Question

Your firm purchases goods from its supplier on terms of 1.8 divided by 15, net 30.

a. What is the effective annual cost to your firm if it chooses not to take the discount and makes its payment on day 30​?

The effective annual cost is_----​%. ​(Round to two decimal​ places.)

b. What is the effective annual cost to your firm if it chooses not to take the discount and makes its payment on day 40​?

The effective annual cost is____​% (Round to two decimal​ places.)

Answer 1

Solution:

a.Calculation of the effective annual cost of trade credit if the firm does not take the discount is and makes its payment on day 30​ :

The formula for the calculation of the effective annual cost of trade credit :

= ( 1 + [Discount rate / (1 – Discount Rate )] ) ⁿ – 1

Where n= No. of days in a period / ( Total payment Period – period for which discount has been offered)

As per the information given in the question we have

Discount rate = 1.8 % = 0.018   ; No. of days in a period = 365 days ;

Total payment Period = 30 days ; Period for which discount has been offered = 15 days

Total payment Period – period for which discount has been offered = 30 – 15 = 15 days

Applying the above values in the formula we have

= ( 1 + (0.018 / (1 – 0.018)) ^{( 365 / 15 )}   - 1                    

= ( 1 + (0.018 / 0.982 )) ^(24.3333)   - 1                              

= ( 1 + 0.018330 ) ^{( 24.3333 )}   - 1                                       

= ( 1.018330 ) ^{( 24.3333 )}   - 1

= 1.5558 – 1 = 0.5558   = 55.58 %                                                

Thus the annual effective cost of credit is = 55.58 %       

Note: ( 1.018330 ) ^{( 24.3333 )}   is calculated using the excel formula =POWER(Number,Power)

=POWER(1.018330,24.3333) = 1.5558

b.Calculation of the effective annual cost of trade credit if the firm does not take the discount is and makes its payment on day 40​ :

The formula for the calculation of the effective annual cost of trade credit :

= ( 1 + [Discount rate / (1 – Discount Rate )] ) ⁿ – 1

Where n= No. of days in a period / ( Total payment Period – period for which discount has been

offered)

As per the information given in the question we have

Discount rate = 1.8 % = 0.018   ; No. of days in a period = 365 days ;

Total payment Period = 40 days ; Period for which discount has been offered = 15 days

Total payment Period – period for which discount has been offered = 40 – 15 = 25 days

Applying the above values in the formula we have

= ( 1 + (0.018 / (1 – 0.018)) ^{( 365 / 25 )}   - 1                    

= ( 1 + (0.018 / 0.982 )) ^{( 14.6 )}   - 1                                  

= ( 1 + 0.018330 ) ^{( 14.6 )}   - 1                                            

= ( 1.018330 ) ^{( 14.6 )}   - 1

= 1.3037 – 1 = 0.3037   = 30.37 %                                                

Thus the annual effective cost of credit is = 30.37 %       

Note: ( 1.018330 ) ^{( 14.6 )}   is calculated using the excel formula =POWER(Number,Power)

=POWER(1.018330,14.6) = 1.3037