Question

Cheyenne Inc. has $532,750 to invest. The company is trying to decide between two alternative uses of the funds. One alternative provides $70,693 at the end of each year for 12 years, and the other is to receive a single lump-sum payment of $1,672,000 at the end of the 12 years. Which alternative should Cheyenne select? Assume the interest rate is constant over the entire investment. e Textbook and Media Cheyenne Inc. has completed the purchase of new Dell computers. The fair value of the equipment is $725,252. The purchase agreement specifies an immediate down payment of $176,000 and semiannual payments of $67.718 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? Interest rate % semiannually e Textbook and Media

Answer 1

Answer-1:

Year Alternative-1 Alternative-2 DF @10% CF DCF CFDCF 1 0.909 $ 70,693 $ 64,260 0.826 $ 70,693 $ 58,392 0.751 $ 70,693 $ 53,090 0.683 $ 70,693 $ 48,283 0.621 $ 70,693 $ 43,900 6 0.564 $ 70,693 $ 39,871 0.513 $ 70,693 $ 36,266 0.467 $ 70,693 $ 33,014 0.424 $ 70,693 $ 29,974 10 0.386 $ 70,693 $ 27,287 0.35 $ 70,693 $ 24,743 12 0.319 $ 70,693 $ 22,551 $ 1,672,000 $ 533,368 Total DCF $ 481,631 $ 533,368 Less: Investment $ 532,750 $ 532,750 NPV S (51,119) S 618 11

As alternative-2 gives positive NPV, Cheyenne should select alternative-2 i.e getting lump-sum at the end of year 12.

Answer-2:

Fair value of equipment   $725,252

Less: Down payment       $176,000

Loan Amount                   $549,252

Loan term = 5 years

Semi-annual payment of $67,718 will come when annual interest rate is taken as 8% calculated as below:-

B 8% А 1 Annual interest rate 2 Loan term in years 3 Loan amount 549252 5 Semi annual payment ($67,718) 6 Semi annual payment formula =PMT(B1/2,B2*2,B3)

Note:- In excel sheet, in cell B1 you have to input the interest rate to get the desired semi-annual payment of $67,718

Hence semi-annual rate is 4%

Answer-3:

Calculation of Maturity value of the notes:

$ 704,000 8% А 1 Principal 2 Interest rate (annual) 3 Interest rate (semi-annual) 4 Time (annual) 5 Time (semi annual) 7 Maturity Value 8 Maturity Value formula $ 1,219,100 =B22*(1+B24)^B26

Cheyenne holded the notes for 2 years and now the due date is 5 years away. Hence the bank's discount is calculated as below:-

А 1 Maturity value 2 discount rate (annual) 3 Discount rate (semi-annual) 4. Time (annual) 5 Time (semi annual) $ 1,219,100 8% 4% 7 Discount = (B31*(1+B33)^B35)-1219100 $ 585,466

The bank will subtracts the discount from the note's maturity value and pays Cheyenne $633,634 for the note calculated as below:-

Maturity value Less: Discount Discounted value of note $ $ S 1,219,100 585,466 633,634

Hence amount received on sale of note is $633,634.