Time Value of Money Concept

The following situations involve the application of the time value of money concept. Use the full factor when calculating your results.

Use the appropriate present or future value table:

FV of $1, PV of $1, FV of Annuity of $1 and PV of Annuity of $1

1. Janelle Carter deposited $9,790 in the bank on January 1, 2000, at an interest rate of 12% compounded annually. How much has accumulated in the account by January 1, 2017? Round to the nearest whole dollar.
$

2. Mike Smith deposited $21,410 in the bank on January 1, 2007. On January 2, 2017, this deposit has accumulated to $42,117. Interest is compounded annually on the account. What rate of interest did Mike earn on the deposit? Round to the nearest whole percent.
%

3. Lee Spony made a deposit in the bank on January 1, 2010. The bank pays interest at the rate of 7% compounded annually. On January 1, 2017, the deposit has accumulated to $12,070. How much money did Lee originally deposit on January1, 2010? Round to the nearest whole dollar.
$

4. Nancy Holmes deposited $6,930 in the bank on January 1 a few years ago. The bank pays an interest rate of 8% compounded annually, and the deposit is now worth $12,827. How many years has the deposit been invested? Round to the nearest whole year.
years

The Canyon Company is preparing its annual earnings per share amounts to be disclosed on its 2019 income statement. It has collected the following information at the end of 2019:

• Net income: $125,000. Corporate income tax rate: 30%
• Common stock outstanding on January 1, 2019:   12,000 shares, $10 par
• Common stock issuances during 2019:
  • April 2 - 2,500 shares;
  • October 1 - 4,000 shares.
• Stock split: On November 1, the company declared a two-for-one stock split.
• Common stock prices: The common stock sold at an average market price of $20 per share during the year.
• 8% convertible preferred stock outstanding on December 31, 2019: 3,000 shares. The preferred stock was issued in 2010. Each share of $100 par preferred stock is convertible into 5 shares of common stock. Current dividends have been paid. To date, no preferred stock has been converted.
• Compensatory share options outstanding: Key executives may currently acquire 1,000 shares of common stock at $15 per share. The option were granted in 2010. To date, none have been exercised.
• $200,000 of 8% convertible bonds: Each bond is convertible into 28 shares of common stock.

Required:

Prepare supporting calculation for Canyon Company and compute its:

1. Basic earnings per share.
2. Diluted earnings per share.

I. On September 12, 2010, Mardi Gras Mambo Inc. received a $6,000 8%, 120 day note on account from Throwin’ Things Corporation

a. Is the note a note receivable or a note payable for Mardi Gras Mambo?

b Is Mardi Gras Mambo the maker or the payee of the note?

c What is the face amount of the note?

d What is the total amount of cash that is due at maturity (i.e., what is the maturity value of the note)?

e What is the due date of the note?

f What is the principal of the note?

g As of September 30, 2010, how much interest has Mardi Gras Mambo accrued on the note?

h. Prepare the journal entries for the following transactions:

(1) September 12

(2) September 30

(3) At maturity date (assume no entries regarding the note have been made since September 30)

II. Assume that the note is non-interest bearing and that the market rate of interest for similar securities is 8% (all other terms are the same). Answer each of the following:

a What is the total amount of cash that is due at maturity (i.e., what is the maturity value of the note)?

b. What is the principal of the note?

c. Prepare the journal entries for the following transactions:

(1) September 12

(2) September 30

(3) At maturity date (assume no entries regarding the note have been made since September 30

Year Stock A Returns Stock B Returns

2008 -18.00% -14.50%

2009 33.00 21.80

2010 15.00 30.50

2011 -0.50 -7.60

2012 27.00 26.30

1. Calculate the average rate of return for each stock during the period 2008–2012.
2. Assume that someone held a portfolio consisting of 50 percent Stock A and 50 percent Stock B. What would have been the realized rate of return on the portfolio in each year from 2008 through 2012? What would have been the average return on the portfolio during this period?
3. 1. Calculate the standard deviation of returns for each stock and for the portfolio.
   2. Calculate the coefficient of variation for each stock and for the portfolio. If you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?
4. Assume a third stock, Stock C, is available for inclusion in the portfolio. Stock C produced the following returns during the 2008-2012 period

