Question

Answer the following questions related to Dubois Inc.

(a) Dubois Inc. has \(600,000 to invest. The company is trying to decide between two alternative uses of the funds. One alternative provides \)80,000 at the end of each year for 12 years, and the other is to receive a single lump-sum payment of \(1,900,000 at the end of the 12 years. Which alternative should Dubois select? Assume the interest rate is constant over the entire investment.

(b) Dubois Inc. has completed the purchase of new Dell computers. The fair value of the equipment is \)824,150. The purchase agreement specifies an immediate down payment of \(200,000 and semiannual payments of \)76,952 beginning at the end of 6 months for 5 years. What is the interest rate, to the nearest percent, used in discounting this purchase transaction?

(c) Dubois Inc. loans money to John Kruk Corporation in the amount of \(800,000. Dubois accepts an 8% note due in 7 years with interest payable semiannually. After 2 years (and receipt of interest for 2 years), Dubois needs money and therefore sells the note to Chicago National Bank, which demands interest on the note of 10% compounded semiannually. What is the amount Dubois will receive on the sale of the note?

(d) Dubois Inc. wishes to accumulate \)1,300,000 by December 31, 2027, to retire bonds outstanding. The company deposits \(200,000 on December 31, 2017, which will earn interest at 10% compounded quarterly, to help in the retirement of this debt. In addition, the company wants to know how much should be deposited at the end of each quarter for 10 years to ensure that \)1,300,000 is available at the end of 2027. (The quarterly deposits will also earn at a rate of 10%, compounded quarterly.) (Round to even dollars.)

Short answer

The alternative two should be chosen in part A, the interest rate for part B is 4%, the amount receivable in part C is $765,214.4 and the annuity value of quarterly deposits is $11,320.

Step-by-step solution

Computation of part A

Amount to be invested	600,000
Annual receipts in alternative 1	80,000
The effective Interest rate in alternative 1	8% (as per the present value of ordinary annuity table)
Lump-sum receipts in alternative 2	1,900,000
The effective interest rate in alternative 2	10% (as per the future value table )
Alternative two should be chosen as it has a higher effective interest rate

Computation of part B

The fair value of equipment	824,150
Down payment	200,000
Present value of total semi-annual payments	624,150
Semi-annual payment	76,952
Interest rate	4% (as per the present value of ordinary annuity table)

Computation of part C

$\begin{array}{rcl}\mathrm{Amount}\mathrm{receivable}& =& \mathrm{PVAF}+\mathrm{PVIF}\\ & =& 800,000\times 4\%\times 7.7217+800,000\times 0.6139\\ & =& 247,094.4+491,120\\ & =& \$765,214.4\end{array}$

Computation of part D

Initial Amount Deposited	200,000
Table factor	2.68506 (2.5%, 40)
FV of Initial Amount deposited	537,012
Total amount required	1,300,000
Balance amount required	762988
Table factor	67.40255 (2.5%, 40)
Annuity value of quarterly deposits	11320