Cost: Total property, plant, and equipment (PP&E) | 30,815                 |
| Accumulated depreciation | 16,465                 |
| Net PP&E                         | 14,350                 |
| Average net PP&E                 | 12,200                 |
| Net sales                        | 21,670                 |
| Net income                       | 2,705                   |
Topic: Accounting

What is the total comprehensive income of the business (in € millions) based on the information from the business's financial records?

|                                               | 毛 millions |
|-----------------------------------------------|------------:|
| Revenues for the year                         |      12,500 |
| Total expenses for the year                   |      10,000 |
| Gains from available-for-sale securities      |       1,475 |
| Loss on foreign currency translation adjustments on a foreign subsidiary |         325 |
| Dividends paid                                |         500 |