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CHAPTER 18 B - 1
14. The interest rate for the term of the discount is:
Interest rate = .01/.99
Interest rate = .0101, or 1.01%
And the interest is for:
25 – 10 = 15 days
So, using the EAR equation, the effective annual interest rate is:
a. The periodic interest rate is:
Interest rate = .03/.97
Interest rate = .0309, or 3.09%
And the EAR is:
b. The EAR is:
c. The EAR is:
15. The total sales of the firm are equal to the total credit sales since all sales are on credit, so:
Total credit sales = 3,500($395)
Total credit sales = $1,382,500
The average collection period is the percentage of accounts taking the discount times the discount
period, plus the percentage of accounts not taking the discount times the days’ until full payment is
required, so:
CHAPTER 18 B - 2
And the average receivables are the credit sales divided by the receivables turnover so:
16. The receivables turnover is:
Receivables turnover = 365/Average collection period
Receivables turnover = 365/36
Receivables turnover = 10.1389 times
And the annual credit sales are:
Intermediate
17. a. If you borrow $55,000,000 for one month, you will pay interest of:
Interest = $55,000,000(.0068)
Interest = $374,000
However, with the compensating balance, you will only get the use of:
b. To end up with $20,000,000, you must borrow:
Amount to borrow = $20,000,000/(1 – .04)
Amount to borrow = $20,833,333.33
The total interest you will pay on the loan is:
18. a. The EAR of your investment account is:
b. To calculate the EAR of the loan, we can divide the interest on the loan by the amount of the
loan. The interest on the loan includes the opportunity cost of the compensating balance. The
opportunity cost is the amount of the compensating balance times the potential interest rate you
could have earned. The compensating balance is only on the unused portion of the credit line, so:
Opportunity cost = .05($60,000,000 – 45,000,000)(1.0074)4
And the interest you will pay to the bank on the loan is:
c. The compensating balance is only applied to the unused portion of the credit line, so the EAR of
a loan on the full credit line is:
EAR = 1.01634 – 1
19. a. A 45-day collection period means sales collections each quarter are:
Collections = 1/2 current sales + 1/2 old sales
A 36-day payables period means payables each quarter are:
Payables = 3/5 current orders + 2/5 old orders
So, the cash inflows each quarter are:
Q1 = $63 + 1/2($160) – 2/5(.45)($160) – 3/5(.45)($145) – .30($160) – $15
CHAPTER 18 B - 4
The company’s cash budget will be:
WILDCAT, INC.
Cash Budget
(in millions)
Q1
Q2
Q3
Q4
Beginning cash balance
$36.00
$48.05
$19.65
$21.55
Net cash inflow
12.05
–28.40
1.90
37.15
Ending cash balance
$48.05
$19.65
$21.55
$58.70
Minimum cash balance
–20.00
–20.00
–20.00
–20.00
Cumulative surplus (deficit)
$28.05
–$0.35
$1.55
$38.70
With a $20,000,000 minimum cash balance, the short-term financial plan will be:
WILDCAT, INC.
Short-Term Financial Plan
(in millions)
b.
Q1
Q2
Q3
Q4
Minimum cash balance
$20.00
$20.00
$20.00
$20.00
Net cash inflow
12.05
–28.40
1.90
37.15
New short-term investments
–12.37
0
–1.91
–37.20
Income on short-term investments
.32
.57
.01
.05
Short-term investments sold
0
27.83
0
0
New short-term borrowing
0
0
0
0
Interest on short-term borrowing
0
0
0
0
Short-term borrowing repaid
0
0
0
0
Ending cash balance
$20.00
$20.00
$20.00
$20.00
Minimum cash balance
–20.00
–20.00
–20.00
–20.00
Cumulative surplus (deficit)
$0
$0
$0
$0
Beginning short-term investments
$16.00
$28.37
$.54
$2.45
Ending short-term investments
28.37
.54
2.45
39.65
Beginning short-term debt
0
0
0
0
Ending short-term debt
0
0
0
0
CHAPTER 18 B - 5
WILDCAT, INC.
