[Anonymous]

This is from the NINJA questions in BEC

Given a 10% discount rate with cash inflows of $3,000 at the end of each year for five years and an initial investment of $11,000, what is the net present value?

A.$(9,500)

B.$370

C.$4,000

D.$11,370

I choose A. But the solution says B. I thought it wanted NPV?

Solution:

The net present value is the excess of the discounted present value of future cash returns less the investment cost.

The formula to calculate present value for any single future payment is PV = Payment ÷ (1 + r)n, where r is the interest rate and n is the number of periods.

The present value of the payment in the first year is $3,000 ÷ 1.1, or $2,727.
The present value of the payment in the second year is $3,000 ÷ (1.1 × 1.1), or $2,479.
The present value of the payment in the third year is $3,000 ÷ (1.1 × 1.1 × 1.1), or $2,254.
The present value of the payment in the fourth year is $3,000 ÷ (1.1 × 1.1 × 1.1 × 1.1), or $2,049.
The present value of the payment in the fifth year is $3,000 ÷ (1.1 × 1.1 × 1.1 × 1.1 × 1.1), or $1,863.
The sum of the present value of the five future payments is $11,372. The cost of the investment is $11,000, so the net present value is $11,372 – $11,000, or $372, rounded to $370.

[Anonymous]

Bump

[Biff-1955-Tannen]

Not really sure how else to explain this, the explanation provided tells you step by step how to calculate the answer. All the net present value is, is the excess of the PV of the annuity less the initial investment.

So if you calculate the present value of the annuity with the formula “payment X [[1-(1 + r)^-n] / r]

$3,000 x [[1-(1.1)^-5] / .1
$3,000 x [1-.620921] / .1
$3,000 x .37907 / .1
$3,000 x 3.79079
$11,372 = PV of annuity
Then you subtract the initial investment ($11,000) from this.
$11,372 – $11,000 = $372.

AUD - 93
BEC - 83
FAR - 83
REG - 84

Nobody calls me chicken

AUD 93 Jan 16
BEC 83 Feb 16
FAR 83 Apr 16
REG 84 May 16

99% Ninja MCQ only

[CPA8675309]

For NPV calculations, the first step is to calculate the present value of the cash inflows. In this case, a 5 year ordinary annuity of $3000 discounted at 10%. Step 2 is to subtract the initial investment from the present value of cash inflows. This question was a little more difficult in that usually the CPA exam gives you the present value factor (usually a few to choose from). You should know the time value of money formulas though just in case they're not given like in your example.

How did you arrive at your answer? Knowing this might help to steer you in the right direction.

AUD - 77
BEC - 85
FAR - 84
REG - 85

I'm done!!

[Author]

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