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SOAL

A company is considering entering into a joint venture that will require an investment of $10 million. The project is expected to generate cash flows of $4 million, $3 million, and $4 million in each of the next three years, respectively. Assuming a discount rate of 10 percent, what is the project’s NPV?

(a) $879,000

(b) -$309,000

(c) $243,000

(d) -$1,523,000

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To calculate the Net Present Value (NPV) of the project, we use the formula:

$$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - C_0$$

Where:

• $CF_t$ = Cash flow at time $t$

• $r$ = Discount rate (10% or 0.10)

• $C_0$ = Initial investment ($10 million)

Given cash flows:

• Year 1: $4 million

• Year 2: $3 million

• Year 3: $4 million

• Discount rate: 10%

• Initial investment: $10 million

Now compute the present value (PV) of each cash flow:

$$PV_1 = \frac{4}{(1.10)^1} = 3.636 \text{ million}$$ $$PV_2 = \frac{3}{(1.10)^2} = 2.479 \text{ million}$$ $$PV_3 = \frac{4}{(1.10)^3} = 3.005 \text{ million}$$

Sum of PVs:

$$Total\ PV = 3.636 + 2.479 + 3.005 = 9.12 \text{ million}$$

Then,

$$NPV = 9.12 - 10 = -0.88 \text{ million} = -\$880,000 \text{ (approximately)}$$

Correct answer: -$879,000, which corresponds to option A.