a) Dubois Inc. has completed the purchase of new Dell computers. The fair value

Question

a) Dubois Inc. has completed the purchase of new Dell computers. The fair value of the equipment is $824,400. The purchase agreement specifies an immediate down payment of $227,800 and semiannual payments of $69,940 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?

b) Dubois Inc. loans money to John Kruk Corporation in the amount of $838,800. 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? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

c) Dubois Inc. wishes to accumulate $1,350,000 by December 31, 2024, to retire bonds outstanding. The company deposits $227,800 on December 31, 2014, 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 $1,350,000 is available at the end of 2024. (The quarterly deposits will also earn at a rate of 10%, compounded quarterly.) (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Explanation / Answer

a)

Fair Value = $824,400

Down Payment = $227800

Remaining Amount = $596600

Remaining Amount is Payable in 10 Equal Installments of $69,940 in 5 years

Formula to Calculate Interest Rate:

PV = PMT / i [ 1- 1/ (1 + i) n ] (1 + iT)

PV = Present Value, i = X, n = Number of Payment Period, T = Time in Years

PV = 596600 , n = 5x2 = 10, T = 5

596600 = 69940/ i [ 1- 1 / (1 + i) 10 ] (1 + ix5)

i[1-1/(1+i)^10](1+i*5)=596600/69940

i = 7.26% or 7%

So, the Interest Rate used in Discounting is 7%

b.

Semi annual Interest Amount (PMT) = 8%*838800*1/2 = $ 33552

Time left to maturity after 2 year = 5 year

Period left to maturity (nper) =5*2 = 10semi annual

interest rate demanded by bank =10% compounded semiannually

rate = 5% semiannually

FV = $ 838800

Amount Dubois will receive on the sale of the note = pv(rate,nper,pmt,fv)

Amount Dubois will receive on the sale of the note = pv(5%,10,33552,838800)

Amount Dubois will receive on the sale of the note = $ 774,030.09

c.Future value of the bond amout that need to be paid=1350000

time remaining (2014 to 24)=10 years

Quaters 10*4 =40

Interest rate on Deposit=10%

Compounded Quarterly (10%/4) =2.05%

Deposit made =227800

Future Value of investment made =227800*(1+0.025)^40=611657.54

Hence remainingamount need in future =1350000-611657.54=738342.46

Quarterly deposit to have total in 2024=PMT(10%,40,-738342.46)=1668.22

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.