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4-6A. (Cash budget) The Sharpe Corporation’s projected sales for the first eight months of 2004
are as follows:

January \$ 90,000 May \$300,000
February 120,000 June 270,000
March 135,000 July 225,000
April 240,000 August 150,000

Of Sharpe’s sales, 10 percent is for cash, another 60 percent is collected in the month following
sale, and 30 percent is collected in the second month following sale. November and December
sales for 2003 were \$220,000 and \$175,000, respectively.
Sharpe purchases its raw materials two months in advance of its sales equal to 60 percent of their
final sales price. The supplier is paid one month after it makes delivery. For example, purchases
for April sales are made in February and payment is made in March.
In addition, Sharpe pays \$10,000 per month for rent and \$20,000 each month for other expenditures.
Tax prepayments of \$22,500 are made each quarter, beginning in March.
The company’s cash balance at December 31, 2003, was \$22,000; a minimum balance of \$15,000
must be maintained at all times. Assume that any short-term financing needed to maintain the cash
balance is paid off in the month following the month of financing if sufficient funds are available.
Interest on short-term loans (12 percent) is paid monthly. Borrowing to meet estimated monthly
cash needs takes place at the beginning of the month. Thus, if in the month of April the firm expects
to have a need for an additional \$60,500, these funds would be borrowed at the beginning of April
with interest of \$605 (.12 ??1/12 ??\$60,500) owed for April and paid at the beginning of May.

a. Prepare a cash budget for Sharpe covering the first seven months of 2004.
b. Sharpe has \$200,000 in notes payable due in July that must be repaid or renegotiated for
an extension. Will the firm have ample cash to repay the notes?

5-1A. (Compound interest) To what amount will the following investments accumulate?
a. \$5,000 invested for 10 years at 10 percent compounded annually
b. \$8,000 invested for 7 years at 8 percent compounded annually
c. \$775 invested for 12 years at 12 percent compounded annually
d. \$21,000 invested for 5 years at 5 percent compounded annually

5-2A. (Compound value solving for n) How many years will the following take?
a. \$500 to grow to \$1,039.50 if invested at 5 percent compounded annually
b. \$35 to grow to \$53.87 if invested at 9 percent compounded annually
c. \$100 to grow to \$298.60 if invested at 20 percent compounded annually
d. \$53 to grow to \$78.76 if invested at 2 percent compounded annually

5-3A. (Compound value solving for i) At what annual rate would the following have to be invested?
a. \$500 to grow to \$1,948.00 in 12 years
b. \$300 to grow to \$422.10 in 7 years
c. \$50 to grow to \$280.20 in 20 years
d. \$200 to grow to \$497.60 in 5 years

5-4A. (Present value) What is the present value of the following future amounts?
a. \$800 to be received 10 years from now discounted back to the present at 10 percent
b. \$300 to be received 5 years from now discounted back to the present at 5 percent
c. \$1,000 to be received 8 years from now discounted back to the present at 3 percent
d. \$1,000 to be received 8 years from now discounted back to the present at 20 percent

5-5A. (Compound annuity) What is the accumulated sum of each of the following streams of
payments?
a. \$500 a year for 10 years compounded annually at 5 percent
b. \$100 a year for 5 years compounded annually at 10 percent
c. \$35 a year for 7 years compounded annually at 7 percent
d. \$25 a year for 3 years compounded annually at 2 percent

5-6A. (Present value of an annuity) What is the present value of the following annuities?
a. \$2,500 a year for 10 years discounted back to the present at 7 percent
b. \$70 a year for 3 years discounted back to the present at 3 percent
c. \$280 a year for 7 years discounted back to the present at 6 percent
d. \$500 a year for 10 years discounted back to the present at 10 percent

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Customer: replied 8 years ago.
Thank you. Would you mind clarifying the work for solution 5-1 to 5-5? I'm trying to understand which answers go to what? Sorry a bit confused.
Customer: replied 8 years ago.
Sorry nevermind, I think I may have figured it out. Thank you again.
Explanation:
Ans 5-1
Future Value FV = PV(1+r)^n
Here PV, r and n are given. We have calculated FV in last column. 4 rows correspond to 4 questions (a,b,c,d) in this qs.

Ans 5-2:
This qs requires calculation of n. We have used same formula as used in qs 5-1. Here we have calculated FV for n = 1,2,3 .... and see for what n we get required FV.
For four qs of this qs we have separate calculation. Answers are
a) 15 years
b) 5 yrs
c) 6 yrs
d) 20 yrs

Ans 5-3:
Again we have used same formula. Here I have written i instead of r as in question you have mentioned calculation of i. Both represent same thing- interest rate.
Formula is FV = PV(1+i) ^n
=> i = (FV/PV)^(1/n) - 1

Ans 5-4:
using same formula we have to calculate PV.
Formula is FV = PV(1+i) ^n
=> PV = FV/ (1+i)^n

Ans 5-5:
This is annuity problem.
Formula is:
Accumulated FV = (R(1+i)^n -1)/i

Ans 5-6:
here we have one additional job. We have to find the PV of accumulated FV.
So first we calculate FV . (second last column).
Accumulated FV = (R(1+i)^n -1)/i

then we find PV of that FV using formula:
PV = FV/ (1+i)^n