Year   Stock C

2008                                          32.00%

2009                                        –11.75

2010                                          10.75

2011                                          32.25

2012                                          –6.75

6. Calculate (or read from the computer screen) the average return, standard deviation, and coefficient of variation for Stock C.
7. Assume that the portfolio now consists of 33.33 percent Stock A, 33.33 percent Stock B, and 33.33 percent Stock C. How does this composition affect the portfolio return, standard deviation, and coefficient of variation versus when 50 percent was invested in A and in B

3. Consider the following situation and answer the subsequent questions to the best of your engineering ability and judgment. a. There are two Schultz Creek watersheds, East and West. The East drains into unincorporated communities east of Flagstaff, and the West drains into the City of Flagstaff itself. The key point about ‘unincorporated’ is that this means these residents did not live in a city or town, and for some infrastructure aspects like storm drainage, there were no requirements or regulations. Prior to 2010 both of these watersheds were heavily forested and due to almost a hundred years of fire suppression instead of fire management, both watersheds had accumulated thick, water-absorbing masses of pine needles and decomposed pine needles on the forest floor. This prevented the watersheds from ‘delivering’ runoff to its streams in normal years because all of the precipitation was stored in the pine needle layers, sometimes referred to as ‘duff’. Only in heavy snow and rain years, about once every 5-7 years, would the streams flow, instead of every one or two years. i. The East Schultz Creek Watershed is approximately 14 square miles in area. The West is about 6 square miles in area. Assume that the following hydrologic soil group percentages hold for both watersheds prior to 2010: 5% HSG D, 8% HSG C, 15% HSG B, and the rest is HSG A, due to the extensive duff in the watershed.

1. It has come to your attention that someone in the company has not been consistent in entering financial data – some years are missing the relative percentage change or the net profit as presented below in Table 1.  You are required to calculate the Relative Percentage Change in the company for the blanks below and the Net Profit for the other blanks.

Show all working out below including the formula used for each year and include the completed table here.

               Table 1: Net Profit ($) per financial year

2. Using Excel, create a column chartof the Net Profit calculated in part (a) for the years 2010-2019. For full marks, label the axis and provide an appropriate title.

(c) Using Excel, create a Sparkling of the Relative Percentage Change calculated in part (a) for the years 2011-2019. For full marks, use the Sparkling options to mark if there are any negative values and include a horizontal axis to easily visualise changes. The sparkline should be included here however you will also use it in the report body text.

You opened an account and deposited X Dollars on January 1, 2002 in National City Bank. Any balance in the account will earn 5% per year. You withdrew $500 on January 1, 2006 and $500 on January 1, 2008. You closed out this account on January 1, 2011 and received $700. How much did you initially deposit (X) in National City at the time you opened the account?

Use the Divergence Theorem to evaluate

F · dS,

where

F(x, y, z) = z²xi +

+ cos z

j + (x²z + y²)k

and S is the top half of the sphere

x² + y² + z² = 4.

(Hint: Note that S is not a closed surface. First compute integrals over S₁ and S₂, where S₁ is the disk

x² + y² ≤ 4,

oriented downward, and S₂ = S₁ ∪ S.)

Using only real numbers between 0 and 100, inclusive, show the set of three numbers whose product is 64 and whose sum is minimal is give by {4, 4, 4}.

(a) When is an absolute minimum or maximum guaranteed?

(b) State the steps to find an absolute minimum and maximum.

(c) Is the space closed and bounded? Explain.

(d) Use Lagrange Multipliers to find the minimum and maximum

please label and write neatly.