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Alex
3 years ago
13

The fixed cost of Brendon Willows, a baseball bat manufacturing company, is $500,000 per year. The cost of wood and labor to man

ufacture one bat is $5. If the customers pay $25 to buy one bat, how many bats does Brendon Willows need to sell to break even?A. 20,000B. 25,000C. 100,000D. 150,000
Business
1 answer:
Inessa [10]3 years ago
7 0

Answer:

option (B) 25,000

Explanation:

Data provided in the question:

Fixed cost = $500,000 per year

Cost of wood and labor to manufacture one bat = $5

Selling price of the bat = $25

Now,

At breakeven, total cost equals to the total revenue

let the breakeven quantity be 'x'

thus,

$500,000 + $5x = $25x

or

$25x - $5x = $500,000

or

$20x = $500,000

or

x = 25,000

Hence,

the correct answer is option (B) 25,000

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Matt inherited as a trust a fifteen-year annuity-immediate with annual payments. He has been told that the annuity payments earn
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Answer:

effective annual interest rate = 6.32%

annual payment = $1,585

Explanation:

I believe that this is an ordinary annuity, so we can use the future and present value of an ordinary annuity formula:

FV = annual payment x FV annuity factor, so annual payment = FV / FV annuity factor

PV = annual payment x PV annuity factor, so annual payment = PV / PV annuity factor

we can equal both equations:

PV / PV annuity factor = FV / FV annuity factor

FV / PV = FV annuity factor / PV annuity factor

$37,804.39 / $15,077.10 = FV annuity factor / PV annuity factor

2.5074 = FV annuity factor / PV annuity factor

the easiest way to solve this is to use an annuity table since we already know that there are 15 periods (I used an excel spreadsheet):

%,15 periods      FV annuity factor     PV annuity factor        FV/PV

1                                 16.097                   13.865                      1.1609

2                                17.293                   12.849                      1.34586

3                                18.599                    11.938                      1.55797

4                               20.024                     11.118                       1.80104

5                                21.579                   10.380                      2.07890

<u>6                               23.276                   9.7122                       2.3966</u>

<u>7                                25.129                   9.1079                       2.7590</u>

8                                27.152                   8.5595                       3.1721

9                                29.361                   8.0607                      3.6425

10                               31.772                   7.6061                         4.4112

The interest rate must be between 6 and 7%:

%,15 periods      FV annuity factor     PV annuity factor        FV/PV

6                               23.276                   9.7122                       2.3966

6.1                             23.45404              9.6461                       2.43145

6.2                            23.63369              9.5858                      2.46549

6.3                            23.81491               9.52467                     2.50034

6.31                           23.83312               9.51851                     2.50387

<u>6.32                          23.85135               9.51236                     2.5074</u>

6.4                            23.99773              9.46337                     2.53585

effective interest rate = 6.32% per year

annual payment = $37,804.39 / 23.85135 = $1,585

           

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