Do the following sets of vectors span R^3?

1) [1,3,1], [3,9,4], [8,24,10], [-10,-30,-13]

2) [1,2,3], [-1,-2,-4], [1,2,2]

3) [-1,-3,-1], [-4,-12,-3]

4)[1,2,-2], [7,5,7], [-4,-1,-11]

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 2011 to 2016 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 2018 to 2022. If Reeby
Sports will lose its competitive edge by 2022, then it cannot continue earning more than
its10% cost of capital. Therefore ROE is reduced to 10%startingin 2023.1
The payout ratio is set at .30 from 2018 onwards. Notice that the long-term
growth rate, which settles inafter 2023, is ROE × ( 1 – dividend payout ratio) = .10 × (1 -
.30) = .07.
The spreadsheet allows you to vary ROE and the dividend payout ratio separately
for 2018-2022 and for 2023-2024.2But let’s start with the initial input values. To
calculate share value, we have to estimate a horizon value at H = 2022 and add its PV to
the PV of dividends from 2017 to 2022. Using the constant-growth DCF formula,
PV = 0.71 = 23.72 H .10- .07
The PV of dividends from 2017 to 2022 is $3.43 at the start of 2017, so share value is:3
6
PV = 3.43+ 23.72 = $16.82
(1.1)
The spreadsheet also calculates the PV of dividends through 2024 and the horizon
value at 2024. Notice that the PV at the start of 2017 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 2022, assuming that Reeby
Sports will have exhausted valuable growth opportunities by that date. With PVGO = 0,
PV = EPS/r.4So we could discard the constant-growth DCF formula and just divide EPS
in 2023 by the cost of capital:
PVH = 2.37 = $23.72 .10
This PVis 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 2018 and all later years.You should get PV = $13.82. Thus PVGO = 16.82
– 13.82 = $3.00 per share for investments made in 2017onward.
George Reeby has also identified a "comparable," Molly Sports. We could use its
P/E ratio of 13.1 to calculate horizon value in 2022 and PV at the start of 2017. Using
the original inputs for ROE, EPS in 2023 is 2.37.5
H
6
PV 13.1 2.37 $31.05
PV 3.43 31.05 $20.96
(1.10)
= ´ =
= + =
We couldalso use Molly’s P/E ratio to calculate Reeby Sports’ PV at the start of 2017
directly from 2017 EPS:
PV = 13.1 ´ 2.03 = $26.59

The Question is ?
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
2024?You can check by changing ROE for 2023-2024 from .10 to .15. (The ROE for
2025 and 2026 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 2017. Do you think these inputs are reasonable?

The following data is provided for a market 500 Index:                                                               
                                                                                    
                        Year     Total return     Year     Total return                 
                        2010    9.0%                2020    2.0%                
                        2011    11.0%             2021    3.0%                
                        2012    -3.0%               2022    3.0%                
                        2013    1.0%                2023    -1.0%               
                        2014    5.0%                2024    5.0%                
                        2015    -12.0%             2025    4.0%                
                        2016    3.0%                2026    -3.0%               
                        2017    4.9%                2027    3.5%                
                        2018    -7.0%               2028    7.0%                
                        2019    0.1%                2029    5.8%                
                                                                                    
Calculate the 20-year arithmetic average annual rate of return on the market Index.

A) 2.07%

B) 0.10%

C) 2.59%

D) 5.62%                                                          

1. How many sherds/m³ would you expect to find at the source (e.g. x = 0)

2. How many sherds/m³ would you expect to find at a site located 18km from the kilns?  

3. Calculate the correlation coefficient for this data set (e.g. r)

You find the following corporate bond quotes. To calculate the number of years until maturity, assume that it is currently January 15, 2016. The bonds have a par value of $2,000.

Xenon Inc. has Coupon: 5.400, Maturity: Jan. 15, 2020, Last Price: 94.183, Last Yield: ??, EST $ Vol (000s) 57,362.

Kenny Corp. has Coupon: 7.125, Maturity: Jan. 15, 2019, Last Price: ??, Last Yield: 5.14, EST $ Vol (000s) 48,941.

Williams Co. has Coupon: ??, Maturity: Jan. 15, 2026, Last Price: 94.735, Last Yield: 6.85, EST $ Vol (000s) 48,302.

What price would you expect to pay for the Kenny Corp. bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Price: $

What is the bond's current yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Current yield: %

Rexon Company leases non-specialized equipment to Ten-Care Company beginning January 1, 2019. The lease terms, provisions, and related events are as follows:

Required:

1. Assuming that the lease is a sales-type lease from Rexon’s point of view, calculate the amount of the equal rental receipts.

Additional Instruction

$

2. Prepare a table summarizing the lease receipts and interest income earned by Rexon.

Additional Instructions

3a. Prepare the journal entries for 2019.

General Journal Instructions

PAGE 2019

GENERAL JOURNAL

3b. Prepare the journal entries for 2020.

PAGE 2020

GENERAL JOURNAL

Find the absolute maximum of g(x,y)=x^2+y^2-2y+1 on the disk x^2+y^2 less than or equal to 4. Solve 2 ways, parametrization and lagrange multipliers. Please solve using both methods!

Show that the cylinder x 2 + y 2 = 4 and the sphere x 2 + y 2 + z 2 − 8y − 6z + 21 = 0 are tangent at the point (0, 2, 3). That is, show that the cylinder and sphere intersect at that point, and that they share the same tangent plane at that point.

Universal Leasing leases electronic equipment to a variety of businesses. The company’s primary service is providing alternate financing by acquiring equipment and leasing it to customers under long-term leases. Universal earns interest under these arrangements at a 11% annual rate.

Universal purchased an electronic typesetting machine on December 31, 2020, for $99,000 and then leased it to Desktop, Inc., a local publisher. The six-year operating lease term commenced January 1, 2021, and the lease contract specified annual payments of $8,900 beginning December 31, 2021, and on each December 31 through 2026. The machine’s estimated useful life is 15 years with no estimated residual value.

The publisher had the option to terminate the lease after four years. At the beginning of the lease, there was no reason to believe the lease would be terminated.

Required:
1. Prepare the appropriate entries for Universal Leasing from the beginning of the lease through the end of 2021.
2. At the beginning of 2022, there was a significant indication that Desktop’s economic incentive to terminate the lease had changed causing both companies to believe termination of the lease at the end of four years (three years remaining) is "reasonably certain." Prepare any appropriate entry for Universal Leasing at January 1, 2022, to reflect the change in the lease term.
3. Prepare the appropriate entry pertaining to the lease for Universal Leasing at December 31, 2022.