CHAPTER 6-9 - To find the interest rate at which the firm...

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To find the interest rate at which the firm will break even, we need to find the interest rate using the PV (or FV) of a lump sum. Using the PV equation for a lump sum, we get: $94,000 = $165,000 / ( 1 + r ) 4 r = ($165,000 / $94,000) 1/4 – 1 = .1510 or 15.10% 47. We want to find the value of the cash flows today, so we will find the PV of the annuity, and then bring the lump sum PV back to today. The annuity has 18 payments, so the PV of the annuity is: PVA = $4,000{[1 – (1/1.10) 18 ] / .10} = $32,805.65 Since this is an ordinary annuity equation, this is the PV one period before the first payment, so it is the PV at t = 7. To find the value today, we find the PV of this lump sum. The value today is: PV = $32,805.65 / 1.10 7 = $16,834.48 48. This question is asking for the present value of an annuity, but the interest rate changes during the life of the annuity. We need to find the present value of the cash flows for the last eight years first. The PV of these cash flows is: PVA 2 = $1,500 [{1 – 1 / [1 + (.07/12)] 96 } / (.07/12)] = $110,021.35 Note that this is the PV of this annuity exactly seven years from today. Now we can discount this lump sum to today.
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