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Caiden
sample-assignment_1.docxSOLUTION
7.1. Blake Company has 3400 hourly workers. They work 40 hours a week, at the rate of $7.00 an hour and they are paid every Friday. The company has decided to pay them twice a month. The cost of printing and processing each check is $1.25. The cost of capital to the company is 14%. Find the present value of the annual savings created by this decision. Find the value added to the company by this procedure.
$178,272, $185,640
Solution:
The no. of hourly workers = 3400
The no. of working hours in a week = 40 hours
Rate of payment to the workers = $7 per hour
Total pay of a worker per week = $7 * 40 = $280
Number of weekly payments = 52
Total weekly payroll including the cost of printing and processing each check
= 3400 * (280 + 1.25)
= $956,250
The cost of capital = 14%
The weekly cost of capital = 14% / 52
Present Value of weekly payments = Σ $ 956,250
(1+0.14/52) i
Where i = 1 to 52
Present Value of weekly payments = $956,250 * [1 - (1+0.14/52)-52 / 0.14 /52]
= $46,343,061.43
Annual payroll without including printing and processing cost = 3400 * 52 * 40 * 7
= $49,504,000
Semi-monthly payroll including the cost of printing and processing each check
= $(49,504,000/24) + (3400*1.25)
= $2,066,916.667
Semi-monthly cost of capital = 14% / 24
Present Value of semi-monthly payments = Σ $2066916.667
(1+0.14/24) i
Where i = 1 to 24
Present Value of semi-monthly payments = $2066916.667 * [1- (1+0.14/24)-24 / 0.14 /24]
= $46,164,788.99
Present value of annual savings = Present Value of weekly payments - Present Value of semi-monthly payments
= $ 178,272
The value that is added to the company by this can be calculated as follows:
Amount saved on printing and processing checks = (52-24) * 1.25 * 3400 = $119,000
Amount that the firm is able to use for one week = 3400 * 40 * 7 = $952,000
Interest earned on 952,000 for 26 weeks = $952,000 * (14%/52) * 26 = $66,640
Total value added = $119,000 + $66,640
= $ 185,640
The present value of annual savings is $178,272 and the value added as the result of this procedure is $185,640.
141
7.2. James Corporation has the following terms with its suppliers: 2/10, net 60. It normally takes the discount and pays within ten days. However, due to cash shortage, it intends to delay the payment. Find the cost of this short-term financing for James.
15.89%
Solution
The cost of short-term financing is r.
Suppose the amount of sale is $100. The customer can either pay $98 after 10 days, or $100 after 60 days. To find the cost of this type of financing, the borrower is paying $2 for the use of $98 for a period of 50 days.
At r,
Present value of payment with 2% discount made after 10 days = Present value of full payment made after 60 days
98/ (1+r) 10/365 = 100 / (1+r) 60/365
0.98 = (1+r) 10/365/ (1+r) 60/365
1+r = (0.98)-365/50
1+ r = 1.1589
r = 0.1589
= 15.89%
The short term financing cost is 15.89%
7.3. Chatterton Company has obtained a $75,000 short-term loan from the bank with the understanding that Chatterton will repay the loan in two equal monthly installments of $38,250 each. The first installment is due after 30 days, and the second after 60 days. Find the cost of this loan for Chatterton.
17.44%
Solution
Let the cost of the loan be r
Amount of loan = $ 75,000
Amount of each installment =$ 38,250
The present value of the loan is equal to the present value of the two installments
$ 75,000 = $ 38,250 + $ 38,250
(1+r) 30/365 (1+r) 60/365
Let (1+r) 30/365 = x
75,000 = ($ 38250/x) + ($ 38250/x2)
75000 x2 = 38250 x + 38250
75000 x2- 38250 x – 38250 = 0
Dividing throughout the equation by 250 we get
300 -153 x – 153 = 0
x = - (-153) ± √ ((153)2 – 4 * 300 * (-153))
2* 300
x = (153 ± 454.98) / 600
Taking the positive root we get
x = (153 + 454.98) / 600
x = 1.0133
(1+r) 30/365 = x
1+r = (1.0133)365/30
1+r = 1.1744
r = 0.1744 or 17.44%
The cost of the loan is 17.44%
7.4. (A) De la Mare Company has $140,000 in accounts receivable that will be collected within 75 days. Since de la Mare needs cash immediately, it has decided to factor them and has received $130,000. Find the cost of this loan for de la Mare.
43.43%
Solution
Let the cost of the loan be r
At r, the present value of the loan must be equal to the present value of the accounts receivable. Therefore
130,000 = 140,000
(1+r) 75/365
(1+r) 75/365 = 14/13
1+r = (14/13)365/75
1+r = 1.4343
r = 0.4343 or 43.43 %
The cost of loan for de la Mare is 43.43%
(B) Donne Factoring Company, who took the receivables, actually was able to collect only $135,000 after 90 days. Find the rate of return on this investment for Donne.
16.54%
Solution
Let the rate of return on investment be R
At R, present value of the amount received must be equal to the present value of the amount invested
130,000 = 135,000
(1+R) 90/365
(1+R) 90/365 = 135/130
1+R = (135/130)365/90
1+R = 1.1654
r = 0.1654 or 16.54 %
The rate of return on investment for Donne is 16.54%
