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?

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.)

Explanation / Answer

a)

First Calculate what is the total amount taken on loan, i.e. equipment price - down payment made

Loan Amount = 824,400 - 227,800 = 596,600

Now calculate rate using the excel formula as follows

=RATE(10,69940,-596600,0,0)

Here 10 is the total number of payments made, which is 5 * 2 = 10

69940 is the semiannual payments made

596600 is principle amount, which should have opposite sign of payments made

We get rate as 3.00%, which is a semi annual rate. The amount is discounted at a 6% annual rate of interest

b) Since the note is been sold after 2 years, the scenario would be as follows

Coupon rate = 8%

Maturity remaining is 5 years

Expected Yield by Chicago national bank is 10%

Calculate price of the bond using the excel formula

=PRICE(A1,A2,8%,10%,100,2) = 92.28

This is for a $100 face value note, so the amount Dubois receives = 838,800 * 92.28 = 774,030.09

c)

First calculate 10% rate compounded quarterly to a annual interest rate as follows

(1 + 10% / 4)4 -1 = 10.38%

Now calculate the future value of 227,800 invested today for 10 years at 10.38% rate

= FV(10.38%,10,0,-227800,0) = $611,657.54

Since the total amount accumulated at the end of 10 years should be $1,350,000, calculate how much has to be accumulated from quarterly payments

= 1,350,000 - 611,657.54 = $738,342.46

Installments can be calculated using following formula

=PMT(2.5%,40,0,-738342.46,0) = $10,957.22

This has to be invested every quarter to get the total amount at the end of the maturity

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