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
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This note was uploaded on 07/15/2010 for the course FINANCE 318 taught by Professor Spurlin during the Spring '08 term at LA Tech.
 Spring '08
 spurlin
 Interest, Interest Rate

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