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Questionproject initially costs $100,000\$ 100,000 to get stairted and has a discount rate of 9%9 \%. It has a useful life of five years. You expect the project to have a NPV of $15,000\$ 15,000. nat would be the equal yearly cashflow generated by the project need to be to reach the target NPV
Multiple Choice \30,785.59$29,565.63$29,006.36$28,693.5730,785.59 \$29,565.63 \$29,006.36 \$28,693.57 \28,075.47 28,075.47

Studdy Solution

STEP 1

1. The initial cost of the project is 100,000.<br/>2.Thediscountrateis9100,000.<br />2. The discount rate is 9%.<br />3. The project has a useful life of five years.<br />4. The target Net Present Value (NPV) is 15,000.
5. We need to find the equal yearly cash flow that achieves this NPV.

STEP 2

1. Understand the concept of NPV and its formula.
2. Set up the NPV equation with the given values.
3. Solve for the yearly cash flow.

STEP 3

Understand the concept of NPV and its formula.
The Net Present Value (NPV) is calculated using the formula:
NPV=∑t=1nCt(1+r)t−C0 NPV = \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} - C_0
where: - Ct C_t is the cash flow in year t t , - r r is the discount rate, - n n is the number of years, - C0 C_0 is the initial investment.

STEP 4

Set up the NPV equation with the given values.
Given: - C0=100,000 C_0 = 100,000 - r=0.09 r = 0.09 - n=5 n = 5 - NPV=15,000 NPV = 15,000
We need to find C C such that:
15,000=∑t=15C(1+0.09)t−100,000 15,000 = \sum_{t=1}^{5} \frac{C}{(1 + 0.09)^t} - 100,000

STEP 5

Solve for the yearly cash flow.
Rearrange the equation to solve for C C :
15,000+100,000=∑t=15C(1.09)t 15,000 + 100,000 = \sum_{t=1}^{5} \frac{C}{(1.09)^t}
115,000=C(11.09+11.092+11.093+11.094+11.095) 115,000 = C \left( \frac{1}{1.09} + \frac{1}{1.09^2} + \frac{1}{1.09^3} + \frac{1}{1.09^4} + \frac{1}{1.09^5} \right)
Calculate the sum of the present value factors:
∑t=151(1.09)t=0.9174+0.8417+0.7722+0.7084+0.6499=3.3886 \sum_{t=1}^{5} \frac{1}{(1.09)^t} = 0.9174 + 0.8417 + 0.7722 + 0.7084 + 0.6499 = 3.3886
Now solve for C C :
115,000=C×3.3886 115,000 = C \times 3.3886
C=115,0003.3886 C = \frac{115,000}{3.3886}
C≈33,935.59 C \approx 33,935.59
However, this does not match any of the provided options. Let's re-evaluate the calculation:
C=115,0003.88965 C = \frac{115,000}{3.88965}
C≈29,565.63 C \approx 29,565.63
The equal yearly cash flow needed is:
29,565.63 \boxed{29,565.63}

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