Short-Term Financial Plan
(in millions)
Q1
Q2
Q3
Q4
Minimum cash balance
$30.00
$30.00
$30.00
$30.00
Net cash inflow
12.05
–28.40
1.90
37.15
New short-term investments
–12.17
0
0
–28.64
Income on short-term investments
.12
.36
0
0
Short-term investments sold
0
18.17
0
0
New short-term borrowing
0
9.87
0
0
Interest on short-term borrowing
0
0
–.30
–.25
Short-term borrowing repaid
0
0
–1.60
–8.26
Ending cash balance
$30.00
$30.00
$30.00
$30.00
Minimum cash balance
–30.00
–30.00
–30.00
–30.00
Cumulative surplus (deficit)
$0
$0
$0
$0
Beginning short-term investments
$6.00
$18.17
$0
$0
Ending short-term investments
18.17
0
0
28.64
Beginning short-term debt
0
0
9.87
8.26
Ending short-term debt
0
9.87
8.26
0
Below you will find the interest paid (or received) for each quarter:
Q1: excess funds of $6 invested for 1 quarter earns .02($6) = $.12 income
b. And with a minimum cash balance of $10,000,000, the short-term financial plan will be:
WILDCAT, INC.
Short-Term Financial Plan
(in millions)
Q1
Q2
Q3
Q4
Minimum cash balance
$10.00
$10.00
$10.00
$10.00
Net cash inflow
12.05
–28.40
1.90
37.15
New short-term investments
–12.57
0
–2.12
–37.41
Income on short-term investments
.52
.77
.22
.26
Short-term investments sold
0
27.63
0
0
New short-term borrowing
0
0
0
0
Interest on short-term borrowing
0
0
0
0
Short-term borrowing repaid
0
0
0
0
CHAPTER 18 B - 6
Ending cash balance
$10.00
$10.00
$10.00
$10.00
Minimum cash balance
–10.00
–10.00
–10.00
–10.00
Cumulative surplus (deficit)
$0
$0
$0
$0
Beginning short-term investments
$26.00
$38.57
$10.94
$13.06
Ending short-term investments
38.57
10.94
13.06
50.47
Beginning short-term debt
0
0
0
0
Ending short-term debt
0
0
0
0
Below you will find the interest paid (or received) for each quarter:
Since cash has an opportunity cost, the firm can boost its profit if it keeps its minimum cash
balance low and invests the cash instead. However, the tradeoff is that in the event of unforeseen
circumstances, the firm may not be able to meet its short-run obligations if enough cash is not
available.
Challenge
21. a. For every dollar borrowed, you pay interest of:
Interest = $1(.0185) = $.0185
You also must maintain a compensating balance of 5 percent of the funds borrowed, so for each
dollar borrowed, you will only receive:
At the end of the year the compensating will be returned, so your net cash flow at the end of the
year will be:
CHAPTER 18 B - 7
End of year cash flow = $1.07608 – .05
End of year cash flow = $1.02608
The present value of the end of year cash flow is the amount you receive at the beginning of the
year, so the EAR is:
FV = PV(1 + R)
$1.02608 = $.95(1 + R)
effective annual interest rate, so:
Interest = $150,000,000[(1.0185)4 – 1]
Interest = $11,411,841.55
credit line also has a fee of .165 percent, so you will only get to use:
Amount received = .95($150,000,000) – .00165($400,000,000)
Amount received = $141,840,000
EAR = .08046, or 8.046%
Interest = $20,000,000(.087) = $1,740,000
Additionally, the compensating balance on the loan is:
Compensating balance = $20,000,000(.04) = $800,000
Since this is a discount loan, you will receive the loan amount minus the interest payment. You will
also not get to use the compensating balance. So, the amount of money you will actually receive on a
$20 million loan is:
Cash received = $20,000,000 – 1,740,000 – 800,000 = $17,460,000
The EAR is the interest amount divided by the loan amount, so:
CHAPTER 18 B - 8
year is $17,460,000. At the end of the year, your cash flow is the loan repayment, but you will also
receive your compensating balance back, so:
End of year cash flow = $20,000,000 – 800,000
$19,200,000 = $17,460,000(1 + R)
R = $19,200,000/$17,460,000 – 1
