Question

Problem #1 Your company is considering changing terms to offer a discount. The average price of the products you sell is $10.00. You will allow customers who pay with 15 day to continue to pay $10. But those who do not take the discount and take an additional 10 days to pay will pay $10.25 for each product. The average default rate is 3%. The discount rate you will use for this problem is 0.75%. The units sold are expected to increase from 15,000 units to 15,525. The increase in sales will allow the variable cost to fall from $7.55 to $7.50 A. How much is the NPV for this credit policy change? B. What do you recommend? C. Since the sales volume is an estimate it may be wrong in either direction by 5 units. How much is the NPV if sales are 5 units more than and less than 15,525? D. What do you recommend?

Answer 1

A.

It is given that total 15525 units of the product is to be sold if there is new discount policy where customer who pays within 15 days get discount and who pays after 15 days pays more. Net amount received is discounted at the rate of 0.75% to arrive at the Net Present value of the amount received. There is no time factor given in the question, therefore, it is assumed that time factor used for discounting will be 1.

A B Normal Units 1 Particulars 2 Average Price of the Product 3 for those who pay within 15 days 4 for those who pay after 15 days $ 10.00 10.00 $ 10.25 5 Total Units to be sold 15525 6 Default rate for payment 3% 7 8 Units sold to defaulted customers 466 9 Balance Units 15059 10 Decreased Variable Cost 7.50 11 Discount Rate 0.75% 12 13 Collection from defaulted customers$ 4,773.94 14 Collection from regular customers $150,592.50 15 Total Sales Collection $155,366.44 16 Total Variable Cost $116,437.50 17 Gross Profit 38,928.94 S 38,639.14 18 Net Present Value

Formula used in the above table are as follows -

A Normal Units 10 10 1 Particulars 2 Average Price of the Product 3 for those who pay within 15 days 4 for those who pay after 15 days 10.25 15525 0.03 -B6*B7 =+B6-B8 7.5 0.0075 6 Total Units to be sold 7 Default rate for payment 8 Units sold to defaulted customers 9 Balance Units 10 Decreased Variable Cost 11 Discount Rate 12 13 Collection from defaulted customers=+B8*B4 14 Collection from regular customers -+B9*B3 =+B13+B14 -B6*B10 -B15-B16 =B17/ (1+0.75%)^1 15 Total Sales Collection 16 Total Variable Cost 17 Gross Profit 18 Net Present Value

B.

Since NPV is positive, it is recommended to opt for discount scheme.

C.

Scenario when units will be 5 number less and more than the expected unit of 15525.

A C 5 Units less 10.00 S 10.00 S 10.25 S 1 Particulars 5 Units more 2 Average Price of the Product 3 for those who pay within 15 days 4 for those who pay after 15 days 10.00 10.00 10.25 15530 3% 466 15064 15520 3% 466 6 Total Units to be sold 7 Default rate for payment 8 Units sold to defaulted customers 9 Balance Units 15054 7.50 S 0.75% 10 Decreased Variable Cost 7.50 0.75% 11 Discount Rate 12 13 Collection from defaulted customers$ 4,772.40 4,775.48 $150,544.00 s150,641.00 $155,316.40 s155,416.48 14 Collection from regular customers 15 Total Sales Collection 16 Total Variable Cost $116,400.00 $116,475.00 $ 38,916.40 38,941.48 S 38,626.70 S 38,651.59 17 Gross Profit 18 Net Present Value

Formula used above are as follows -

A C 5 Units less 10 10 10.25 5 Units more 1 Particulars 10 10 10.25 2 Average Price of the Product 3 for those who pay within 15 days 4 for those who pay after 15 days 6 Total Units to be sold 7 Default rate for payment 15520 15530 0.03 +D6*D7 =+D6-D8 0.03 -C6*C7 +C6-C8 7.5 0.0075 8 Units sold to defaulted customers 9 Balance Units 10 Decreased Variable Cost 7.5 0.0075 11 Discount Rate 12 - D8*D4 -+D9*D3 +D13+ D14 -+D6*D10 13 Collection from defaulted customers=+C8*C4 14 Collection from regular customers -C9*C3 -C13+C14 -C6*C10 C15-C16 -C17/(1+0.75%)^1 | =D17/(1+0.75%)^1 15 Total Sales Collection 16 Total Variable Cost 17 Gross Profit +D15 -D16 18 Net Present Value

D.

Since NPV is positive, it is recommended to opt for discount scheme.

I hope this answer will help in your task.