Future Value and Present Value

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.To find the PVA, we use the equation:

PVA = C({1 – [1/(1 + r)]t } / r )
PVA = $60,000{[1 – (1/1.0825)9 ] / .0825}
PVA = $370,947.84

The present value of the revenue is greater than the cost, so your company can afford the equipment.

7.Here we need to find the FVA. The equation to find the FVA is:

FVA = C{[(1 + r)t – 1] / r}

FVA for 20 years = $3,000[(1.08520 – 1) / .085]
FVA for 20 years = $145,131.04

FVA for 40 years = $3,000[(1.08540 – 1) / .085]
FVA for 40 years = $887,047.61

Notice that doubling the number of periods does not double the FVA.

8.Here we have the FVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the FVA equation:

FVA = C{[(1 + r)t – 1] / r}
$40,000 = $C[(1.05257 – 1) / .0525]

We can now solve this equation for the annuity payment. Doing so, we get:

C = $40,000 / 8.204106
C = $4,875.55

9.Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the PVA equation:

PVA = C({1 – [1/(1 + r)]t } / r)
$30,000 = C{[1 – (1/1.09)7 ] / .09}

We can now solve this equation for the annuity payment. Doing so, we get:

C = $30,000 / 5.03295
C = $5,960.72

10.This cash flow is a perpetuity. To find the PV of a perpetuity, we use the equation:

PV = C / r
PV = $20,000 / .08 = $250,000.00

11.Here we need to find the interest rate that equates the perpetuity cash flows with the PV of the cash flows. Using the PV of a perpetuity equation:

PV = C / r
$270,000 = $20,000 / r

We can now solve for the interest rate as follows:

r = $20,000 / $270,000
r = .0741 or 7.41%

12.For discrete compounding, to find the EAR, we use the equation:

EAR = [1 + (APR / m)]m – 1

EAR = [1 + (.08 / 4)]4 – 1= 8.24%

EAR = [1 + (.10 / 12)]12 – 1= 10.47%

EAR = [1 + (.14 / 365)]365 – 1 = 15.02%

EAR = [1 + (.18 / 2)]2 – 1 = 18.81%

13.Here...
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