Question

CHAPTER 6 INSTRUCTIONS: Answer each letter in the following problems. Show work when necessary. Problem 1 a) How much must be invested now to receive $40,000 for eight years if the first $40,000 is received today and the rate is 10%? b) Find the present value of an investment in equipment if it is expected to provide annual savings of $40,000 for 12 years and to have a resale value of $75,000 at the end of that period. Assume an interest rate of 6% and that savings are realized at year end. c) On January 1, 2020 Trager Co. issued ten-year bonds with a face value of $700,000 and a stated interest rate of 10% payable semiannually on July 1 and January 1. The bonds were sold to yield 12%. Calculate the issue price of the bonds.

Answer 1

(a) $ Solution a) Annual receipts Time Rate of Interest 40,000 8 years 10% PV of Annuity due ( 10%, 8) (b) 5.8684 Amount to be Invested (a xb) $ 2,34,736 (a) $ Solution b) Annual Savings Time Rate of Interest Resale Value 40,000 8 years 10% 75,000 $ (b) c PV factor ( 6%, 12) PV of annuity factor ( 6%, 12) (d) 0.49697 8.38384 PV of Annual savings add: PV of Resale Value Present Value of Investment (a xd) (bx c) $3,35,353.60 $ 37,272.75 $3,72,626.35 $ Solution c) Face Value of Bonds PV factor (12%/2, 10 years x2) Present Value of Face Value 7,00,000 0.3118 2,18,260 (a) $ $ Interest @ 5% semi annual PV annuity factor (6%, 10x2) Present Value of Interest 35,000 11.46992 4,01,447 (b) $ Issue Price of Bond (a+b) $ 6,19,707

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