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# Pime Value Concepts Applied to Solve Business Problems

Answer the following questions related to Derek Lee Inc. :

(a) Derek Lee Inc. has \$572,000 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 Lee select? Assume the interest rate is constant over the entire investment.

(b) Derek Lee Inc. has completed the purchase of new Dell computers. The fair market 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) Derek Lee Inc. loans money to John Kruk Corporation in the amount of 600,000. Lee accepts an 8% note due in 7 years with interest payable semiannually. After 2 years (and receipt of interest for 2 years), Lee 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 Lee will receive on the sale of the note?

(d) Derek Lee Inc. wishes to accumulate \$1,300,000 by December 31, 2017, to retire bonds outstanding. The company deposits \$300,000 on December 31, 2007, 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 2017. (The quarterly deposits will also earn at a rate of 10%, compounded quarterly.) (Round to even dollars.)

#### Solution Preview

(a) Derek Lee Inc. has \$572,000 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 Lee select? Assume the interest rate is constant over the entire investment.

Here we have two options, the present value of which is the same at 572,000. We should calculate the implicit interest rate in the two options to decide the better one. In option 1 we get 80,000 per year for 12 years. This is an annuity and we can calculate the PV using the PVIFA table. We get

572,000=80,000 X PVIFA (12,r%)
PVIFA (12, r%) = 572,000/80,000=7.15.

Looking in the PVIFA table under 12 years, we get a factor of 7.161 under 9%. The interest rate in this option is approximately 9%.

In option 2 we have a lump sum of 1,900,000 at the end of 12 years. The PV factors for lump sum are in the PVIF table. ...

#### Solution Summary

The solution answers various questions relating to concepts of time value applied to Derek Lee Inc. It deals with calculating annuities and sale prices as well.

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