Question

(Time Value Concepts Applied to Solve Business Problems)
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 iPad tablets. 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, 2029, to retire
bonds outstanding. The company deposits $200,000 on December 31, 2019,
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 2029. (The quarterly deposits will also earn at a rate of
10%, compounded quarterly.) (Round to even dollars.)

Answer 1

Answer:

a.)

Present value Approach

Present value = Future Value (PVF n, i)

$600,000 = $1,900,000 (PVF, 12, i)

PVF, 12, i= $600,000 / $1,900,000

PVF, 12, i= 0.316

0.316 is the present value of $1 discounted at between 10% and 11% for 12 years

.

Future value Approach

Future value = Present Value (FVF n, i)

$1,900,000 = $600,000 (PVF, 12, i)

PVF, 12, i= $1,900,000 / $600,000

PVF, 12, i= 3.167

3.167 is the future value of $1 invested at between 10% and 11% for 12 years

.

Conclusion

Dubois Inc. should choose Alternative 2 as it provides a higher rate of return.

.

b.)

Formula = PV–OA = R (PVF–OAn, i)

$824,150 -$200,000 = $76,952 ((PVF–OA 10,i)

$624,150 = = $76,952 ((PVF–OA 10,i)

PV–OA10, i = $624,150 / $76,952

PV–OA10, I = 8.1109 (approx. 8%)

.

So the i = .04 or 4% for six month

8.11090 is the present value of a 10-period annuity of $1 discounted at 4%. The interest rate is 4% semiannually, or 8% annually

.

c.)

1. Formula: PV-OA=R (PVF-OA, n ,i)

PV-OA = $32,000 (PVF-OA 10, 5%)

                        = $32,000 X (7.72173)

                        = $247,095

Note: Using the PVOA table, the factor of 10 payments at 5% is 7.72173.

2. Formula: PV=FV (PVF, n, i)

                   PV= $800,000 (PVF, 10, 5%)

                        =$800,000 X (0.61391)

                        = $491,128

Note: Using the PV of $1 table, the factor of 10 payments (5 years × 2 periods per year) at 5% (10% / 2 periods per year) is 0.61391

Combined PV = $491,128 + $247,095 = $738,223 will be received by Dubois.

.

d.)

Formula (future value of $200,000 deposit): FV= PV (FVF n, i)

                                                                        =$200,000*(1+ 10%/4) ^ (4*10)

                                                                        = $537,013

The remaining amount = $762,987

(1,300,000-537,013)

The FV of annuity = 762,987 / 1.025^40-1/ 0.025

                             = 762,987/ 67.4026

                             = $11,320

The quarter end deposit should be = $11,320