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cestrela7 [59]
3 years ago
5

You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value

(PV)? Assume that all annuities earn the same positive interest rate. An annuity that pays $1,000 at the beginning of each year An annuity that pays $500 at the beginning of every six months An annuity that pays $1,000 at the end of each year An annuity that pays $500 at the end of every six months
Business
1 answer:
olasank [31]3 years ago
7 0

Answer:

Ans. The greates present value is the one that pays $1,000 at the beginning of each year, for 10 years. Assuming a 10% effective annual rate, this present value is equal to $6,759.02

Explanation:

Hi, in order to find the present value of an annuity, first we have to take into account if this annuity is paid at the beginning or at the end of each period. This is the formula for an annuity that pays at the beginning of each year.

PresentValue=A+\frac{A((1+r)^{n-1}-1) }{r(1+r)^{n-1} }

In the case of an annuity that pays at the end of each year is:

PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }

Where:

A= annuity

r= rate of return

n= periods that will be paid

But, there are 2 types of annuities here(that pay at the beginning of the period), one is paid every year and other that pays every 6 months. Since we are going to assume a rate of return of 10% effective annually, for the first type (pays every year at the beginning) r=10% and n=10, and for the second one (pays at the beginning of every 6 months) r=4.8809% and n=20.

Let me show you the formula to turn an annual effective rate into a semi-annual effective rate.

r(semi-annual)=(1+r(annual))^{\frac{1}{2} } -1=(1+0.1)^{\frac{1}{2} } -1=0.048809

Let´s find each present value.

A) Pays 1,000 at the beginning of each year

PresentValue=1,000+\frac{1,000((1+0.1)^{9}-1) }{0.1((1+0.1)^{9} } =6,759.02

B) Pays at the beginning of every six months

PresentValue=500+\frac{500((1+0.048809)^{19}-1) }{0.048809((1+0.048809)^{19} }=6,601.75

C) Pays 1,000 at the end of each year

PresentValue=\frac{1,000((1+0.1)^{10}-1) }{0.1(1+0.1)^{10} }=6,144.57

D) Pays 500 at the end of every six months

PresentValue=\frac{500((1+0.048809)^{20}-1) }{0.048809(1+0.048809)^{20} }=6,294.52

So the answer is A) the one that pays 1,000 at the beginning of each year.

Best of luck.

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8 0
3 years ago
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The following summarized data (amounts in millions) are taken from the September 27, 2014, and September 28, 2013, comparative f
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Answer:

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b) Current Ratio = Current Assets / Current Liabilities

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Explanation:

<h3>Apple Inc. </h3><h3>Income Statement</h3>

For the Fiscal Years Ended September 27 and September 28, respectively:

                                                             2014                2013

Net sales                                           $108,400            $65,370

Costs of sales                                      64,580              39,690

Operating income                               33,950               18,530

Net income                                       $26,050              $14,160

Balance Sheet:

Assets

Current assets:

Cash and cash equivalents                                            $9,580      $10,630

Short-term marketable securities                                   16,280         14,510

Accounts receivable, less allowances of $84 & $99     5,520          5,670

Inventories                                                                           930           1,200

Deferred tax assets                                                          2,170            1,780

Vendor non-trade receivables                                       6,500           4,560

Other current assets                                                      4,680           3,590

Total current assets                                                     45,660          41,940

Long-term marketable securities                               85,770          25,540

Property, plant, and equipment, net                            7,930          22,670

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Acquired intangible assets, net                                   3,690               490

Other assets                                                                  3,710              2,410

Total assets                                                             $147,820        $93,940

Liabilities and Shareholders Equity

Current liabilities:

Accounts payable                                                     $14,780          $12,160

Accrued expenses                                                      9,400             5,870

Deferred revenue                                                       4,250              3,130

Commercial paper                                                      6,548             0

Total current liabilities                                              34,978             21,160

Deferred revenue: noncurrent                                   1,840              1,290

Long-term debt                                                        23,452            17,760

Other noncurrent liabilities                                      10,260             5,680

Total liabilities                                                          70,530           45,890

Shareholders' Equity:

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par value, 1,900,000 shares authorized; 929,430 & 916,130

shares issued & outstanding, respectively            13,490             10,810

Retained earnings                                                  63,200           37,320

Accumulated other comprehensive income (loss)    600                (-80)

Total shareholders' equity                                     77,290           48,050

Total liabilities & shareholders' equity              $147,820        $ 93,940

At September 29, 2012, total assets were $47,820 and total shareholders' equity was $31,800.

b) Working Capital is the excess of current assets over current liabilities.  It shows the amount of finance needed for meeting day-to-day operations of an entity.  Working capital measures a company's liquidity, operational efficiency, and its short-term financial health.  A healthy entity has some excess of current assets over current liabilities in order to continue to run the business operations in the short-run.  Working capital can also be measured in relative terms with the use of ratios, especially the current ratio and the acid-test ratio.

c) ROE means Return on equity.  It is a financial performance measure calculated by dividing net income by shareholders' equity.   Since shareholders' equity is equal to a company's assets minus its debt, ROE is considered as the return on net assets.  As with return on capital, a ROE measures management's ability to generate income from the equity available to it.

d) Return on Investment (ROI) is a financial performance measure which evaluates the efficiency of an investment or compares the efficiency of a number of different investments.  ROI tries to directly measure the amount of return on a particular investment, relative to the investment's cost.  As a financial metric, it measures the probability of gaining a return from an investment.

6 0
3 years ago
Scott Corporation produces a part for use in the production of one of its products. The per-unit costs associated with the annua
denpristay [2]

Answer:

It is cheaper to buy the part. The company will save $5,000.

Explanation:

Giving the following information:

UNitary production cost:

Direct Materials $10.50

Direct labor $24.00

Variable factory overhead $ 5.50

Total avoidable Fixed factory overhead= (12*1,000) - 5,000= 7,000

Larson Company has offered to sell 1,000 units of the same part to Scott Corporation for $42 per unit.

First, we need to calculate the total cost of making the units:

Total cost= (10.5 + 24 + 5.5)*1,000 + 7,000= $47,000

Now, the total cost of buying them:

Buy= 1,000*42= $42,000

It is cheaper to buy the part. The company will save $5,000.

3 0
3 years ago
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