Question

Suzanne had a summer job working in the business office of Blast-It TV and Stereo, a local chain of home electronics stores. When Michael Jacobssen, the owner of the chain, heard she had completed one year of business courses, he asked Suzanne to calculate the profitability of two new large-screen televisions. He plans to offer a special payment plan for the two new models to attract customers to his stores. He wants to heavily promote the more profitable TV.

When Michael gave Suzanne the information about the two TVs, he told her to ignore all taxes when making her calculations. The cost of television A to the company is $1950 and the cost of television B to the company is $2160, after all trade discounts have been applied. The company plans to sell television A for a $500 down payment and $230 per month for 12 months, beginning 1 month from the date of the purchase. The company plans to sell television B for a $100 down payment and $260 per month for 18 months, beginning 1 month from the date of purchase. The monthly payments for both TVs reflect an interest rate of 15.5% compounded monthly.

Michael wants Suzanne to calculate the profit of television A and television B as a percent of the TV’s cost to the company. To calculate profit, Michael deducts overhead (which he calculates as 15% of cost) and the cost of the item from the selling price of the item. When he sells items that are paid for at a later time, he calculates the selling price as the cash value of the item. (Remember that cash value equals the down payment plus the present value of the periodic payments.)

Suzanne realized that she could calculate the profitability of each television by using her knowledge of ordinary annuities. She went to work on her assignment to provide Michael with the information he requested.

Questions:

a. What is the cash value of television A? Round your answer to the nearest dollar.

b. What is the cash value of television B? Round your answer to the nearest dollar.

c. Given Michael’s system of calculations, how much overhead should be assigned to television A?

d. How much overhead should be assigned to television B?

e. According to Michael’s system of calculations, what is the profit of television A as a percent of its cost?

f. What is the profit of television B as a percent of its cost?

g. Which TV should Suzanne recommend be more heavily promoted?

Answer 1

Interest rate = 15.5% compounded monthly.

Monthly interest rate = 15.5%/12 = 1.291667%

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Part-a:

The cash value of television A = Down Payment + The present value of the periodic payments.

= 500 + 230*PVIFA(1.291667%,12)

= 500 + 230*11.0504

= 500 + 2,541.59

= $3,041.59

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Part-b:

The cash value of television B = Down Payment + The present value of the periodic payments.

= 100 + 260*PVIFA(1.291667%,18)

= 100 + 260* 15.9692

= 100 + 4,151.99

= 4,251.99

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Part-c:

Cost of Television-A = $1,950

Overhead assigned to television A = 1,950*15%

= $292.50

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Part-d:

Cost of Television-B = $2,160

Overhead assigned to television A = 2,160*15%

= $324

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Part-e:

The profit of television A as a percent of its cost:

Particulars	Television-A
Selling Price (a)	3,041.59
Cost (b)	1,950.00
Overheads (c ) = (b)*15%	292.50
Total Cost (d) = (b)+ (c   )	2,242.50
Profit ($) (e ) = (a)-(d)	799.09
Profit as a % of cost	40.98%
(e )/(b) * 100
Profit as a % of Total Cost	35.63%
(e )/(d) * 100

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Part-f:

The profit of television B as a percent of its cost:

Particulars	Television-B
Selling Price (a)	4,251.99
Cost (b)	2,160.00
Overheads (c ) = (b)*15%	324.00
Total Cost (d) = (b)+ (c   )	2,484.00
Profit ($) (e ) = (a)-(d)	1,767.99
Profit as a % of cost	81.85%
(e )/(b) * 100
Profit as a % of Total Cost	71.18%
(e )/(d) * 100

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Part-g:

Suzanne should recommend Television - B to be heavily promoted since it yields higher profit than Television-A.